diff options
author | lloyd <[email protected]> | 2014-01-01 21:20:55 +0000 |
---|---|---|
committer | lloyd <[email protected]> | 2014-01-01 21:20:55 +0000 |
commit | 197dc467dec28a04c3b2f30da7cef122dfbb13e9 (patch) | |
tree | cdbd3ddaec051c72f0a757db461973d90c37b97a /src/math | |
parent | 62faac373c07cfe10bc8c309e89ebdd30d8e5eaa (diff) |
Shuffle things around. Add NIST X.509 test to build.
Diffstat (limited to 'src/math')
51 files changed, 0 insertions, 8875 deletions
diff --git a/src/math/bigint/big_code.cpp b/src/math/bigint/big_code.cpp deleted file mode 100644 index 972312cdb..000000000 --- a/src/math/bigint/big_code.cpp +++ /dev/null @@ -1,150 +0,0 @@ -/* -* BigInt Encoding/Decoding -* (C) 1999-2010,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <botan/divide.h> -#include <botan/charset.h> -#include <botan/hex.h> - -namespace Botan { - -/* -* Encode a BigInt -*/ -void BigInt::encode(byte output[], const BigInt& n, Base base) - { - if(base == Binary) - { - n.binary_encode(output); - } - else if(base == Hexadecimal) - { - secure_vector<byte> binary(n.encoded_size(Binary)); - n.binary_encode(&binary[0]); - - hex_encode(reinterpret_cast<char*>(output), - &binary[0], binary.size()); - } - else if(base == Decimal) - { - BigInt copy = n; - BigInt remainder; - copy.set_sign(Positive); - const size_t output_size = n.encoded_size(Decimal); - for(size_t j = 0; j != output_size; ++j) - { - divide(copy, 10, copy, remainder); - output[output_size - 1 - j] = - Charset::digit2char(static_cast<byte>(remainder.word_at(0))); - if(copy.is_zero()) - break; - } - } - else - throw Invalid_Argument("Unknown BigInt encoding method"); - } - -/* -* Encode a BigInt -*/ -std::vector<byte> BigInt::encode(const BigInt& n, Base base) - { - std::vector<byte> output(n.encoded_size(base)); - encode(&output[0], n, base); - if(base != Binary) - for(size_t j = 0; j != output.size(); ++j) - if(output[j] == 0) - output[j] = '0'; - return output; - } - -/* -* Encode a BigInt -*/ -secure_vector<byte> BigInt::encode_locked(const BigInt& n, Base base) - { - secure_vector<byte> output(n.encoded_size(base)); - encode(&output[0], n, base); - if(base != Binary) - for(size_t j = 0; j != output.size(); ++j) - if(output[j] == 0) - output[j] = '0'; - return output; - } - -/* -* Encode a BigInt, with leading 0s if needed -*/ -secure_vector<byte> BigInt::encode_1363(const BigInt& n, size_t bytes) - { - const size_t n_bytes = n.bytes(); - if(n_bytes > bytes) - throw Encoding_Error("encode_1363: n is too large to encode properly"); - - const size_t leading_0s = bytes - n_bytes; - - secure_vector<byte> output(bytes); - encode(&output[leading_0s], n, Binary); - return output; - } - -/* -* Decode a BigInt -*/ -BigInt BigInt::decode(const byte buf[], size_t length, Base base) - { - BigInt r; - if(base == Binary) - r.binary_decode(buf, length); - else if(base == Hexadecimal) - { - secure_vector<byte> binary; - - if(length % 2) - { - // Handle lack of leading 0 - const char buf0_with_leading_0[2] = - { '0', static_cast<char>(buf[0]) }; - - binary = hex_decode_locked(buf0_with_leading_0, 2); - - binary += hex_decode_locked(reinterpret_cast<const char*>(&buf[1]), - length - 1, - false); - } - else - binary = hex_decode_locked(reinterpret_cast<const char*>(buf), - length, false); - - r.binary_decode(&binary[0], binary.size()); - } - else if(base == Decimal) - { - for(size_t i = 0; i != length; ++i) - { - if(Charset::is_space(buf[i])) - continue; - - if(!Charset::is_digit(buf[i])) - throw Invalid_Argument("BigInt::decode: " - "Invalid character in decimal input"); - - const byte x = Charset::char2digit(buf[i]); - - if(x >= 10) - throw Invalid_Argument("BigInt: Invalid decimal string"); - - r *= 10; - r += x; - } - } - else - throw Invalid_Argument("Unknown BigInt decoding method"); - return r; - } - -} diff --git a/src/math/bigint/big_io.cpp b/src/math/bigint/big_io.cpp deleted file mode 100644 index b561c218f..000000000 --- a/src/math/bigint/big_io.cpp +++ /dev/null @@ -1,55 +0,0 @@ -/* -* BigInt Input/Output -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <iostream> - -namespace Botan { - -/* -* Write the BigInt into a stream -*/ -std::ostream& operator<<(std::ostream& stream, const BigInt& n) - { - BigInt::Base base = BigInt::Decimal; - if(stream.flags() & std::ios::hex) - base = BigInt::Hexadecimal; - else if(stream.flags() & std::ios::oct) - throw std::runtime_error("Octal output of BigInt not supported"); - - if(n == 0) - stream.write("0", 1); - else - { - if(n < 0) - stream.write("-", 1); - const std::vector<byte> buffer = BigInt::encode(n, base); - size_t skip = 0; - while(skip < buffer.size() && buffer[skip] == '0') - ++skip; - stream.write(reinterpret_cast<const char*>(&buffer[0]) + skip, - buffer.size() - skip); - } - if(!stream.good()) - throw Stream_IO_Error("BigInt output operator has failed"); - return stream; - } - -/* -* Read the BigInt from a stream -*/ -std::istream& operator>>(std::istream& stream, BigInt& n) - { - std::string str; - std::getline(stream, str); - if(stream.bad() || (stream.fail() && !stream.eof())) - throw Stream_IO_Error("BigInt input operator has failed"); - n = BigInt(str); - return stream; - } - -} diff --git a/src/math/bigint/big_ops2.cpp b/src/math/bigint/big_ops2.cpp deleted file mode 100644 index 37b6a5df1..000000000 --- a/src/math/bigint/big_ops2.cpp +++ /dev/null @@ -1,221 +0,0 @@ -/* -* BigInt Assignment Operators -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <botan/internal/mp_core.h> -#include <botan/internal/bit_ops.h> -#include <algorithm> - -namespace Botan { - -/* -* Addition Operator -*/ -BigInt& BigInt::operator+=(const BigInt& y) - { - const size_t x_sw = sig_words(), y_sw = y.sig_words(); - - const size_t reg_size = std::max(x_sw, y_sw) + 1; - grow_to(reg_size); - - if(sign() == y.sign()) - bigint_add2(mutable_data(), reg_size - 1, y.data(), y_sw); - else - { - s32bit relative_size = bigint_cmp(data(), x_sw, y.data(), y_sw); - - if(relative_size < 0) - { - secure_vector<word> z(reg_size - 1); - bigint_sub3(&z[0], y.data(), reg_size - 1, data(), x_sw); - std::swap(m_reg, z); - set_sign(y.sign()); - } - else if(relative_size == 0) - { - zeroise(m_reg); - set_sign(Positive); - } - else if(relative_size > 0) - bigint_sub2(mutable_data(), x_sw, y.data(), y_sw); - } - - return (*this); - } - -/* -* Subtraction Operator -*/ -BigInt& BigInt::operator-=(const BigInt& y) - { - const size_t x_sw = sig_words(), y_sw = y.sig_words(); - - s32bit relative_size = bigint_cmp(data(), x_sw, y.data(), y_sw); - - const size_t reg_size = std::max(x_sw, y_sw) + 1; - grow_to(reg_size); - - if(relative_size < 0) - { - if(sign() == y.sign()) - bigint_sub2_rev(mutable_data(), y.data(), y_sw); - else - bigint_add2(mutable_data(), reg_size - 1, y.data(), y_sw); - - set_sign(y.reverse_sign()); - } - else if(relative_size == 0) - { - if(sign() == y.sign()) - { - clear(); - set_sign(Positive); - } - else - bigint_shl1(mutable_data(), x_sw, 0, 1); - } - else if(relative_size > 0) - { - if(sign() == y.sign()) - bigint_sub2(mutable_data(), x_sw, y.data(), y_sw); - else - bigint_add2(mutable_data(), reg_size - 1, y.data(), y_sw); - } - - return (*this); - } - -/* -* Multiplication Operator -*/ -BigInt& BigInt::operator*=(const BigInt& y) - { - const size_t x_sw = sig_words(), y_sw = y.sig_words(); - set_sign((sign() == y.sign()) ? Positive : Negative); - - if(x_sw == 0 || y_sw == 0) - { - clear(); - set_sign(Positive); - } - else if(x_sw == 1 && y_sw) - { - grow_to(y_sw + 2); - bigint_linmul3(mutable_data(), y.data(), y_sw, word_at(0)); - } - else if(y_sw == 1 && x_sw) - { - grow_to(x_sw + 2); - bigint_linmul2(mutable_data(), x_sw, y.word_at(0)); - } - else - { - grow_to(size() + y.size()); - - secure_vector<word> z(data(), data() + x_sw); - secure_vector<word> workspace(size()); - - bigint_mul(mutable_data(), size(), &workspace[0], - &z[0], z.size(), x_sw, - y.data(), y.size(), y_sw); - } - - return (*this); - } - -/* -* Division Operator -*/ -BigInt& BigInt::operator/=(const BigInt& y) - { - if(y.sig_words() == 1 && is_power_of_2(y.word_at(0))) - (*this) >>= (y.bits() - 1); - else - (*this) = (*this) / y; - return (*this); - } - -/* -* Modulo Operator -*/ -BigInt& BigInt::operator%=(const BigInt& mod) - { - return (*this = (*this) % mod); - } - -/* -* Modulo Operator -*/ -word BigInt::operator%=(word mod) - { - if(mod == 0) - throw BigInt::DivideByZero(); - - if(is_power_of_2(mod)) - { - word result = (word_at(0) & (mod - 1)); - clear(); - grow_to(2); - m_reg[0] = result; - return result; - } - - word remainder = 0; - - for(size_t j = sig_words(); j > 0; --j) - remainder = bigint_modop(remainder, word_at(j-1), mod); - clear(); - grow_to(2); - - if(remainder && sign() == BigInt::Negative) - m_reg[0] = mod - remainder; - else - m_reg[0] = remainder; - - set_sign(BigInt::Positive); - - return word_at(0); - } - -/* -* Left Shift Operator -*/ -BigInt& BigInt::operator<<=(size_t shift) - { - if(shift) - { - const size_t shift_words = shift / MP_WORD_BITS, - shift_bits = shift % MP_WORD_BITS, - words = sig_words(); - - grow_to(words + shift_words + (shift_bits ? 1 : 0)); - bigint_shl1(mutable_data(), words, shift_words, shift_bits); - } - - return (*this); - } - -/* -* Right Shift Operator -*/ -BigInt& BigInt::operator>>=(size_t shift) - { - if(shift) - { - const size_t shift_words = shift / MP_WORD_BITS, - shift_bits = shift % MP_WORD_BITS; - - bigint_shr1(mutable_data(), sig_words(), shift_words, shift_bits); - - if(is_zero()) - set_sign(Positive); - } - - return (*this); - } - -} diff --git a/src/math/bigint/big_ops3.cpp b/src/math/bigint/big_ops3.cpp deleted file mode 100644 index cad730197..000000000 --- a/src/math/bigint/big_ops3.cpp +++ /dev/null @@ -1,191 +0,0 @@ -/* -* BigInt Binary Operators -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <botan/divide.h> -#include <botan/internal/mp_core.h> -#include <botan/internal/bit_ops.h> -#include <algorithm> - -namespace Botan { - -/* -* Addition Operator -*/ -BigInt operator+(const BigInt& x, const BigInt& y) - { - const size_t x_sw = x.sig_words(), y_sw = y.sig_words(); - - BigInt z(x.sign(), std::max(x_sw, y_sw) + 1); - - if((x.sign() == y.sign())) - bigint_add3(z.mutable_data(), x.data(), x_sw, y.data(), y_sw); - else - { - s32bit relative_size = bigint_cmp(x.data(), x_sw, y.data(), y_sw); - - if(relative_size < 0) - { - bigint_sub3(z.mutable_data(), y.data(), y_sw, x.data(), x_sw); - z.set_sign(y.sign()); - } - else if(relative_size == 0) - z.set_sign(BigInt::Positive); - else if(relative_size > 0) - bigint_sub3(z.mutable_data(), x.data(), x_sw, y.data(), y_sw); - } - - return z; - } - -/* -* Subtraction Operator -*/ -BigInt operator-(const BigInt& x, const BigInt& y) - { - const size_t x_sw = x.sig_words(), y_sw = y.sig_words(); - - s32bit relative_size = bigint_cmp(x.data(), x_sw, y.data(), y_sw); - - BigInt z(BigInt::Positive, std::max(x_sw, y_sw) + 1); - - if(relative_size < 0) - { - if(x.sign() == y.sign()) - bigint_sub3(z.mutable_data(), y.data(), y_sw, x.data(), x_sw); - else - bigint_add3(z.mutable_data(), x.data(), x_sw, y.data(), y_sw); - z.set_sign(y.reverse_sign()); - } - else if(relative_size == 0) - { - if(x.sign() != y.sign()) - bigint_shl2(z.mutable_data(), x.data(), x_sw, 0, 1); - } - else if(relative_size > 0) - { - if(x.sign() == y.sign()) - bigint_sub3(z.mutable_data(), x.data(), x_sw, y.data(), y_sw); - else - bigint_add3(z.mutable_data(), x.data(), x_sw, y.data(), y_sw); - z.set_sign(x.sign()); - } - return z; - } - -/* -* Multiplication Operator -*/ -BigInt operator*(const BigInt& x, const BigInt& y) - { - const size_t x_sw = x.sig_words(), y_sw = y.sig_words(); - - BigInt z(BigInt::Positive, x.size() + y.size()); - - if(x_sw == 1 && y_sw) - bigint_linmul3(z.mutable_data(), y.data(), y_sw, x.word_at(0)); - else if(y_sw == 1 && x_sw) - bigint_linmul3(z.mutable_data(), x.data(), x_sw, y.word_at(0)); - else if(x_sw && y_sw) - { - secure_vector<word> workspace(z.size()); - bigint_mul(z.mutable_data(), z.size(), &workspace[0], - x.data(), x.size(), x_sw, - y.data(), y.size(), y_sw); - } - - if(x_sw && y_sw && x.sign() != y.sign()) - z.flip_sign(); - return z; - } - -/* -* Division Operator -*/ -BigInt operator/(const BigInt& x, const BigInt& y) - { - BigInt q, r; - divide(x, y, q, r); - return q; - } - -/* -* Modulo Operator -*/ -BigInt operator%(const BigInt& n, const BigInt& mod) - { - if(mod.is_zero()) - throw BigInt::DivideByZero(); - if(mod.is_negative()) - throw Invalid_Argument("BigInt::operator%: modulus must be > 0"); - if(n.is_positive() && mod.is_positive() && n < mod) - return n; - - BigInt q, r; - divide(n, mod, q, r); - return r; - } - -/* -* Modulo Operator -*/ -word operator%(const BigInt& n, word mod) - { - if(mod == 0) - throw BigInt::DivideByZero(); - - if(is_power_of_2(mod)) - return (n.word_at(0) & (mod - 1)); - - word remainder = 0; - - for(size_t j = n.sig_words(); j > 0; --j) - remainder = bigint_modop(remainder, n.word_at(j-1), mod); - - if(remainder && n.sign() == BigInt::Negative) - return mod - remainder; - return remainder; - } - -/* -* Left Shift Operator -*/ -BigInt operator<<(const BigInt& x, size_t shift) - { - if(shift == 0) - return x; - - const size_t shift_words = shift / MP_WORD_BITS, - shift_bits = shift % MP_WORD_BITS; - - const size_t x_sw = x.sig_words(); - - BigInt y(x.sign(), x_sw + shift_words + (shift_bits ? 1 : 0)); - bigint_shl2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits); - return y; - } - -/* -* Right Shift Operator -*/ -BigInt operator>>(const BigInt& x, size_t shift) - { - if(shift == 0) - return x; - if(x.bits() <= shift) - return 0; - - const size_t shift_words = shift / MP_WORD_BITS, - shift_bits = shift % MP_WORD_BITS, - x_sw = x.sig_words(); - - BigInt y(x.sign(), x_sw - shift_words); - bigint_shr2(y.mutable_data(), x.data(), x_sw, shift_words, shift_bits); - return y; - } - -} diff --git a/src/math/bigint/big_rand.cpp b/src/math/bigint/big_rand.cpp deleted file mode 100644 index 78b9ee244..000000000 --- a/src/math/bigint/big_rand.cpp +++ /dev/null @@ -1,48 +0,0 @@ -/* -* BigInt Random Generation -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <botan/parsing.h> - -namespace Botan { - -/* -* Randomize this number -*/ -void BigInt::randomize(RandomNumberGenerator& rng, - size_t bitsize) - { - set_sign(Positive); - - if(bitsize == 0) - clear(); - else - { - secure_vector<byte> array = rng.random_vec((bitsize + 7) / 8); - - if(bitsize % 8) - array[0] &= 0xFF >> (8 - (bitsize % 8)); - array[0] |= 0x80 >> ((bitsize % 8) ? (8 - bitsize % 8) : 0); - binary_decode(&array[0], array.size()); - } - } - -/* -* Generate a random integer within given range -*/ -BigInt BigInt::random_integer(RandomNumberGenerator& rng, - const BigInt& min, const BigInt& max) - { - BigInt range = max - min; - - if(range <= 0) - throw Invalid_Argument("random_integer: invalid min/max values"); - - return (min + (BigInt(rng, range.bits() + 2) % range)); - } - -} diff --git a/src/math/bigint/bigint.cpp b/src/math/bigint/bigint.cpp deleted file mode 100644 index 45c351256..000000000 --- a/src/math/bigint/bigint.cpp +++ /dev/null @@ -1,350 +0,0 @@ -/* -* BigInt Base -* (C) 1999-2011,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/bigint.h> -#include <botan/internal/mp_core.h> -#include <botan/get_byte.h> -#include <botan/parsing.h> -#include <botan/internal/rounding.h> - -namespace Botan { - -/* -* Construct a BigInt from a regular number -*/ -BigInt::BigInt(u64bit n) - { - set_sign(Positive); - - if(n == 0) - return; - - const size_t limbs_needed = sizeof(u64bit) / sizeof(word); - - m_reg.resize(4*limbs_needed); - for(size_t i = 0; i != limbs_needed; ++i) - m_reg[i] = ((n >> (i*MP_WORD_BITS)) & MP_WORD_MASK); - } - -/* -* Construct a BigInt of the specified size -*/ -BigInt::BigInt(Sign s, size_t size) - { - m_reg.resize(round_up<size_t>(size, 8)); - m_signedness = s; - } - -/* -* Copy constructor -*/ -BigInt::BigInt(const BigInt& other) - { - m_reg = other.m_reg; - m_signedness = other.m_signedness; - } - -/* -* Construct a BigInt from a string -*/ -BigInt::BigInt(const std::string& str) - { - Base base = Decimal; - size_t markers = 0; - bool negative = false; - - if(str.length() > 0 && str[0] == '-') - { - markers += 1; - negative = true; - } - - if(str.length() > markers + 2 && str[markers ] == '0' && - str[markers + 1] == 'x') - { - markers += 2; - base = Hexadecimal; - } - - *this = decode(reinterpret_cast<const byte*>(str.data()) + markers, - str.length() - markers, base); - - if(negative) set_sign(Negative); - else set_sign(Positive); - } - -/* -* Construct a BigInt from an encoded BigInt -*/ -BigInt::BigInt(const byte input[], size_t length, Base base) - { - set_sign(Positive); - *this = decode(input, length, base); - } - -/* -* Construct a BigInt from an encoded BigInt -*/ -BigInt::BigInt(RandomNumberGenerator& rng, size_t bits) - { - set_sign(Positive); - randomize(rng, bits); - } - -/* -* Grow the internal storage -*/ -void BigInt::grow_to(size_t n) - { - if(n > size()) - m_reg.resize(round_up<size_t>(n, 8)); - } - -/* -* Comparison Function -*/ -s32bit BigInt::cmp(const BigInt& other, bool check_signs) const - { - if(check_signs) - { - if(other.is_positive() && this->is_negative()) - return -1; - - if(other.is_negative() && this->is_positive()) - return 1; - - if(other.is_negative() && this->is_negative()) - return (-bigint_cmp(this->data(), this->sig_words(), - other.data(), other.sig_words())); - } - - return bigint_cmp(this->data(), this->sig_words(), - other.data(), other.sig_words()); - } - -/* -* Return byte n of this number -*/ -byte BigInt::byte_at(size_t n) const - { - const size_t WORD_BYTES = sizeof(word); - size_t word_num = n / WORD_BYTES, byte_num = n % WORD_BYTES; - if(word_num >= size()) - return 0; - else - return get_byte(WORD_BYTES - byte_num - 1, m_reg[word_num]); - } - -/* -* Return bit n of this number -*/ -bool BigInt::get_bit(size_t n) const - { - return ((word_at(n / MP_WORD_BITS) >> (n % MP_WORD_BITS)) & 1); - } - -/* -* Return bits {offset...offset+length} -*/ -u32bit BigInt::get_substring(size_t offset, size_t length) const - { - if(length > 32) - throw Invalid_Argument("BigInt::get_substring: Substring size too big"); - - u64bit piece = 0; - for(size_t i = 0; i != 8; ++i) - { - const byte part = byte_at((offset / 8) + (7-i)); - piece = (piece << 8) | part; - } - - const u64bit mask = (static_cast<u64bit>(1) << length) - 1; - const size_t shift = (offset % 8); - - return static_cast<u32bit>((piece >> shift) & mask); - } - -/* -* Convert this number to a u32bit, if possible -*/ -u32bit BigInt::to_u32bit() const - { - if(is_negative()) - throw Encoding_Error("BigInt::to_u32bit: Number is negative"); - if(bits() >= 32) - throw Encoding_Error("BigInt::to_u32bit: Number is too big to convert"); - - u32bit out = 0; - for(u32bit j = 0; j != 4; ++j) - out = (out << 8) | byte_at(3-j); - return out; - } - -/* -* Set bit number n -*/ -void BigInt::set_bit(size_t n) - { - const size_t which = n / MP_WORD_BITS; - const word mask = static_cast<word>(1) << (n % MP_WORD_BITS); - if(which >= size()) grow_to(which + 1); - m_reg[which] |= mask; - } - -/* -* Clear bit number n -*/ -void BigInt::clear_bit(size_t n) - { - const size_t which = n / MP_WORD_BITS; - const word mask = static_cast<word>(1) << (n % MP_WORD_BITS); - if(which < size()) - m_reg[which] &= ~mask; - } - -/* -* Clear all but the lowest n bits -*/ -void BigInt::mask_bits(size_t n) - { - if(n == 0) { clear(); return; } - if(n >= bits()) return; - - const size_t top_word = n / MP_WORD_BITS; - const word mask = (static_cast<word>(1) << (n % MP_WORD_BITS)) - 1; - - if(top_word < size()) - clear_mem(&m_reg[top_word+1], size() - (top_word + 1)); - - m_reg[top_word] &= mask; - } - -/* -* Count how many bytes are being used -*/ -size_t BigInt::bytes() const - { - return (bits() + 7) / 8; - } - -/* -* Count how many bits are being used -*/ -size_t BigInt::bits() const - { - const size_t words = sig_words(); - - if(words == 0) - return 0; - - size_t full_words = words - 1, top_bits = MP_WORD_BITS; - word top_word = word_at(full_words), mask = MP_WORD_TOP_BIT; - - while(top_bits && ((top_word & mask) == 0)) - { mask >>= 1; top_bits--; } - - return (full_words * MP_WORD_BITS + top_bits); - } - -/* -* Calcluate the size in a certain base -*/ -size_t BigInt::encoded_size(Base base) const - { - static const double LOG_2_BASE_10 = 0.30102999566; - - if(base == Binary) - return bytes(); - else if(base == Hexadecimal) - return 2*bytes(); - else if(base == Decimal) - return static_cast<size_t>((bits() * LOG_2_BASE_10) + 1); - else - throw Invalid_Argument("Unknown base for BigInt encoding"); - } - -/* -* Set the sign -*/ -void BigInt::set_sign(Sign s) - { - if(is_zero()) - m_signedness = Positive; - else - m_signedness = s; - } - -/* -* Reverse the value of the sign flag -*/ -void BigInt::flip_sign() - { - set_sign(reverse_sign()); - } - -/* -* Return the opposite value of the current sign -*/ -BigInt::Sign BigInt::reverse_sign() const - { - if(sign() == Positive) - return Negative; - return Positive; - } - -/* -* Return the negation of this number -*/ -BigInt BigInt::operator-() const - { - BigInt x = (*this); - x.flip_sign(); - return x; - } - -/* -* Return the absolute value of this number -*/ -BigInt BigInt::abs() const - { - BigInt x = (*this); - x.set_sign(Positive); - return x; - } - -/* -* Encode this number into bytes -*/ -void BigInt::binary_encode(byte output[]) const - { - const size_t sig_bytes = bytes(); - for(size_t i = 0; i != sig_bytes; ++i) - output[sig_bytes-i-1] = byte_at(i); - } - -/* -* Set this number to the value in buf -*/ -void BigInt::binary_decode(const byte buf[], size_t length) - { - const size_t WORD_BYTES = sizeof(word); - - clear(); - m_reg.resize(round_up<size_t>((length / WORD_BYTES) + 1, 8)); - - for(size_t i = 0; i != length / WORD_BYTES; ++i) - { - const size_t top = length - WORD_BYTES*i; - for(size_t j = WORD_BYTES; j > 0; --j) - m_reg[i] = (m_reg[i] << 8) | buf[top - j]; - } - - for(size_t i = 0; i != length % WORD_BYTES; ++i) - m_reg[length / WORD_BYTES] = (m_reg[length / WORD_BYTES] << 8) | buf[i]; - } - -} diff --git a/src/math/bigint/bigint.h b/src/math/bigint/bigint.h deleted file mode 100644 index 08b7d53fc..000000000 --- a/src/math/bigint/bigint.h +++ /dev/null @@ -1,570 +0,0 @@ -/* -* BigInt -* (C) 1999-2008,2012 Jack Lloyd -* 2007 FlexSecure -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_BIGINT_H__ -#define BOTAN_BIGINT_H__ - -#include <botan/rng.h> -#include <botan/secmem.h> -#include <botan/mp_types.h> -#include <iosfwd> - -namespace Botan { - -/** -* Arbitrary precision integer -*/ -class BOTAN_DLL BigInt - { - public: - /** - * Base enumerator for encoding and decoding - */ - enum Base { Decimal = 10, Hexadecimal = 16, Binary = 256 }; - - /** - * Sign symbol definitions for positive and negative numbers - */ - enum Sign { Negative = 0, Positive = 1 }; - - /** - * DivideByZero Exception - */ - struct BOTAN_DLL DivideByZero : public Exception - { DivideByZero() : Exception("BigInt divide by zero") {} }; - - /** - * Create empty BigInt - */ - BigInt() { m_signedness = Positive; } - - /** - * Create BigInt from 64 bit integer - * @param n initial value of this BigInt - */ - BigInt(u64bit n); - - /** - * Copy Constructor - * @param other the BigInt to copy - */ - BigInt(const BigInt& other); - - /** - * Create BigInt from a string. If the string starts with 0x the - * rest of the string will be interpreted as hexadecimal digits. - * Otherwise, it will be interpreted as a decimal number. - * - * @param str the string to parse for an integer value - */ - BigInt(const std::string& str); - - /** - * Create a BigInt from an integer in a byte array - * @param buf the byte array holding the value - * @param length size of buf - * @param base is the number base of the integer in buf - */ - BigInt(const byte buf[], size_t length, Base base = Binary); - - /** - * Create a random BigInt of the specified size - * @param rng random number generator - * @param bits size in bits - */ - BigInt(RandomNumberGenerator& rng, size_t bits); - - /** - * Create BigInt of specified size, all zeros - * @param sign the sign - * @param n size of the internal register in words - */ - BigInt(Sign sign, size_t n); - - /** - * Move constructor - */ - BigInt(BigInt&& other) - { - this->swap(other); - } - - /** - * Move assignment - */ - BigInt& operator=(BigInt&& other) - { - if(this != &other) - this->swap(other); - - return (*this); - } - - /** - * Copy assignment - */ - BigInt& operator=(const BigInt&) = default; - - /** - * Swap this value with another - * @param other BigInt to swap values with - */ - void swap(BigInt& other) - { - m_reg.swap(other.m_reg); - std::swap(m_signedness, other.m_signedness); - } - - /** - * += operator - * @param y the BigInt to add to this - */ - BigInt& operator+=(const BigInt& y); - - /** - * -= operator - * @param y the BigInt to subtract from this - */ - BigInt& operator-=(const BigInt& y); - - /** - * *= operator - * @param y the BigInt to multiply with this - */ - BigInt& operator*=(const BigInt& y); - - /** - * /= operator - * @param y the BigInt to divide this by - */ - BigInt& operator/=(const BigInt& y); - - /** - * Modulo operator - * @param y the modulus to reduce this by - */ - BigInt& operator%=(const BigInt& y); - - /** - * Modulo operator - * @param y the modulus (word) to reduce this by - */ - word operator%=(word y); - - /** - * Left shift operator - * @param shift the number of bits to shift this left by - */ - BigInt& operator<<=(size_t shift); - - /** - * Right shift operator - * @param shift the number of bits to shift this right by - */ - BigInt& operator>>=(size_t shift); - - /** - * Increment operator - */ - BigInt& operator++() { return (*this += 1); } - - /** - * Decrement operator - */ - BigInt& operator--() { return (*this -= 1); } - - /** - * Postfix increment operator - */ - BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; } - - /** - * Postfix decrement operator - */ - BigInt operator--(int) { BigInt x = (*this); --(*this); return x; } - - /** - * Unary negation operator - * @return negative this - */ - BigInt operator-() const; - - /** - * ! operator - * @return true iff this is zero, otherwise false - */ - bool operator !() const { return (!is_nonzero()); } - - /** - * Zeroize the BigInt. The size of the underlying register is not - * modified. - */ - void clear() { zeroise(m_reg); } - - /** - * Compare this to another BigInt - * @param n the BigInt value to compare with - * @param check_signs include sign in comparison? - * @result if (this<n) return -1, if (this>n) return 1, if both - * values are identical return 0 [like Perl's <=> operator] - */ - s32bit cmp(const BigInt& n, bool check_signs = true) const; - - /** - * Test if the integer has an even value - * @result true if the integer is even, false otherwise - */ - bool is_even() const { return (get_bit(0) == 0); } - - /** - * Test if the integer has an odd value - * @result true if the integer is odd, false otherwise - */ - bool is_odd() const { return (get_bit(0) == 1); } - - /** - * Test if the integer is not zero - * @result true if the integer is non-zero, false otherwise - */ - bool is_nonzero() const { return (!is_zero()); } - - /** - * Test if the integer is zero - * @result true if the integer is zero, false otherwise - */ - bool is_zero() const - { - const size_t sw = sig_words(); - - for(size_t i = 0; i != sw; ++i) - if(m_reg[i]) - return false; - return true; - } - - /** - * Set bit at specified position - * @param n bit position to set - */ - void set_bit(size_t n); - - /** - * Clear bit at specified position - * @param n bit position to clear - */ - void clear_bit(size_t n); - - /** - * Clear all but the lowest n bits - * @param n amount of bits to keep - */ - void mask_bits(size_t n); - - /** - * Return bit value at specified position - * @param n the bit offset to test - * @result true, if the bit at position n is set, false otherwise - */ - bool get_bit(size_t n) const; - - /** - * Return (a maximum of) 32 bits of the complete value - * @param offset the offset to start extracting - * @param length amount of bits to extract (starting at offset) - * @result the integer extracted from the register starting at - * offset with specified length - */ - u32bit get_substring(size_t offset, size_t length) const; - - /** - * Convert this value into a u32bit, if it is in the range - * [0 ... 2**32-1], or otherwise throw an exception. - * @result the value as a u32bit if conversion is possible - */ - u32bit to_u32bit() const; - - /** - * @param n the offset to get a byte from - * @result byte at offset n - */ - byte byte_at(size_t n) const; - - /** - * Return the word at a specified position of the internal register - * @param n position in the register - * @return value at position n - */ - word word_at(size_t n) const - { return ((n < size()) ? m_reg[n] : 0); } - - /** - * Tests if the sign of the integer is negative - * @result true, iff the integer has a negative sign - */ - bool is_negative() const { return (sign() == Negative); } - - /** - * Tests if the sign of the integer is positive - * @result true, iff the integer has a positive sign - */ - bool is_positive() const { return (sign() == Positive); } - - /** - * Return the sign of the integer - * @result the sign of the integer - */ - Sign sign() const { return (m_signedness); } - - /** - * @result the opposite sign of the represented integer value - */ - Sign reverse_sign() const; - - /** - * Flip the sign of this BigInt - */ - void flip_sign(); - - /** - * Set sign of the integer - * @param sign new Sign to set - */ - void set_sign(Sign sign); - - /** - * @result absolute (positive) value of this - */ - BigInt abs() const; - - /** - * Give size of internal register - * @result size of internal register in words - */ - size_t size() const { return m_reg.size(); } - - /** - * Return how many words we need to hold this value - * @result significant words of the represented integer value - */ - size_t sig_words() const - { - const word* x = &m_reg[0]; - size_t sig = m_reg.size(); - - while(sig && (x[sig-1] == 0)) - sig--; - return sig; - } - - /** - * Give byte length of the integer - * @result byte length of the represented integer value - */ - size_t bytes() const; - - /** - * Get the bit length of the integer - * @result bit length of the represented integer value - */ - size_t bits() const; - - /** - * Return a mutable pointer to the register - * @result a pointer to the start of the internal register - */ - word* mutable_data() { return &m_reg[0]; } - - /** - * Return a const pointer to the register - * @result a pointer to the start of the internal register - */ - const word* data() const { return &m_reg[0]; } - - /** - * Increase internal register buffer to at least n words - * @param n new size of register - */ - void grow_to(size_t n); - - /** - * Fill BigInt with a random number with size of bitsize - * @param rng the random number generator to use - * @param bitsize number of bits the created random value should have - */ - void randomize(RandomNumberGenerator& rng, size_t bitsize = 0); - - /** - * Store BigInt-value in a given byte array - * @param buf destination byte array for the integer value - */ - void binary_encode(byte buf[]) const; - - /** - * Read integer value from a byte array with given size - * @param buf byte array buffer containing the integer - * @param length size of buf - */ - void binary_decode(const byte buf[], size_t length); - - /** - * Read integer value from a byte array (secure_vector<byte>) - * @param buf the array to load from - */ - void binary_decode(const secure_vector<byte>& buf) - { - binary_decode(&buf[0], buf.size()); - } - - /** - * @param base the base to measure the size for - * @return size of this integer in base base - */ - size_t encoded_size(Base base = Binary) const; - - /** - * @param rng a random number generator - * @param min the minimum value - * @param max the maximum value - * @return random integer between min and max - */ - static BigInt random_integer(RandomNumberGenerator& rng, - const BigInt& min, - const BigInt& max); - - /** - * Create a power of two - * @param n the power of two to create - * @return bigint representing 2^n - */ - static BigInt power_of_2(size_t n) - { - BigInt b; - b.set_bit(n); - return b; - } - - /** - * Encode the integer value from a BigInt to a std::vector of bytes - * @param n the BigInt to use as integer source - * @param base number-base of resulting byte array representation - * @result secure_vector of bytes containing the integer with given base - */ - static std::vector<byte> encode(const BigInt& n, Base base = Binary); - - /** - * Encode the integer value from a BigInt to a secure_vector of bytes - * @param n the BigInt to use as integer source - * @param base number-base of resulting byte array representation - * @result secure_vector of bytes containing the integer with given base - */ - static secure_vector<byte> encode_locked(const BigInt& n, - Base base = Binary); - - /** - * Encode the integer value from a BigInt to a byte array - * @param buf destination byte array for the encoded integer - * value with given base - * @param n the BigInt to use as integer source - * @param base number-base of resulting byte array representation - */ - static void encode(byte buf[], const BigInt& n, Base base = Binary); - - /** - * Create a BigInt from an integer in a byte array - * @param buf the binary value to load - * @param length size of buf - * @param base number-base of the integer in buf - * @result BigInt representing the integer in the byte array - */ - static BigInt decode(const byte buf[], size_t length, - Base base = Binary); - - /** - * Create a BigInt from an integer in a byte array - * @param buf the binary value to load - * @param base number-base of the integer in buf - * @result BigInt representing the integer in the byte array - */ - static BigInt decode(const secure_vector<byte>& buf, - Base base = Binary) - { - return BigInt::decode(&buf[0], buf.size(), base); - } - - /** - * Create a BigInt from an integer in a byte array - * @param buf the binary value to load - * @param base number-base of the integer in buf - * @result BigInt representing the integer in the byte array - */ - static BigInt decode(const std::vector<byte>& buf, - Base base = Binary) - { - return BigInt::decode(&buf[0], buf.size(), base); - } - - /** - * Encode a BigInt to a byte array according to IEEE 1363 - * @param n the BigInt to encode - * @param bytes the length of the resulting secure_vector<byte> - * @result a secure_vector<byte> containing the encoded BigInt - */ - static secure_vector<byte> encode_1363(const BigInt& n, size_t bytes); - - private: - secure_vector<word> m_reg; - Sign m_signedness; - }; - -/* -* Arithmetic Operators -*/ -BigInt BOTAN_DLL operator+(const BigInt& x, const BigInt& y); -BigInt BOTAN_DLL operator-(const BigInt& x, const BigInt& y); -BigInt BOTAN_DLL operator*(const BigInt& x, const BigInt& y); -BigInt BOTAN_DLL operator/(const BigInt& x, const BigInt& d); -BigInt BOTAN_DLL operator%(const BigInt& x, const BigInt& m); -word BOTAN_DLL operator%(const BigInt& x, word m); -BigInt BOTAN_DLL operator<<(const BigInt& x, size_t n); -BigInt BOTAN_DLL operator>>(const BigInt& x, size_t n); - -/* -* Comparison Operators -*/ -inline bool operator==(const BigInt& a, const BigInt& b) - { return (a.cmp(b) == 0); } -inline bool operator!=(const BigInt& a, const BigInt& b) - { return (a.cmp(b) != 0); } -inline bool operator<=(const BigInt& a, const BigInt& b) - { return (a.cmp(b) <= 0); } -inline bool operator>=(const BigInt& a, const BigInt& b) - { return (a.cmp(b) >= 0); } -inline bool operator<(const BigInt& a, const BigInt& b) - { return (a.cmp(b) < 0); } -inline bool operator>(const BigInt& a, const BigInt& b) - { return (a.cmp(b) > 0); } - -/* -* I/O Operators -*/ -BOTAN_DLL std::ostream& operator<<(std::ostream&, const BigInt&); -BOTAN_DLL std::istream& operator>>(std::istream&, BigInt&); - -} - -namespace std { - -template<> -inline void swap<Botan::BigInt>(Botan::BigInt& x, Botan::BigInt& y) - { - x.swap(y); - } - -} - -#endif diff --git a/src/math/bigint/divide.cpp b/src/math/bigint/divide.cpp deleted file mode 100644 index 8b21bce13..000000000 --- a/src/math/bigint/divide.cpp +++ /dev/null @@ -1,140 +0,0 @@ -/* -* Division Algorithm -* (C) 1999-2007,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/divide.h> -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_madd.h> - -namespace Botan { - -namespace { - -/* -* Handle signed operands, if necessary -*/ -void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r) - { - if(x.sign() == BigInt::Negative) - { - q.flip_sign(); - if(r.is_nonzero()) { --q; r = y.abs() - r; } - } - if(y.sign() == BigInt::Negative) - q.flip_sign(); - } - -bool division_check(word q, word y2, word y1, - word x3, word x2, word x1) - { - // Compute (y3,y2,y1) = (y2,y1) * q - - word y3 = 0; - y1 = word_madd2(q, y1, &y3); - y2 = word_madd2(q, y2, &y3); - - // Return (y3,y2,y1) >? (x3,x2,x1) - - if(y3 > x3) return true; - if(y3 < x3) return false; - - if(y2 > x2) return true; - if(y2 < x2) return false; - - if(y1 > x1) return true; - if(y1 < x1) return false; - - return false; - } - -} - -/* -* Solve x = q * y + r -*/ -void divide(const BigInt& x, const BigInt& y_arg, BigInt& q, BigInt& r) - { - if(y_arg.is_zero()) - throw BigInt::DivideByZero(); - - BigInt y = y_arg; - const size_t y_words = y.sig_words(); - - r = x; - q = 0; - - r.set_sign(BigInt::Positive); - y.set_sign(BigInt::Positive); - - s32bit compare = r.cmp(y); - - if(compare == 0) - { - q = 1; - r = 0; - } - else if(compare > 0) - { - size_t shifts = 0; - word y_top = y.word_at(y.sig_words()-1); - while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; } - y <<= shifts; - r <<= shifts; - - const size_t n = r.sig_words() - 1, t = y_words - 1; - - if(n < t) - throw Internal_Error("BigInt division word sizes"); - - q.grow_to(n - t + 1); - - word* q_words = q.mutable_data(); - - if(n <= t) - { - while(r > y) { r -= y; ++q; } - r >>= shifts; - sign_fixup(x, y_arg, q, r); - return; - } - - BigInt temp = y << (MP_WORD_BITS * (n-t)); - - while(r >= temp) { r -= temp; q_words[n-t] += 1; } - - for(size_t j = n; j != t; --j) - { - const word x_j0 = r.word_at(j); - const word x_j1 = r.word_at(j-1); - const word y_t = y.word_at(t); - - if(x_j0 == y_t) - q_words[j-t-1] = MP_WORD_MAX; - else - q_words[j-t-1] = bigint_divop(x_j0, x_j1, y_t); - - while(division_check(q_words[j-t-1], - y_t, y.word_at(t-1), - x_j0, x_j1, r.word_at(j-2))) - { - q_words[j-t-1] -= 1; - } - - r -= (q_words[j-t-1] * y) << (MP_WORD_BITS * (j-t-1)); - - if(r.is_negative()) - { - r += y << (MP_WORD_BITS * (j-t-1)); - q_words[j-t-1] -= 1; - } - } - r >>= shifts; - } - - sign_fixup(x, y_arg, q, r); - } - -} diff --git a/src/math/bigint/divide.h b/src/math/bigint/divide.h deleted file mode 100644 index 36aed7854..000000000 --- a/src/math/bigint/divide.h +++ /dev/null @@ -1,29 +0,0 @@ -/* -* Division -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_DIVISON_ALGORITHM_H__ -#define BOTAN_DIVISON_ALGORITHM_H__ - -#include <botan/bigint.h> - -namespace Botan { - -/** -* BigInt Division -* @param x an integer -* @param y a non-zero integer -* @param q will be set to x / y -* @param r will be set to x % y -*/ -void BOTAN_DLL divide(const BigInt& x, - const BigInt& y, - BigInt& q, - BigInt& r); - -} - -#endif diff --git a/src/math/bigint/info.txt b/src/math/bigint/info.txt deleted file mode 100644 index b5dabb7bc..000000000 --- a/src/math/bigint/info.txt +++ /dev/null @@ -1,25 +0,0 @@ -load_on auto - -define BIGINT 20131128 - -<header:public> -bigint.h -divide.h -</header:public> - -<source> -big_code.cpp -big_io.cpp -big_ops2.cpp -big_ops3.cpp -big_rand.cpp -bigint.cpp -divide.cpp -</source> - -<requires> -alloc -mp -hex -rng -</requires> diff --git a/src/math/ec_gfp/curve_gfp.h b/src/math/ec_gfp/curve_gfp.h deleted file mode 100644 index 267d5f152..000000000 --- a/src/math/ec_gfp/curve_gfp.h +++ /dev/null @@ -1,161 +0,0 @@ -/* -* Elliptic curves over GF(p) -* -* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke -* 2010-2011,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_GFP_CURVE_H__ -#define BOTAN_GFP_CURVE_H__ - -#include <botan/numthry.h> - -namespace Botan { - -/** -* This class represents an elliptic curve over GF(p) -*/ -class BOTAN_DLL CurveGFp - { - public: - - /** - * Create an uninitialized CurveGFp - */ - CurveGFp() {} - - /** - * Construct the elliptic curve E: y^2 = x^3 + ax + b over GF(p) - * @param p prime number of the field - * @param a first coefficient - * @param b second coefficient - */ - CurveGFp(const BigInt& p, const BigInt& a, const BigInt& b) : - m_p(p), - m_a(a), - m_b(b), - m_p_words(m_p.sig_words()), - m_p_dash(monty_inverse(m_p.word_at(0))) - { - const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS); - - m_r2 = (r * r) % p; - m_a_r = (a * r) % p; - m_b_r = (b * r) % p; - } - - CurveGFp(const CurveGFp&) = default; - - CurveGFp& operator=(const CurveGFp&) = default; - - /** - * @return curve coefficient a - */ - const BigInt& get_a() const { return m_a; } - - /** - * @return curve coefficient b - */ - const BigInt& get_b() const { return m_b; } - - /** - * Get prime modulus of the field of the curve - * @return prime modulus of the field of the curve - */ - const BigInt& get_p() const { return m_p; } - - /** - * @return Montgomery parameter r^2 % p - */ - const BigInt& get_r2() const { return m_r2; } - - /** - * @return a * r mod p - */ - const BigInt& get_a_r() const { return m_a_r; } - - /** - * @return b * r mod p - */ - const BigInt& get_b_r() const { return m_b_r; } - - /** - * @return Montgomery parameter p-dash - */ - word get_p_dash() const { return m_p_dash; } - - /** - * @return p.sig_words() - */ - size_t get_p_words() const { return m_p_words; } - - /** - * swaps the states of *this and other, does not throw - * @param other curve to swap values with - */ - void swap(CurveGFp& other) - { - std::swap(m_p, other.m_p); - - std::swap(m_a, other.m_a); - std::swap(m_b, other.m_b); - - std::swap(m_a_r, other.m_a_r); - std::swap(m_b_r, other.m_b_r); - - std::swap(m_p_words, other.m_p_words); - - std::swap(m_r2, other.m_r2); - std::swap(m_p_dash, other.m_p_dash); - } - - /** - * Equality operator - * @param other curve to compare with - * @return true iff this is the same curve as other - */ - bool operator==(const CurveGFp& other) const - { - return (m_p == other.m_p && - m_a == other.m_a && - m_b == other.m_b); - } - - private: - // Curve parameters - BigInt m_p, m_a, m_b; - - size_t m_p_words; // cache of m_p.sig_words() - - // Montgomery parameters - BigInt m_r2, m_a_r, m_b_r; - word m_p_dash; - }; - -/** -* Equality operator -* @param lhs a curve -* @param rhs a curve -* @return true iff lhs is not the same as rhs -*/ -inline bool operator!=(const CurveGFp& lhs, const CurveGFp& rhs) - { - return !(lhs == rhs); - } - -} - -namespace std { - -template<> inline -void swap<Botan::CurveGFp>(Botan::CurveGFp& curve1, - Botan::CurveGFp& curve2) - { - curve1.swap(curve2); - } - -} // namespace std - -#endif diff --git a/src/math/ec_gfp/info.txt b/src/math/ec_gfp/info.txt deleted file mode 100644 index 1772302a8..000000000 --- a/src/math/ec_gfp/info.txt +++ /dev/null @@ -1,16 +0,0 @@ -define EC_CURVE_GFP 20131128 - -load_on auto - -<header:public> -curve_gfp.h -point_gfp.h -</header:public> - -<source> -point_gfp.cpp -</source> - -<requires> -numbertheory -</requires> diff --git a/src/math/ec_gfp/point_gfp.cpp b/src/math/ec_gfp/point_gfp.cpp deleted file mode 100644 index 9cd5a2aaf..000000000 --- a/src/math/ec_gfp/point_gfp.cpp +++ /dev/null @@ -1,606 +0,0 @@ -/* -* Point arithmetic on elliptic curves over GF(p) -* -* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke -* 2008-2011,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/point_gfp.h> -#include <botan/numthry.h> -#include <botan/reducer.h> -#include <botan/internal/mp_core.h> - -namespace Botan { - -PointGFp::PointGFp(const CurveGFp& curve) : - curve(curve), ws(2 * (curve.get_p_words() + 2)) - { - coord_x = 0; - coord_y = monty_mult(1, curve.get_r2()); - coord_z = 0; - } - -PointGFp::PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y) : - curve(curve), ws(2 * (curve.get_p_words() + 2)) - { - coord_x = monty_mult(x, curve.get_r2()); - coord_y = monty_mult(y, curve.get_r2()); - coord_z = monty_mult(1, curve.get_r2()); - } - -// Montgomery multiplication -void PointGFp::monty_mult(BigInt& z, const BigInt& x, const BigInt& y) const - { - //assert(&z != &x && &z != &y); - - if(x.is_zero() || y.is_zero()) - { - z = 0; - return; - } - - const BigInt& p = curve.get_p(); - const size_t p_size = curve.get_p_words(); - const word p_dash = curve.get_p_dash(); - - const size_t output_size = 2*p_size + 1; - - z.grow_to(output_size); - z.clear(); - - bigint_monty_mul(z.mutable_data(), output_size, - x.data(), x.size(), x.sig_words(), - y.data(), y.size(), y.sig_words(), - p.data(), p_size, p_dash, - &ws[0]); - } - -// Montgomery squaring -void PointGFp::monty_sqr(BigInt& z, const BigInt& x) const - { - //assert(&z != &x); - - if(x.is_zero()) - { - z = 0; - return; - } - - const BigInt& p = curve.get_p(); - const size_t p_size = curve.get_p_words(); - const word p_dash = curve.get_p_dash(); - - const size_t output_size = 2*p_size + 1; - - z.grow_to(output_size); - z.clear(); - - bigint_monty_sqr(z.mutable_data(), output_size, - x.data(), x.size(), x.sig_words(), - p.data(), p_size, p_dash, - &ws[0]); - } - -// Point addition -void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn) - { - if(is_zero()) - { - coord_x = rhs.coord_x; - coord_y = rhs.coord_y; - coord_z = rhs.coord_z; - return; - } - else if(rhs.is_zero()) - return; - - const BigInt& p = curve.get_p(); - - BigInt& rhs_z2 = ws_bn[0]; - BigInt& U1 = ws_bn[1]; - BigInt& S1 = ws_bn[2]; - - BigInt& lhs_z2 = ws_bn[3]; - BigInt& U2 = ws_bn[4]; - BigInt& S2 = ws_bn[5]; - - BigInt& H = ws_bn[6]; - BigInt& r = ws_bn[7]; - - monty_sqr(rhs_z2, rhs.coord_z); - monty_mult(U1, coord_x, rhs_z2); - monty_mult(S1, coord_y, monty_mult(rhs.coord_z, rhs_z2)); - - monty_sqr(lhs_z2, coord_z); - monty_mult(U2, rhs.coord_x, lhs_z2); - monty_mult(S2, rhs.coord_y, monty_mult(coord_z, lhs_z2)); - - H = U2; - H -= U1; - if(H.is_negative()) - H += p; - - r = S2; - r -= S1; - if(r.is_negative()) - r += p; - - if(H.is_zero()) - { - if(r.is_zero()) - { - mult2(ws_bn); - return; - } - - *this = PointGFp(curve); // setting myself to zero - return; - } - - monty_sqr(U2, H); - - monty_mult(S2, U2, H); - - U2 = monty_mult(U1, U2); - - monty_sqr(coord_x, r); - coord_x -= S2; - coord_x -= (U2 << 1); - while(coord_x.is_negative()) - coord_x += p; - - U2 -= coord_x; - if(U2.is_negative()) - U2 += p; - - monty_mult(coord_y, r, U2); - coord_y -= monty_mult(S1, S2); - if(coord_y.is_negative()) - coord_y += p; - - monty_mult(coord_z, monty_mult(coord_z, rhs.coord_z), H); - } - -// *this *= 2 -void PointGFp::mult2(std::vector<BigInt>& ws_bn) - { - if(is_zero()) - return; - else if(coord_y.is_zero()) - { - *this = PointGFp(curve); // setting myself to zero - return; - } - - const BigInt& p = curve.get_p(); - - BigInt& y_2 = ws_bn[0]; - BigInt& S = ws_bn[1]; - BigInt& z4 = ws_bn[2]; - BigInt& a_z4 = ws_bn[3]; - BigInt& M = ws_bn[4]; - BigInt& U = ws_bn[5]; - BigInt& x = ws_bn[6]; - BigInt& y = ws_bn[7]; - BigInt& z = ws_bn[8]; - - monty_sqr(y_2, coord_y); - - monty_mult(S, coord_x, y_2); - S <<= 2; // * 4 - while(S >= p) - S -= p; - - monty_sqr(z4, monty_sqr(coord_z)); - monty_mult(a_z4, curve.get_a_r(), z4); - - M = 3 * monty_sqr(coord_x); - M += a_z4; - while(M >= p) - M -= p; - - monty_sqr(x, M); - x -= (S << 1); - while(x.is_negative()) - x += p; - - monty_sqr(U, y_2); - U <<= 3; - while(U >= p) - U -= p; - - S -= x; - while(S.is_negative()) - S += p; - - monty_mult(y, M, S); - y -= U; - if(y.is_negative()) - y += p; - - monty_mult(z, coord_y, coord_z); - z <<= 1; - if(z >= p) - z -= p; - - coord_x = x; - coord_y = y; - coord_z = z; - } - -// arithmetic operators -PointGFp& PointGFp::operator+=(const PointGFp& rhs) - { - std::vector<BigInt> ws(9); - add(rhs, ws); - return *this; - } - -PointGFp& PointGFp::operator-=(const PointGFp& rhs) - { - PointGFp minus_rhs = PointGFp(rhs).negate(); - - if(is_zero()) - *this = minus_rhs; - else - *this += minus_rhs; - - return *this; - } - -PointGFp& PointGFp::operator*=(const BigInt& scalar) - { - *this = scalar * *this; - return *this; - } - -PointGFp multi_exponentiate(const PointGFp& p1, const BigInt& z1, - const PointGFp& p2, const BigInt& z2) - { - const PointGFp p3 = p1 + p2; - - PointGFp H(p1.curve); // create as zero - size_t bits_left = std::max(z1.bits(), z2.bits()); - - std::vector<BigInt> ws(9); - - while(bits_left) - { - H.mult2(ws); - - const bool z1_b = z1.get_bit(bits_left - 1); - const bool z2_b = z2.get_bit(bits_left - 1); - - if(z1_b == true && z2_b == true) - H.add(p3, ws); - else if(z1_b) - H.add(p1, ws); - else if(z2_b) - H.add(p2, ws); - - --bits_left; - } - - if(z1.is_negative() != z2.is_negative()) - H.negate(); - - return H; - } - -PointGFp operator*(const BigInt& scalar, const PointGFp& point) - { - const CurveGFp& curve = point.get_curve(); - - if(scalar.is_zero()) - return PointGFp(curve); // zero point - - std::vector<BigInt> ws(9); - - if(scalar.abs() <= 2) // special cases for small values - { - byte value = scalar.abs().byte_at(0); - - PointGFp result = point; - - if(value == 2) - result.mult2(ws); - - if(scalar.is_negative()) - result.negate(); - - return result; - } - - const size_t scalar_bits = scalar.bits(); - -#if 0 - - PointGFp x1 = PointGFp(curve); - PointGFp x2 = point; - - size_t bits_left = scalar_bits; - - // Montgomery Ladder - while(bits_left) - { - const bool bit_set = scalar.get_bit(bits_left - 1); - - if(bit_set) - { - x1.add(x2, ws); - x2.mult2(ws); - } - else - { - x2.add(x1, ws); - x1.mult2(ws); - } - - --bits_left; - } - - if(scalar.is_negative()) - x1.negate(); - - return x1; - -#else - const size_t window_size = 4; - - std::vector<PointGFp> Ps(1 << window_size); - Ps[0] = PointGFp(curve); - Ps[1] = point; - - for(size_t i = 2; i != Ps.size(); ++i) - { - Ps[i] = Ps[i-1]; - Ps[i].add(point, ws); - } - - PointGFp H(curve); // create as zero - size_t bits_left = scalar_bits; - - while(bits_left >= window_size) - { - for(size_t i = 0; i != window_size; ++i) - H.mult2(ws); - - const u32bit nibble = scalar.get_substring(bits_left - window_size, - window_size); - - H.add(Ps[nibble], ws); - - bits_left -= window_size; - } - - while(bits_left) - { - H.mult2(ws); - if(scalar.get_bit(bits_left-1)) - H.add(point, ws); - - --bits_left; - } - - if(scalar.is_negative()) - H.negate(); - - return H; -#endif - } - -BigInt PointGFp::get_affine_x() const - { - if(is_zero()) - throw Illegal_Transformation("Cannot convert zero point to affine"); - - const BigInt& r2 = curve.get_r2(); - - BigInt z2 = monty_sqr(coord_z); - z2 = inverse_mod(z2, curve.get_p()); - - z2 = monty_mult(z2, r2); - return monty_mult(coord_x, z2); - } - -BigInt PointGFp::get_affine_y() const - { - if(is_zero()) - throw Illegal_Transformation("Cannot convert zero point to affine"); - - const BigInt& r2 = curve.get_r2(); - - BigInt z3 = monty_mult(coord_z, monty_sqr(coord_z)); - z3 = inverse_mod(z3, curve.get_p()); - z3 = monty_mult(z3, r2); - return monty_mult(coord_y, z3); - } - -bool PointGFp::on_the_curve() const - { - /* - Is the point still on the curve?? (If everything is correct, the - point is always on its curve; then the function will return true. - If somehow the state is corrupted, which suggests a fault attack - (or internal computational error), then return false. - */ - - if(is_zero()) - return true; - - BigInt y2 = monty_mult(monty_sqr(coord_y), 1); - BigInt x3 = monty_mult(coord_x, monty_sqr(coord_x)); - - BigInt ax = monty_mult(coord_x, curve.get_a_r()); - - const BigInt& b_r = curve.get_b_r(); - - BigInt z2 = monty_sqr(coord_z); - - if(coord_z == z2) // Is z equal to 1 (in Montgomery form)? - { - if(y2 != monty_mult(x3 + ax + b_r, 1)) - return false; - } - - BigInt z3 = monty_mult(coord_z, z2); - - BigInt ax_z4 = monty_mult(ax, monty_sqr(z2)); - - BigInt b_z6 = monty_mult(b_r, monty_sqr(z3)); - - if(y2 != monty_mult(x3 + ax_z4 + b_z6, 1)) - return false; - - return true; - } - -// swaps the states of *this and other, does not throw! -void PointGFp::swap(PointGFp& other) - { - curve.swap(other.curve); - coord_x.swap(other.coord_x); - coord_y.swap(other.coord_y); - coord_z.swap(other.coord_z); - ws.swap(other.ws); - } - -bool PointGFp::operator==(const PointGFp& other) const - { - if(get_curve() != other.get_curve()) - return false; - - // If this is zero, only equal if other is also zero - if(is_zero()) - return other.is_zero(); - - return (get_affine_x() == other.get_affine_x() && - get_affine_y() == other.get_affine_y()); - } - -// encoding and decoding -secure_vector<byte> EC2OSP(const PointGFp& point, byte format) - { - if(point.is_zero()) - return secure_vector<byte>(1); // single 0 byte - - const size_t p_bytes = point.get_curve().get_p().bytes(); - - BigInt x = point.get_affine_x(); - BigInt y = point.get_affine_y(); - - secure_vector<byte> bX = BigInt::encode_1363(x, p_bytes); - secure_vector<byte> bY = BigInt::encode_1363(y, p_bytes); - - if(format == PointGFp::UNCOMPRESSED) - { - secure_vector<byte> result; - result.push_back(0x04); - - result += bX; - result += bY; - - return result; - } - else if(format == PointGFp::COMPRESSED) - { - secure_vector<byte> result; - result.push_back(0x02 | static_cast<byte>(y.get_bit(0))); - - result += bX; - - return result; - } - else if(format == PointGFp::HYBRID) - { - secure_vector<byte> result; - result.push_back(0x06 | static_cast<byte>(y.get_bit(0))); - - result += bX; - result += bY; - - return result; - } - else - throw Invalid_Argument("illegal point encoding format specification"); - } - -namespace { - -BigInt decompress_point(bool yMod2, - const BigInt& x, - const CurveGFp& curve) - { - BigInt xpow3 = x * x * x; - - BigInt g = curve.get_a() * x; - g += xpow3; - g += curve.get_b(); - g = g % curve.get_p(); - - BigInt z = ressol(g, curve.get_p()); - - if(z < 0) - throw Illegal_Point("error during decompression"); - - if(z.get_bit(0) != yMod2) - z = curve.get_p() - z; - - return z; - } - -} - -PointGFp OS2ECP(const byte data[], size_t data_len, - const CurveGFp& curve) - { - if(data_len <= 1) - return PointGFp(curve); // return zero - - const byte pc = data[0]; - - BigInt x, y; - - if(pc == 2 || pc == 3) - { - //compressed form - x = BigInt::decode(&data[1], data_len - 1); - - const bool y_mod_2 = ((pc & 0x01) == 1); - y = decompress_point(y_mod_2, x, curve); - } - else if(pc == 4) - { - const size_t l = (data_len - 1) / 2; - - // uncompressed form - x = BigInt::decode(&data[1], l); - y = BigInt::decode(&data[l+1], l); - } - else if(pc == 6 || pc == 7) - { - const size_t l = (data_len - 1) / 2; - - // hybrid form - x = BigInt::decode(&data[1], l); - y = BigInt::decode(&data[l+1], l); - - const bool y_mod_2 = ((pc & 0x01) == 1); - - if(decompress_point(y_mod_2, x, curve) != y) - throw Illegal_Point("OS2ECP: Decoding error in hybrid format"); - } - else - throw Invalid_Argument("OS2ECP: Unknown format type " + std::to_string(pc)); - - PointGFp result(curve, x, y); - - if(!result.on_the_curve()) - throw Illegal_Point("OS2ECP: Decoded point was not on the curve"); - - return result; - } - -} diff --git a/src/math/ec_gfp/point_gfp.h b/src/math/ec_gfp/point_gfp.h deleted file mode 100644 index 017f66e1c..000000000 --- a/src/math/ec_gfp/point_gfp.h +++ /dev/null @@ -1,300 +0,0 @@ -/* -* Point arithmetic on elliptic curves over GF(p) -* -* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke -* 2008-2011 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_POINT_GFP_H__ -#define BOTAN_POINT_GFP_H__ - -#include <botan/curve_gfp.h> -#include <vector> - -namespace Botan { - -/** -* Exception thrown if you try to convert a zero point to an affine -* coordinate -*/ -struct BOTAN_DLL Illegal_Transformation : public Exception - { - Illegal_Transformation(const std::string& err = - "Requested transformation is not possible") : - Exception(err) {} - }; - -/** -* Exception thrown if some form of illegal point is decoded -*/ -struct BOTAN_DLL Illegal_Point : public Exception - { - Illegal_Point(const std::string& err = "Malformed ECP point detected") : - Exception(err) {} - }; - -/** -* This class represents one point on a curve of GF(p) -*/ -class BOTAN_DLL PointGFp - { - public: - enum Compression_Type { - UNCOMPRESSED = 0, - COMPRESSED = 1, - HYBRID = 2 - }; - - /** - * Construct an uninitialized PointGFp - */ - PointGFp() {} - - /** - * Construct the zero point - * @param curve The base curve - */ - PointGFp(const CurveGFp& curve); - - /** - * Copy constructor - */ - PointGFp(const PointGFp&) = default; - - /** - * Move Constructor - */ - PointGFp(PointGFp&& other) - { - this->swap(other); - } - - /** - * Standard Assignment - */ - PointGFp& operator=(const PointGFp&) = default; - - /** - * Move Assignment - */ - PointGFp& operator=(PointGFp&& other) - { - if(this != &other) - this->swap(other); - return (*this); - } - - /** - * Construct a point from its affine coordinates - * @param curve the base curve - * @param x affine x coordinate - * @param y affine y coordinate - */ - PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y); - - /** - * += Operator - * @param rhs the PointGFp to add to the local value - * @result resulting PointGFp - */ - PointGFp& operator+=(const PointGFp& rhs); - - /** - * -= Operator - * @param rhs the PointGFp to subtract from the local value - * @result resulting PointGFp - */ - PointGFp& operator-=(const PointGFp& rhs); - - /** - * *= Operator - * @param scalar the PointGFp to multiply with *this - * @result resulting PointGFp - */ - PointGFp& operator*=(const BigInt& scalar); - - /** - * Multiplication Operator - * @param scalar the scalar value - * @param point the point value - * @return scalar*point on the curve - */ - friend BOTAN_DLL PointGFp operator*(const BigInt& scalar, const PointGFp& point); - - /** - * Multiexponentiation - * @param p1 a point - * @param z1 a scalar - * @param p2 a point - * @param z2 a scalar - * @result (p1 * z1 + p2 * z2) - */ - friend BOTAN_DLL PointGFp multi_exponentiate( - const PointGFp& p1, const BigInt& z1, - const PointGFp& p2, const BigInt& z2); - - /** - * Negate this point - * @return *this - */ - PointGFp& negate() - { - if(!is_zero()) - coord_y = curve.get_p() - coord_y; - return *this; - } - - /** - * Return base curve of this point - * @result the curve over GF(p) of this point - */ - const CurveGFp& get_curve() const { return curve; } - - /** - * get affine x coordinate - * @result affine x coordinate - */ - BigInt get_affine_x() const; - - /** - * get affine y coordinate - * @result affine y coordinate - */ - BigInt get_affine_y() const; - - /** - * Is this the point at infinity? - * @result true, if this point is at infinity, false otherwise. - */ - bool is_zero() const - { return (coord_x.is_zero() && coord_z.is_zero()); } - - /** - * Checks whether the point is to be found on the underlying - * curve; used to prevent fault attacks. - * @return if the point is on the curve - */ - bool on_the_curve() const; - - /** - * swaps the states of *this and other, does not throw! - * @param other the object to swap values with - */ - void swap(PointGFp& other); - - /** - * Equality operator - */ - bool operator==(const PointGFp& other) const; - private: - - /** - * Montgomery multiplication/reduction - * @param x first multiplicand - * @param y second multiplicand - * @param workspace temp space - */ - BigInt monty_mult(const BigInt& x, const BigInt& y) const - { - BigInt result; - monty_mult(result, x, y); - return result; - } - - /** - * Montgomery multiplication/reduction - * @warning z cannot alias x or y - * @param z output - * @param x first multiplicand - * @param y second multiplicand - */ - void monty_mult(BigInt& z, const BigInt& x, const BigInt& y) const; - - /** - * Montgomery squaring/reduction - * @param x multiplicand - */ - BigInt monty_sqr(const BigInt& x) const - { - BigInt result; - monty_sqr(result, x); - return result; - } - - /** - * Montgomery squaring/reduction - * @warning z cannot alias x - * @param z output - * @param x multiplicand - */ - void monty_sqr(BigInt& z, const BigInt& x) const; - - /** - * Point addition - * @param workspace temp space, at least 11 elements - */ - void add(const PointGFp& other, std::vector<BigInt>& workspace); - - /** - * Point doubling - * @param workspace temp space, at least 9 elements - */ - void mult2(std::vector<BigInt>& workspace); - - CurveGFp curve; - BigInt coord_x, coord_y, coord_z; - mutable secure_vector<word> ws; // workspace for Montgomery - }; - -// relational operators -inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs) - { - return !(rhs == lhs); - } - -// arithmetic operators -inline PointGFp operator-(const PointGFp& lhs) - { - return PointGFp(lhs).negate(); - } - -inline PointGFp operator+(const PointGFp& lhs, const PointGFp& rhs) - { - PointGFp tmp(lhs); - return tmp += rhs; - } - -inline PointGFp operator-(const PointGFp& lhs, const PointGFp& rhs) - { - PointGFp tmp(lhs); - return tmp -= rhs; - } - -inline PointGFp operator*(const PointGFp& point, const BigInt& scalar) - { - return scalar * point; - } - -// encoding and decoding -secure_vector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format); - -PointGFp BOTAN_DLL OS2ECP(const byte data[], size_t data_len, - const CurveGFp& curve); - -template<typename Alloc> -PointGFp OS2ECP(const std::vector<byte, Alloc>& data, const CurveGFp& curve) - { return OS2ECP(&data[0], data.size(), curve); } - -} - -namespace std { - -template<> -inline void swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y) - { x.swap(y); } - -} - -#endif diff --git a/src/math/mp/info.txt b/src/math/mp/info.txt deleted file mode 100644 index a47475f7b..000000000 --- a/src/math/mp/info.txt +++ /dev/null @@ -1,23 +0,0 @@ -define BIGINT_MP 20131128 - -<source> -mp_asm.cpp -mp_comba.cpp -mp_karat.cpp -mp_monty.cpp -mp_mulop.cpp -mp_misc.cpp -mp_shift.cpp -</source> - -<header:public> -mp_types.h -</header:public> - -<header:internal> -mp_core.h -</header:internal> - -<requires> -mp_x86_64|mp_x86_32|mp_x86_32_msvc|mp_generic -</requires> diff --git a/src/math/mp/mp_asm.cpp b/src/math/mp/mp_asm.cpp deleted file mode 100644 index a3caba620..000000000 --- a/src/math/mp/mp_asm.cpp +++ /dev/null @@ -1,184 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_asmi.h> -#include <botan/internal/mp_core.h> -#include <botan/exceptn.h> -#include <botan/mem_ops.h> - -namespace Botan { - -extern "C" { - -/* -* Two Operand Addition, No Carry -*/ -word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size) - { - word carry = 0; - - const size_t blocks = y_size - (y_size % 8); - - for(size_t i = 0; i != blocks; i += 8) - carry = word8_add2(x + i, y + i, carry); - - for(size_t i = blocks; i != y_size; ++i) - x[i] = word_add(x[i], y[i], &carry); - - for(size_t i = y_size; i != x_size; ++i) - x[i] = word_add(x[i], 0, &carry); - - return carry; - } - -/* -* Three Operand Addition, No Carry -*/ -word bigint_add3_nc(word z[], const word x[], size_t x_size, - const word y[], size_t y_size) - { - if(x_size < y_size) - { return bigint_add3_nc(z, y, y_size, x, x_size); } - - word carry = 0; - - const size_t blocks = y_size - (y_size % 8); - - for(size_t i = 0; i != blocks; i += 8) - carry = word8_add3(z + i, x + i, y + i, carry); - - for(size_t i = blocks; i != y_size; ++i) - z[i] = word_add(x[i], y[i], &carry); - - for(size_t i = y_size; i != x_size; ++i) - z[i] = word_add(x[i], 0, &carry); - - return carry; - } - -/* -* Two Operand Addition -*/ -void bigint_add2(word x[], size_t x_size, const word y[], size_t y_size) - { - if(bigint_add2_nc(x, x_size, y, y_size)) - x[x_size] += 1; - } - -/* -* Three Operand Addition -*/ -void bigint_add3(word z[], const word x[], size_t x_size, - const word y[], size_t y_size) - { - z[(x_size > y_size ? x_size : y_size)] += - bigint_add3_nc(z, x, x_size, y, y_size); - } - -/* -* Two Operand Subtraction -*/ -word bigint_sub2(word x[], size_t x_size, const word y[], size_t y_size) - { - word borrow = 0; - - const size_t blocks = y_size - (y_size % 8); - - for(size_t i = 0; i != blocks; i += 8) - borrow = word8_sub2(x + i, y + i, borrow); - - for(size_t i = blocks; i != y_size; ++i) - x[i] = word_sub(x[i], y[i], &borrow); - - for(size_t i = y_size; i != x_size; ++i) - x[i] = word_sub(x[i], 0, &borrow); - - return borrow; - } - -/* -* Two Operand Subtraction x = y - x -*/ -void bigint_sub2_rev(word x[], const word y[], size_t y_size) - { - word borrow = 0; - - const size_t blocks = y_size - (y_size % 8); - - for(size_t i = 0; i != blocks; i += 8) - borrow = word8_sub2_rev(x + i, y + i, borrow); - - for(size_t i = blocks; i != y_size; ++i) - x[i] = word_sub(y[i], x[i], &borrow); - - if(borrow) - throw Internal_Error("bigint_sub2_rev: x >= y"); - } - -/* -* Three Operand Subtraction -*/ -word bigint_sub3(word z[], const word x[], size_t x_size, - const word y[], size_t y_size) - { - word borrow = 0; - - const size_t blocks = y_size - (y_size % 8); - - for(size_t i = 0; i != blocks; i += 8) - borrow = word8_sub3(z + i, x + i, y + i, borrow); - - for(size_t i = blocks; i != y_size; ++i) - z[i] = word_sub(x[i], y[i], &borrow); - - for(size_t i = y_size; i != x_size; ++i) - z[i] = word_sub(x[i], 0, &borrow); - - return borrow; - } - -/* -* Two Operand Linear Multiply -*/ -void bigint_linmul2(word x[], size_t x_size, word y) - { - const size_t blocks = x_size - (x_size % 8); - - word carry = 0; - - for(size_t i = 0; i != blocks; i += 8) - carry = word8_linmul2(x + i, y, carry); - - for(size_t i = blocks; i != x_size; ++i) - x[i] = word_madd2(x[i], y, &carry); - - x[x_size] = carry; - } - -/* -* Three Operand Linear Multiply -*/ -void bigint_linmul3(word z[], const word x[], size_t x_size, word y) - { - const size_t blocks = x_size - (x_size % 8); - - word carry = 0; - - for(size_t i = 0; i != blocks; i += 8) - carry = word8_linmul3(z + i, x + i, y, carry); - - for(size_t i = blocks; i != x_size; ++i) - z[i] = word_madd2(x[i], y, &carry); - - z[x_size] = carry; - } - -} - -} diff --git a/src/math/mp/mp_comba.cpp b/src/math/mp/mp_comba.cpp deleted file mode 100644 index 99dcda176..000000000 --- a/src/math/mp/mp_comba.cpp +++ /dev/null @@ -1,920 +0,0 @@ -/* -* Comba Multiplication and Squaring -* (C) 1999-2007,2011 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_asmi.h> - -namespace Botan { - -extern "C" { - -/* -* Comba 4x4 Squaring -*/ -void bigint_comba_sqr4(word z[8], const word x[4]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], x[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); - z[ 1] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], x[ 1]); - z[ 2] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); - z[ 3] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], x[ 2]); - z[ 4] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); - z[ 5] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 3], x[ 3]); - z[ 6] = w0; - z[ 7] = w1; - } - -/* -* Comba 4x4 Multiplication -*/ -void bigint_comba_mul4(word z[8], const word x[4], const word y[4]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); - z[ 1] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); - z[ 2] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); - z[ 3] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); - z[ 4] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); - z[ 5] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); - z[ 6] = w0; - z[ 7] = w1; - } - -/* -* Comba 6x6 Squaring -*/ -void bigint_comba_sqr6(word z[12], const word x[6]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], x[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); - z[ 1] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], x[ 1]); - z[ 2] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); - z[ 3] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], x[ 2]); - z[ 4] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); - z[ 5] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], x[ 3]); - z[ 6] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); - z[ 7] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], x[ 4]); - z[ 8] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); - z[ 9] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 5], x[ 5]); - z[10] = w1; - z[11] = w2; - } - -/* -* Comba 6x6 Multiplication -*/ -void bigint_comba_mul6(word z[12], const word x[6], const word y[6]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); - z[ 1] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); - z[ 2] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); - z[ 3] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); - z[ 4] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); - z[ 5] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); - z[ 6] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); - z[ 7] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); - z[ 8] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); - z[ 9] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); - z[10] = w1; - z[11] = w2; - } - -/* -* Comba 8x8 Squaring -*/ -void bigint_comba_sqr8(word z[16], const word x[8]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], x[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); - z[ 1] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], x[ 1]); - z[ 2] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); - z[ 3] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], x[ 2]); - z[ 4] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); - z[ 5] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], x[ 3]); - z[ 6] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); - z[ 7] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], x[ 4]); - z[ 8] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); - word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); - z[ 9] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); - word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 5], x[ 5]); - z[10] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); - word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); - z[11] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 6], x[ 6]); - z[12] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); - z[13] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 7], x[ 7]); - z[14] = w2; - z[15] = w0; - } - -/* -* Comba 8x8 Multiplication -*/ -void bigint_comba_mul8(word z[16], const word x[8], const word y[8]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); - z[ 1] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); - z[ 2] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); - z[ 3] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); - z[ 4] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); - z[ 5] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); - z[ 6] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); - z[ 7] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); - z[ 8] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); - z[ 9] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); - z[10] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); - z[11] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); - z[12] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); - z[13] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); - z[14] = w2; - z[15] = w0; - } - -/* -* Comba 16x16 Squaring -*/ -void bigint_comba_sqr16(word z[32], const word x[16]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], x[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 1]); - z[ 1] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], x[ 1]); - z[ 2] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 3]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 2]); - z[ 3] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 4]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], x[ 2]); - z[ 4] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 5]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 4]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 3]); - z[ 5] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 6]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 5]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], x[ 3]); - z[ 6] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[ 7]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 6]); - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 5]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 4]); - z[ 7] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[ 8]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[ 7]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 6]); - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], x[ 4]); - z[ 8] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[ 9]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[ 8]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[ 7]); - word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 6]); - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 5]); - z[ 9] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[10]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[ 9]); - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[ 8]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[ 7]); - word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 5], x[ 5]); - z[10] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[11]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[10]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[ 9]); - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[ 8]); - word3_muladd_2(&w1, &w0, &w2, x[ 4], x[ 7]); - word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 6]); - z[11] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[12]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[11]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[10]); - word3_muladd_2(&w2, &w1, &w0, x[ 3], x[ 9]); - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[ 8]); - word3_muladd_2(&w2, &w1, &w0, x[ 5], x[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 6], x[ 6]); - z[12] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 0], x[13]); - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[12]); - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[11]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[10]); - word3_muladd_2(&w0, &w2, &w1, x[ 4], x[ 9]); - word3_muladd_2(&w0, &w2, &w1, x[ 5], x[ 8]); - word3_muladd_2(&w0, &w2, &w1, x[ 6], x[ 7]); - z[13] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 0], x[14]); - word3_muladd_2(&w1, &w0, &w2, x[ 1], x[13]); - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[12]); - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[11]); - word3_muladd_2(&w1, &w0, &w2, x[ 4], x[10]); - word3_muladd_2(&w1, &w0, &w2, x[ 5], x[ 9]); - word3_muladd_2(&w1, &w0, &w2, x[ 6], x[ 8]); - word3_muladd(&w1, &w0, &w2, x[ 7], x[ 7]); - z[14] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 0], x[15]); - word3_muladd_2(&w2, &w1, &w0, x[ 1], x[14]); - word3_muladd_2(&w2, &w1, &w0, x[ 2], x[13]); - word3_muladd_2(&w2, &w1, &w0, x[ 3], x[12]); - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[11]); - word3_muladd_2(&w2, &w1, &w0, x[ 5], x[10]); - word3_muladd_2(&w2, &w1, &w0, x[ 6], x[ 9]); - word3_muladd_2(&w2, &w1, &w0, x[ 7], x[ 8]); - z[15] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 1], x[15]); - word3_muladd_2(&w0, &w2, &w1, x[ 2], x[14]); - word3_muladd_2(&w0, &w2, &w1, x[ 3], x[13]); - word3_muladd_2(&w0, &w2, &w1, x[ 4], x[12]); - word3_muladd_2(&w0, &w2, &w1, x[ 5], x[11]); - word3_muladd_2(&w0, &w2, &w1, x[ 6], x[10]); - word3_muladd_2(&w0, &w2, &w1, x[ 7], x[ 9]); - word3_muladd(&w0, &w2, &w1, x[ 8], x[ 8]); - z[16] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 2], x[15]); - word3_muladd_2(&w1, &w0, &w2, x[ 3], x[14]); - word3_muladd_2(&w1, &w0, &w2, x[ 4], x[13]); - word3_muladd_2(&w1, &w0, &w2, x[ 5], x[12]); - word3_muladd_2(&w1, &w0, &w2, x[ 6], x[11]); - word3_muladd_2(&w1, &w0, &w2, x[ 7], x[10]); - word3_muladd_2(&w1, &w0, &w2, x[ 8], x[ 9]); - z[17] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 3], x[15]); - word3_muladd_2(&w2, &w1, &w0, x[ 4], x[14]); - word3_muladd_2(&w2, &w1, &w0, x[ 5], x[13]); - word3_muladd_2(&w2, &w1, &w0, x[ 6], x[12]); - word3_muladd_2(&w2, &w1, &w0, x[ 7], x[11]); - word3_muladd_2(&w2, &w1, &w0, x[ 8], x[10]); - word3_muladd(&w2, &w1, &w0, x[ 9], x[ 9]); - z[18] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 4], x[15]); - word3_muladd_2(&w0, &w2, &w1, x[ 5], x[14]); - word3_muladd_2(&w0, &w2, &w1, x[ 6], x[13]); - word3_muladd_2(&w0, &w2, &w1, x[ 7], x[12]); - word3_muladd_2(&w0, &w2, &w1, x[ 8], x[11]); - word3_muladd_2(&w0, &w2, &w1, x[ 9], x[10]); - z[19] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 5], x[15]); - word3_muladd_2(&w1, &w0, &w2, x[ 6], x[14]); - word3_muladd_2(&w1, &w0, &w2, x[ 7], x[13]); - word3_muladd_2(&w1, &w0, &w2, x[ 8], x[12]); - word3_muladd_2(&w1, &w0, &w2, x[ 9], x[11]); - word3_muladd(&w1, &w0, &w2, x[10], x[10]); - z[20] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 6], x[15]); - word3_muladd_2(&w2, &w1, &w0, x[ 7], x[14]); - word3_muladd_2(&w2, &w1, &w0, x[ 8], x[13]); - word3_muladd_2(&w2, &w1, &w0, x[ 9], x[12]); - word3_muladd_2(&w2, &w1, &w0, x[10], x[11]); - z[21] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[ 7], x[15]); - word3_muladd_2(&w0, &w2, &w1, x[ 8], x[14]); - word3_muladd_2(&w0, &w2, &w1, x[ 9], x[13]); - word3_muladd_2(&w0, &w2, &w1, x[10], x[12]); - word3_muladd(&w0, &w2, &w1, x[11], x[11]); - z[22] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[ 8], x[15]); - word3_muladd_2(&w1, &w0, &w2, x[ 9], x[14]); - word3_muladd_2(&w1, &w0, &w2, x[10], x[13]); - word3_muladd_2(&w1, &w0, &w2, x[11], x[12]); - z[23] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[ 9], x[15]); - word3_muladd_2(&w2, &w1, &w0, x[10], x[14]); - word3_muladd_2(&w2, &w1, &w0, x[11], x[13]); - word3_muladd(&w2, &w1, &w0, x[12], x[12]); - z[24] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[10], x[15]); - word3_muladd_2(&w0, &w2, &w1, x[11], x[14]); - word3_muladd_2(&w0, &w2, &w1, x[12], x[13]); - z[25] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[11], x[15]); - word3_muladd_2(&w1, &w0, &w2, x[12], x[14]); - word3_muladd(&w1, &w0, &w2, x[13], x[13]); - z[26] = w2; w2 = 0; - - word3_muladd_2(&w2, &w1, &w0, x[12], x[15]); - word3_muladd_2(&w2, &w1, &w0, x[13], x[14]); - z[27] = w0; w0 = 0; - - word3_muladd_2(&w0, &w2, &w1, x[13], x[15]); - word3_muladd(&w0, &w2, &w1, x[14], x[14]); - z[28] = w1; w1 = 0; - - word3_muladd_2(&w1, &w0, &w2, x[14], x[15]); - z[29] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[15], x[15]); - z[30] = w0; - z[31] = w1; - } - -/* -* Comba 16x16 Multiplication -*/ -void bigint_comba_mul16(word z[32], const word x[16], const word y[16]) - { - word w2 = 0, w1 = 0, w0 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 0]); - z[ 0] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 0]); - z[ 1] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 0]); - z[ 2] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 0]); - z[ 3] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 0]); - z[ 4] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 0]); - z[ 5] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 0]); - z[ 6] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 0]); - z[ 7] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[ 8]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[ 8], y[ 0]); - z[ 8] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[ 9]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[ 8]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[ 8], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[ 9], y[ 0]); - z[ 9] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[10]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[ 9]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[ 8]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[ 8], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[ 9], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[10], y[ 0]); - z[10] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[11]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[10]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[ 9]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[ 8]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[ 8], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[ 9], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[10], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[11], y[ 0]); - z[11] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[12]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[11]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[10]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[ 9]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[ 8]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[ 8], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[ 9], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[10], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[11], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[12], y[ 0]); - z[12] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 0], y[13]); - word3_muladd(&w0, &w2, &w1, x[ 1], y[12]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[11]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[10]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[ 9]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[ 8]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[ 8], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[ 9], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[10], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[11], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[12], y[ 1]); - word3_muladd(&w0, &w2, &w1, x[13], y[ 0]); - z[13] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 0], y[14]); - word3_muladd(&w1, &w0, &w2, x[ 1], y[13]); - word3_muladd(&w1, &w0, &w2, x[ 2], y[12]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[11]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[10]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[ 9]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[ 8]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[ 8], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[ 9], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[10], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[11], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[12], y[ 2]); - word3_muladd(&w1, &w0, &w2, x[13], y[ 1]); - word3_muladd(&w1, &w0, &w2, x[14], y[ 0]); - z[14] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 0], y[15]); - word3_muladd(&w2, &w1, &w0, x[ 1], y[14]); - word3_muladd(&w2, &w1, &w0, x[ 2], y[13]); - word3_muladd(&w2, &w1, &w0, x[ 3], y[12]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[11]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[10]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[ 9]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[ 8]); - word3_muladd(&w2, &w1, &w0, x[ 8], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[ 9], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[10], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[11], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[12], y[ 3]); - word3_muladd(&w2, &w1, &w0, x[13], y[ 2]); - word3_muladd(&w2, &w1, &w0, x[14], y[ 1]); - word3_muladd(&w2, &w1, &w0, x[15], y[ 0]); - z[15] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 1], y[15]); - word3_muladd(&w0, &w2, &w1, x[ 2], y[14]); - word3_muladd(&w0, &w2, &w1, x[ 3], y[13]); - word3_muladd(&w0, &w2, &w1, x[ 4], y[12]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[11]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[10]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[ 9]); - word3_muladd(&w0, &w2, &w1, x[ 8], y[ 8]); - word3_muladd(&w0, &w2, &w1, x[ 9], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[10], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[11], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[12], y[ 4]); - word3_muladd(&w0, &w2, &w1, x[13], y[ 3]); - word3_muladd(&w0, &w2, &w1, x[14], y[ 2]); - word3_muladd(&w0, &w2, &w1, x[15], y[ 1]); - z[16] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 2], y[15]); - word3_muladd(&w1, &w0, &w2, x[ 3], y[14]); - word3_muladd(&w1, &w0, &w2, x[ 4], y[13]); - word3_muladd(&w1, &w0, &w2, x[ 5], y[12]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[11]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[10]); - word3_muladd(&w1, &w0, &w2, x[ 8], y[ 9]); - word3_muladd(&w1, &w0, &w2, x[ 9], y[ 8]); - word3_muladd(&w1, &w0, &w2, x[10], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[11], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[12], y[ 5]); - word3_muladd(&w1, &w0, &w2, x[13], y[ 4]); - word3_muladd(&w1, &w0, &w2, x[14], y[ 3]); - word3_muladd(&w1, &w0, &w2, x[15], y[ 2]); - z[17] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 3], y[15]); - word3_muladd(&w2, &w1, &w0, x[ 4], y[14]); - word3_muladd(&w2, &w1, &w0, x[ 5], y[13]); - word3_muladd(&w2, &w1, &w0, x[ 6], y[12]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[11]); - word3_muladd(&w2, &w1, &w0, x[ 8], y[10]); - word3_muladd(&w2, &w1, &w0, x[ 9], y[ 9]); - word3_muladd(&w2, &w1, &w0, x[10], y[ 8]); - word3_muladd(&w2, &w1, &w0, x[11], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[12], y[ 6]); - word3_muladd(&w2, &w1, &w0, x[13], y[ 5]); - word3_muladd(&w2, &w1, &w0, x[14], y[ 4]); - word3_muladd(&w2, &w1, &w0, x[15], y[ 3]); - z[18] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 4], y[15]); - word3_muladd(&w0, &w2, &w1, x[ 5], y[14]); - word3_muladd(&w0, &w2, &w1, x[ 6], y[13]); - word3_muladd(&w0, &w2, &w1, x[ 7], y[12]); - word3_muladd(&w0, &w2, &w1, x[ 8], y[11]); - word3_muladd(&w0, &w2, &w1, x[ 9], y[10]); - word3_muladd(&w0, &w2, &w1, x[10], y[ 9]); - word3_muladd(&w0, &w2, &w1, x[11], y[ 8]); - word3_muladd(&w0, &w2, &w1, x[12], y[ 7]); - word3_muladd(&w0, &w2, &w1, x[13], y[ 6]); - word3_muladd(&w0, &w2, &w1, x[14], y[ 5]); - word3_muladd(&w0, &w2, &w1, x[15], y[ 4]); - z[19] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 5], y[15]); - word3_muladd(&w1, &w0, &w2, x[ 6], y[14]); - word3_muladd(&w1, &w0, &w2, x[ 7], y[13]); - word3_muladd(&w1, &w0, &w2, x[ 8], y[12]); - word3_muladd(&w1, &w0, &w2, x[ 9], y[11]); - word3_muladd(&w1, &w0, &w2, x[10], y[10]); - word3_muladd(&w1, &w0, &w2, x[11], y[ 9]); - word3_muladd(&w1, &w0, &w2, x[12], y[ 8]); - word3_muladd(&w1, &w0, &w2, x[13], y[ 7]); - word3_muladd(&w1, &w0, &w2, x[14], y[ 6]); - word3_muladd(&w1, &w0, &w2, x[15], y[ 5]); - z[20] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 6], y[15]); - word3_muladd(&w2, &w1, &w0, x[ 7], y[14]); - word3_muladd(&w2, &w1, &w0, x[ 8], y[13]); - word3_muladd(&w2, &w1, &w0, x[ 9], y[12]); - word3_muladd(&w2, &w1, &w0, x[10], y[11]); - word3_muladd(&w2, &w1, &w0, x[11], y[10]); - word3_muladd(&w2, &w1, &w0, x[12], y[ 9]); - word3_muladd(&w2, &w1, &w0, x[13], y[ 8]); - word3_muladd(&w2, &w1, &w0, x[14], y[ 7]); - word3_muladd(&w2, &w1, &w0, x[15], y[ 6]); - z[21] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[ 7], y[15]); - word3_muladd(&w0, &w2, &w1, x[ 8], y[14]); - word3_muladd(&w0, &w2, &w1, x[ 9], y[13]); - word3_muladd(&w0, &w2, &w1, x[10], y[12]); - word3_muladd(&w0, &w2, &w1, x[11], y[11]); - word3_muladd(&w0, &w2, &w1, x[12], y[10]); - word3_muladd(&w0, &w2, &w1, x[13], y[ 9]); - word3_muladd(&w0, &w2, &w1, x[14], y[ 8]); - word3_muladd(&w0, &w2, &w1, x[15], y[ 7]); - z[22] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[ 8], y[15]); - word3_muladd(&w1, &w0, &w2, x[ 9], y[14]); - word3_muladd(&w1, &w0, &w2, x[10], y[13]); - word3_muladd(&w1, &w0, &w2, x[11], y[12]); - word3_muladd(&w1, &w0, &w2, x[12], y[11]); - word3_muladd(&w1, &w0, &w2, x[13], y[10]); - word3_muladd(&w1, &w0, &w2, x[14], y[ 9]); - word3_muladd(&w1, &w0, &w2, x[15], y[ 8]); - z[23] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[ 9], y[15]); - word3_muladd(&w2, &w1, &w0, x[10], y[14]); - word3_muladd(&w2, &w1, &w0, x[11], y[13]); - word3_muladd(&w2, &w1, &w0, x[12], y[12]); - word3_muladd(&w2, &w1, &w0, x[13], y[11]); - word3_muladd(&w2, &w1, &w0, x[14], y[10]); - word3_muladd(&w2, &w1, &w0, x[15], y[ 9]); - z[24] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[10], y[15]); - word3_muladd(&w0, &w2, &w1, x[11], y[14]); - word3_muladd(&w0, &w2, &w1, x[12], y[13]); - word3_muladd(&w0, &w2, &w1, x[13], y[12]); - word3_muladd(&w0, &w2, &w1, x[14], y[11]); - word3_muladd(&w0, &w2, &w1, x[15], y[10]); - z[25] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[11], y[15]); - word3_muladd(&w1, &w0, &w2, x[12], y[14]); - word3_muladd(&w1, &w0, &w2, x[13], y[13]); - word3_muladd(&w1, &w0, &w2, x[14], y[12]); - word3_muladd(&w1, &w0, &w2, x[15], y[11]); - z[26] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[12], y[15]); - word3_muladd(&w2, &w1, &w0, x[13], y[14]); - word3_muladd(&w2, &w1, &w0, x[14], y[13]); - word3_muladd(&w2, &w1, &w0, x[15], y[12]); - z[27] = w0; w0 = 0; - - word3_muladd(&w0, &w2, &w1, x[13], y[15]); - word3_muladd(&w0, &w2, &w1, x[14], y[14]); - word3_muladd(&w0, &w2, &w1, x[15], y[13]); - z[28] = w1; w1 = 0; - - word3_muladd(&w1, &w0, &w2, x[14], y[15]); - word3_muladd(&w1, &w0, &w2, x[15], y[14]); - z[29] = w2; w2 = 0; - - word3_muladd(&w2, &w1, &w0, x[15], y[15]); - z[30] = w0; - z[31] = w1; - } - -} - -} diff --git a/src/math/mp/mp_core.h b/src/math/mp/mp_core.h deleted file mode 100644 index c25cb994f..000000000 --- a/src/math/mp/mp_core.h +++ /dev/null @@ -1,175 +0,0 @@ -/* -* MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_CORE_OPS_H__ -#define BOTAN_MP_CORE_OPS_H__ - -#include <botan/mp_types.h> - -namespace Botan { - -/* -* The size of the word type, in bits -*/ -const size_t MP_WORD_BITS = BOTAN_MP_WORD_BITS; - -extern "C" { - -/** -* Two operand addition -* @param x the first operand (and output) -* @param x_size size of x -* @param y the second operand -* @param y_size size of y (must be >= x_size) -*/ -void bigint_add2(word x[], size_t x_size, - const word y[], size_t y_size); - -/** -* Three operand addition -*/ -void bigint_add3(word z[], - const word x[], size_t x_size, - const word y[], size_t y_size); - -/** -* Two operand addition with carry out -*/ -word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size); - -/** -* Three operand addition with carry out -*/ -word bigint_add3_nc(word z[], - const word x[], size_t x_size, - const word y[], size_t y_size); - -/** -* Two operand subtraction -*/ -word bigint_sub2(word x[], size_t x_size, - const word y[], size_t y_size); - -/** -* Two operand subtraction, x = y - x; assumes y >= x -*/ -void bigint_sub2_rev(word x[], const word y[], size_t y_size); - -/** -* Three operand subtraction -*/ -word bigint_sub3(word z[], - const word x[], size_t x_size, - const word y[], size_t y_size); - -/* -* Shift Operations -*/ -void bigint_shl1(word x[], size_t x_size, - size_t word_shift, size_t bit_shift); - -void bigint_shr1(word x[], size_t x_size, - size_t word_shift, size_t bit_shift); - -void bigint_shl2(word y[], const word x[], size_t x_size, - size_t word_shift, size_t bit_shift); - -void bigint_shr2(word y[], const word x[], size_t x_size, - size_t word_shift, size_t bit_shift); - -/* -* Simple O(N^2) Multiplication and Squaring -*/ -void bigint_simple_mul(word z[], - const word x[], size_t x_size, - const word y[], size_t y_size); - -void bigint_simple_sqr(word z[], const word x[], size_t x_size); - -/* -* Linear Multiply -*/ -void bigint_linmul2(word x[], size_t x_size, word y); -void bigint_linmul3(word z[], const word x[], size_t x_size, word y); - -/** -* Montgomery Reduction -* @param z integer to reduce, of size exactly 2*(p_size+1). - Output is in the first p_size+1 words, higher - words are set to zero. -* @param p modulus -* @param p_size size of p -* @param p_dash Montgomery value -* @param workspace array of at least 2*(p_size+1) words -*/ -void bigint_monty_redc(word z[], - const word p[], size_t p_size, - word p_dash, - word workspace[]); - -/* -* Montgomery Multiplication -*/ -void bigint_monty_mul(word z[], size_t z_size, - const word x[], size_t x_size, size_t x_sw, - const word y[], size_t y_size, size_t y_sw, - const word p[], size_t p_size, word p_dash, - word workspace[]); - -/* -* Montgomery Squaring -*/ -void bigint_monty_sqr(word z[], size_t z_size, - const word x[], size_t x_size, size_t x_sw, - const word p[], size_t p_size, word p_dash, - word workspace[]); - -/** -* Compare x and y -*/ -s32bit bigint_cmp(const word x[], size_t x_size, - const word y[], size_t y_size); - -/** -* Compute ((n1<<bits) + n0) / d -*/ -word bigint_divop(word n1, word n0, word d); - -/** -* Compute ((n1<<bits) + n0) % d -*/ -word bigint_modop(word n1, word n0, word d); - -/* -* Comba Multiplication / Squaring -*/ -void bigint_comba_mul4(word z[8], const word x[4], const word y[4]); -void bigint_comba_mul6(word z[12], const word x[6], const word y[6]); -void bigint_comba_mul8(word z[16], const word x[8], const word y[8]); -void bigint_comba_mul16(word z[32], const word x[16], const word y[16]); - -void bigint_comba_sqr4(word out[8], const word in[4]); -void bigint_comba_sqr6(word out[12], const word in[6]); -void bigint_comba_sqr8(word out[16], const word in[8]); -void bigint_comba_sqr16(word out[32], const word in[16]); - -} - -/* -* High Level Multiplication/Squaring Interfaces -*/ -void bigint_mul(word z[], size_t z_size, word workspace[], - const word x[], size_t x_size, size_t x_sw, - const word y[], size_t y_size, size_t y_sw); - -void bigint_sqr(word z[], size_t z_size, word workspace[], - const word x[], size_t x_size, size_t x_sw); - -} - -#endif diff --git a/src/math/mp/mp_generic/info.txt b/src/math/mp/mp_generic/info.txt deleted file mode 100644 index c87dd00ca..000000000 --- a/src/math/mp/mp_generic/info.txt +++ /dev/null @@ -1,6 +0,0 @@ -load_on dep - -<header:internal> -mp_madd.h -mp_asmi.h -</header:internal> diff --git a/src/math/mp/mp_generic/mp_asmi.h b/src/math/mp/mp_generic/mp_asmi.h deleted file mode 100644 index 018055696..000000000 --- a/src/math/mp/mp_generic/mp_asmi.h +++ /dev/null @@ -1,207 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_ASM_INTERNAL_H__ -#define BOTAN_MP_ASM_INTERNAL_H__ - -#include <botan/internal/mp_madd.h> - -namespace Botan { - -extern "C" { - -/* -* Word Addition -*/ -inline word word_add(word x, word y, word* carry) - { - word z = x + y; - word c1 = (z < x); - z += *carry; - *carry = c1 | (z < *carry); - return z; - } - -/* -* Eight Word Block Addition, Two Argument -*/ -inline word word8_add2(word x[8], const word y[8], word carry) - { - x[0] = word_add(x[0], y[0], &carry); - x[1] = word_add(x[1], y[1], &carry); - x[2] = word_add(x[2], y[2], &carry); - x[3] = word_add(x[3], y[3], &carry); - x[4] = word_add(x[4], y[4], &carry); - x[5] = word_add(x[5], y[5], &carry); - x[6] = word_add(x[6], y[6], &carry); - x[7] = word_add(x[7], y[7], &carry); - return carry; - } - -/* -* Eight Word Block Addition, Three Argument -*/ -inline word word8_add3(word z[8], const word x[8], - const word y[8], word carry) - { - z[0] = word_add(x[0], y[0], &carry); - z[1] = word_add(x[1], y[1], &carry); - z[2] = word_add(x[2], y[2], &carry); - z[3] = word_add(x[3], y[3], &carry); - z[4] = word_add(x[4], y[4], &carry); - z[5] = word_add(x[5], y[5], &carry); - z[6] = word_add(x[6], y[6], &carry); - z[7] = word_add(x[7], y[7], &carry); - return carry; - } - -/* -* Word Subtraction -*/ -inline word word_sub(word x, word y, word* carry) - { - word t0 = x - y; - word c1 = (t0 > x); - word z = t0 - *carry; - *carry = c1 | (z > t0); - return z; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2(word x[8], const word y[8], word carry) - { - x[0] = word_sub(x[0], y[0], &carry); - x[1] = word_sub(x[1], y[1], &carry); - x[2] = word_sub(x[2], y[2], &carry); - x[3] = word_sub(x[3], y[3], &carry); - x[4] = word_sub(x[4], y[4], &carry); - x[5] = word_sub(x[5], y[5], &carry); - x[6] = word_sub(x[6], y[6], &carry); - x[7] = word_sub(x[7], y[7], &carry); - return carry; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2_rev(word x[8], const word y[8], word carry) - { - x[0] = word_sub(y[0], x[0], &carry); - x[1] = word_sub(y[1], x[1], &carry); - x[2] = word_sub(y[2], x[2], &carry); - x[3] = word_sub(y[3], x[3], &carry); - x[4] = word_sub(y[4], x[4], &carry); - x[5] = word_sub(y[5], x[5], &carry); - x[6] = word_sub(y[6], x[6], &carry); - x[7] = word_sub(y[7], x[7], &carry); - return carry; - } - -/* -* Eight Word Block Subtraction, Three Argument -*/ -inline word word8_sub3(word z[8], const word x[8], - const word y[8], word carry) - { - z[0] = word_sub(x[0], y[0], &carry); - z[1] = word_sub(x[1], y[1], &carry); - z[2] = word_sub(x[2], y[2], &carry); - z[3] = word_sub(x[3], y[3], &carry); - z[4] = word_sub(x[4], y[4], &carry); - z[5] = word_sub(x[5], y[5], &carry); - z[6] = word_sub(x[6], y[6], &carry); - z[7] = word_sub(x[7], y[7], &carry); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul2(word x[8], word y, word carry) - { - x[0] = word_madd2(x[0], y, &carry); - x[1] = word_madd2(x[1], y, &carry); - x[2] = word_madd2(x[2], y, &carry); - x[3] = word_madd2(x[3], y, &carry); - x[4] = word_madd2(x[4], y, &carry); - x[5] = word_madd2(x[5], y, &carry); - x[6] = word_madd2(x[6], y, &carry); - x[7] = word_madd2(x[7], y, &carry); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul3(word z[8], const word x[8], word y, word carry) - { - z[0] = word_madd2(x[0], y, &carry); - z[1] = word_madd2(x[1], y, &carry); - z[2] = word_madd2(x[2], y, &carry); - z[3] = word_madd2(x[3], y, &carry); - z[4] = word_madd2(x[4], y, &carry); - z[5] = word_madd2(x[5], y, &carry); - z[6] = word_madd2(x[6], y, &carry); - z[7] = word_madd2(x[7], y, &carry); - return carry; - } - -/* -* Eight Word Block Multiply/Add -*/ -inline word word8_madd3(word z[8], const word x[8], word y, word carry) - { - z[0] = word_madd3(x[0], y, z[0], &carry); - z[1] = word_madd3(x[1], y, z[1], &carry); - z[2] = word_madd3(x[2], y, z[2], &carry); - z[3] = word_madd3(x[3], y, z[3], &carry); - z[4] = word_madd3(x[4], y, z[4], &carry); - z[5] = word_madd3(x[5], y, z[5], &carry); - z[6] = word_madd3(x[6], y, z[6], &carry); - z[7] = word_madd3(x[7], y, z[7], &carry); - return carry; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd(word* w2, word* w1, word* w0, word a, word b) - { - word carry = *w0; - *w0 = word_madd2(a, b, &carry); - *w1 += carry; - *w2 += (*w1 < carry) ? 1 : 0; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd_2(word* w2, word* w1, word* w0, word a, word b) - { - word carry = 0; - a = word_madd2(a, b, &carry); - b = carry; - - word top = (b >> (BOTAN_MP_WORD_BITS-1)); - b <<= 1; - b |= (a >> (BOTAN_MP_WORD_BITS-1)); - a <<= 1; - - carry = 0; - *w0 = word_add(*w0, a, &carry); - *w1 = word_add(*w1, b, &carry); - *w2 = word_add(*w2, top, &carry); - } - -} - -} - -#endif diff --git a/src/math/mp/mp_generic/mp_madd.h b/src/math/mp/mp_generic/mp_madd.h deleted file mode 100644 index 17713f55f..000000000 --- a/src/math/mp/mp_generic/mp_madd.h +++ /dev/null @@ -1,73 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2008,2013 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_WORD_MULADD_H__ -#define BOTAN_MP_WORD_MULADD_H__ - -#include <botan/mp_types.h> - -namespace Botan { - -extern "C" { - -/* -* Word Multiply/Add -*/ -inline word word_madd2(word a, word b, word* c) - { -#if defined(BOTAN_HAS_MP_DWORD) - const dword s = static_cast<dword>(a) * b + *c; - *c = static_cast<word>(s >> BOTAN_MP_WORD_BITS); - return static_cast<word>(s); -#else - static_assert(BOTAN_MP_WORD_BITS == 64, "Unexpected word size"); - - word hi = 0, lo = 0; - - mul64x64_128(a, b, &lo, &hi); - - lo += *c; - hi += (lo < *c); // carry? - - *c = hi; - return lo; -#endif - } - -/* -* Word Multiply/Add -*/ -inline word word_madd3(word a, word b, word c, word* d) - { -#if defined(BOTAN_HAS_MP_DWORD) - const dword s = static_cast<dword>(a) * b + c + *d; - *d = static_cast<word>(s >> BOTAN_MP_WORD_BITS); - return static_cast<word>(s); -#else - static_assert(BOTAN_MP_WORD_BITS == 64, "Unexpected word size"); - - word hi = 0, lo = 0; - - mul64x64_128(a, b, &lo, &hi); - - lo += c; - hi += (lo < c); // carry? - - lo += *d; - hi += (lo < *d); // carry? - - *d = hi; - return lo; -#endif - } - -} - -} - -#endif diff --git a/src/math/mp/mp_karat.cpp b/src/math/mp/mp_karat.cpp deleted file mode 100644 index b549a05c8..000000000 --- a/src/math/mp/mp_karat.cpp +++ /dev/null @@ -1,303 +0,0 @@ -/* -* Karatsuba Multiplication/Squaring -* (C) 1999-2010 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_asmi.h> -#include <botan/mem_ops.h> - -namespace Botan { - -namespace { - -static const size_t KARATSUBA_MULTIPLY_THRESHOLD = 32; -static const size_t KARATSUBA_SQUARE_THRESHOLD = 32; - -/* -* Karatsuba Multiplication Operation -*/ -void karatsuba_mul(word z[], const word x[], const word y[], size_t N, - word workspace[]) - { - if(N < KARATSUBA_MULTIPLY_THRESHOLD || N % 2) - { - if(N == 6) - return bigint_comba_mul6(z, x, y); - else if(N == 8) - return bigint_comba_mul8(z, x, y); - else if(N == 16) - return bigint_comba_mul16(z, x, y); - else - return bigint_simple_mul(z, x, N, y, N); - } - - const size_t N2 = N / 2; - - const word* x0 = x; - const word* x1 = x + N2; - const word* y0 = y; - const word* y1 = y + N2; - word* z0 = z; - word* z1 = z + N; - - const s32bit cmp0 = bigint_cmp(x0, N2, x1, N2); - const s32bit cmp1 = bigint_cmp(y1, N2, y0, N2); - - clear_mem(workspace, 2*N); - - //if(cmp0 && cmp1) - { - if(cmp0 > 0) - bigint_sub3(z0, x0, N2, x1, N2); - else - bigint_sub3(z0, x1, N2, x0, N2); - - if(cmp1 > 0) - bigint_sub3(z1, y1, N2, y0, N2); - else - bigint_sub3(z1, y0, N2, y1, N2); - - karatsuba_mul(workspace, z0, z1, N2, workspace+N); - } - - karatsuba_mul(z0, x0, y0, N2, workspace+N); - karatsuba_mul(z1, x1, y1, N2, workspace+N); - - const word ws_carry = bigint_add3_nc(workspace + N, z0, N, z1, N); - word z_carry = bigint_add2_nc(z + N2, N, workspace + N, N); - - z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1); - bigint_add2_nc(z + N + N2, N2, &z_carry, 1); - - if((cmp0 == cmp1) || (cmp0 == 0) || (cmp1 == 0)) - bigint_add2(z + N2, 2*N-N2, workspace, N); - else - bigint_sub2(z + N2, 2*N-N2, workspace, N); - } - -/* -* Karatsuba Squaring Operation -*/ -void karatsuba_sqr(word z[], const word x[], size_t N, word workspace[]) - { - if(N < KARATSUBA_SQUARE_THRESHOLD || N % 2) - { - if(N == 6) - return bigint_comba_sqr6(z, x); - else if(N == 8) - return bigint_comba_sqr8(z, x); - else if(N == 16) - return bigint_comba_sqr16(z, x); - else - return bigint_simple_sqr(z, x, N); - } - - const size_t N2 = N / 2; - - const word* x0 = x; - const word* x1 = x + N2; - word* z0 = z; - word* z1 = z + N; - - const s32bit cmp = bigint_cmp(x0, N2, x1, N2); - - clear_mem(workspace, 2*N); - - //if(cmp) - { - if(cmp > 0) - bigint_sub3(z0, x0, N2, x1, N2); - else - bigint_sub3(z0, x1, N2, x0, N2); - - karatsuba_sqr(workspace, z0, N2, workspace+N); - } - - karatsuba_sqr(z0, x0, N2, workspace+N); - karatsuba_sqr(z1, x1, N2, workspace+N); - - const word ws_carry = bigint_add3_nc(workspace + N, z0, N, z1, N); - word z_carry = bigint_add2_nc(z + N2, N, workspace + N, N); - - z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1); - bigint_add2_nc(z + N + N2, N2, &z_carry, 1); - - /* - * This is only actually required if cmp is != 0, however - * if cmp==0 then workspace[0:N] == 0 and avoiding the jump - * hides a timing channel. - */ - bigint_sub2(z + N2, 2*N-N2, workspace, N); - } - -/* -* Pick a good size for the Karatsuba multiply -*/ -size_t karatsuba_size(size_t z_size, - size_t x_size, size_t x_sw, - size_t y_size, size_t y_sw) - { - if(x_sw > x_size || x_sw > y_size || y_sw > x_size || y_sw > y_size) - return 0; - - if(((x_size == x_sw) && (x_size % 2)) || - ((y_size == y_sw) && (y_size % 2))) - return 0; - - const size_t start = (x_sw > y_sw) ? x_sw : y_sw; - const size_t end = (x_size < y_size) ? x_size : y_size; - - if(start == end) - { - if(start % 2) - return 0; - return start; - } - - for(size_t j = start; j <= end; ++j) - { - if(j % 2) - continue; - - if(2*j > z_size) - return 0; - - if(x_sw <= j && j <= x_size && y_sw <= j && j <= y_size) - { - if(j % 4 == 2 && - (j+2) <= x_size && (j+2) <= y_size && 2*(j+2) <= z_size) - return j+2; - return j; - } - } - - return 0; - } - -/* -* Pick a good size for the Karatsuba squaring -*/ -size_t karatsuba_size(size_t z_size, size_t x_size, size_t x_sw) - { - if(x_sw == x_size) - { - if(x_sw % 2) - return 0; - return x_sw; - } - - for(size_t j = x_sw; j <= x_size; ++j) - { - if(j % 2) - continue; - - if(2*j > z_size) - return 0; - - if(j % 4 == 2 && (j+2) <= x_size && 2*(j+2) <= z_size) - return j+2; - return j; - } - - return 0; - } - -} - -/* -* Multiplication Algorithm Dispatcher -*/ -void bigint_mul(word z[], size_t z_size, word workspace[], - const word x[], size_t x_size, size_t x_sw, - const word y[], size_t y_size, size_t y_sw) - { - if(x_sw == 1) - { - bigint_linmul3(z, y, y_sw, x[0]); - } - else if(y_sw == 1) - { - bigint_linmul3(z, x, x_sw, y[0]); - } - else if(x_sw <= 4 && x_size >= 4 && - y_sw <= 4 && y_size >= 4 && z_size >= 8) - { - bigint_comba_mul4(z, x, y); - } - else if(x_sw <= 6 && x_size >= 6 && - y_sw <= 6 && y_size >= 6 && z_size >= 12) - { - bigint_comba_mul6(z, x, y); - } - else if(x_sw <= 8 && x_size >= 8 && - y_sw <= 8 && y_size >= 8 && z_size >= 16) - { - bigint_comba_mul8(z, x, y); - } - else if(x_sw <= 16 && x_size >= 16 && - y_sw <= 16 && y_size >= 16 && z_size >= 32) - { - bigint_comba_mul16(z, x, y); - } - else if(x_sw < KARATSUBA_MULTIPLY_THRESHOLD || - y_sw < KARATSUBA_MULTIPLY_THRESHOLD || - !workspace) - { - bigint_simple_mul(z, x, x_sw, y, y_sw); - } - else - { - const size_t N = karatsuba_size(z_size, x_size, x_sw, y_size, y_sw); - - if(N) - karatsuba_mul(z, x, y, N, workspace); - else - bigint_simple_mul(z, x, x_sw, y, y_sw); - } - } - -/* -* Squaring Algorithm Dispatcher -*/ -void bigint_sqr(word z[], size_t z_size, word workspace[], - const word x[], size_t x_size, size_t x_sw) - { - if(x_sw == 1) - { - bigint_linmul3(z, x, x_sw, x[0]); - } - else if(x_sw <= 4 && x_size >= 4 && z_size >= 8) - { - bigint_comba_sqr4(z, x); - } - else if(x_sw <= 6 && x_size >= 6 && z_size >= 12) - { - bigint_comba_sqr6(z, x); - } - else if(x_sw <= 8 && x_size >= 8 && z_size >= 16) - { - bigint_comba_sqr8(z, x); - } - else if(x_sw <= 16 && x_size >= 16 && z_size >= 32) - { - bigint_comba_sqr16(z, x); - } - else if(x_size < KARATSUBA_SQUARE_THRESHOLD || !workspace) - { - bigint_simple_sqr(z, x, x_sw); - } - else - { - const size_t N = karatsuba_size(z_size, x_size, x_sw); - - if(N) - karatsuba_sqr(z, x, N, workspace); - else - bigint_simple_sqr(z, x, x_sw); - } - } - -} diff --git a/src/math/mp/mp_misc.cpp b/src/math/mp/mp_misc.cpp deleted file mode 100644 index 0efd5fd19..000000000 --- a/src/math/mp/mp_misc.cpp +++ /dev/null @@ -1,79 +0,0 @@ -/* -* MP Misc Functions -* (C) 1999-2008 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_madd.h> - -namespace Botan { - -extern "C" { - -/* -* Compare two MP integers -*/ -s32bit bigint_cmp(const word x[], size_t x_size, - const word y[], size_t y_size) - { - if(x_size < y_size) { return (-bigint_cmp(y, y_size, x, x_size)); } - - while(x_size > y_size) - { - if(x[x_size-1]) - return 1; - x_size--; - } - - for(size_t i = x_size; i > 0; --i) - { - if(x[i-1] > y[i-1]) - return 1; - if(x[i-1] < y[i-1]) - return -1; - } - - return 0; - } - -/* -* Do a 2-word/1-word Division -*/ -word bigint_divop(word n1, word n0, word d) - { - word high = n1 % d, quotient = 0; - - for(size_t i = 0; i != MP_WORD_BITS; ++i) - { - word high_top_bit = (high & MP_WORD_TOP_BIT); - - high <<= 1; - high |= (n0 >> (MP_WORD_BITS-1-i)) & 1; - quotient <<= 1; - - if(high_top_bit || high >= d) - { - high -= d; - quotient |= 1; - } - } - - return quotient; - } - -/* -* Do a 2-word/1-word Modulo -*/ -word bigint_modop(word n1, word n0, word d) - { - word z = bigint_divop(n1, n0, d); - word dummy = 0; - z = word_madd2(z, d, &dummy); - return (n0-z); - } - -} - -} diff --git a/src/math/mp/mp_monty.cpp b/src/math/mp/mp_monty.cpp deleted file mode 100644 index 095457dbe..000000000 --- a/src/math/mp/mp_monty.cpp +++ /dev/null @@ -1,101 +0,0 @@ -/* -* Montgomery Reduction -* (C) 1999-2011 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_madd.h> -#include <botan/internal/mp_asmi.h> -#include <botan/mem_ops.h> - -namespace Botan { - -extern "C" { - -/* -* Montgomery Reduction Algorithm -*/ -void bigint_monty_redc(word z[], - const word p[], size_t p_size, - word p_dash, word ws[]) - { - const size_t z_size = 2*(p_size+1); - - const size_t blocks_of_8 = p_size - (p_size % 8); - - for(size_t i = 0; i != p_size; ++i) - { - word* z_i = z + i; - - const word y = z_i[0] * p_dash; - - /* - bigint_linmul3(ws, p, p_size, y); - bigint_add2(z_i, z_size - i, ws, p_size+1); - */ - - word carry = 0; - - for(size_t j = 0; j != blocks_of_8; j += 8) - carry = word8_madd3(z_i + j, p + j, y, carry); - - for(size_t j = blocks_of_8; j != p_size; ++j) - z_i[j] = word_madd3(p[j], y, z_i[j], &carry); - - word z_sum = z_i[p_size] + carry; - carry = (z_sum < z_i[p_size]); - z_i[p_size] = z_sum; - - for(size_t j = p_size + 1; carry && j != z_size - i; ++j) - { - ++z_i[j]; - carry = !z_i[j]; - } - } - - word borrow = 0; - for(size_t i = 0; i != p_size; ++i) - ws[i] = word_sub(z[p_size + i], p[i], &borrow); - - ws[p_size] = word_sub(z[p_size+p_size], 0, &borrow); - - copy_mem(ws + p_size + 1, z + p_size, p_size + 1); - - copy_mem(z, ws + borrow*(p_size+1), p_size + 1); - clear_mem(z + p_size + 1, z_size - p_size - 1); - } - -void bigint_monty_mul(word z[], size_t z_size, - const word x[], size_t x_size, size_t x_sw, - const word y[], size_t y_size, size_t y_sw, - const word p[], size_t p_size, word p_dash, - word ws[]) - { - bigint_mul(&z[0], z_size, &ws[0], - &x[0], x_size, x_sw, - &y[0], y_size, y_sw); - - bigint_monty_redc(&z[0], - &p[0], p_size, p_dash, - &ws[0]); - } - -void bigint_monty_sqr(word z[], size_t z_size, - const word x[], size_t x_size, size_t x_sw, - const word p[], size_t p_size, word p_dash, - word ws[]) - { - bigint_sqr(&z[0], z_size, &ws[0], - &x[0], x_size, x_sw); - - bigint_monty_redc(&z[0], - &p[0], p_size, p_dash, - &ws[0]); - } - -} - -} diff --git a/src/math/mp/mp_mulop.cpp b/src/math/mp/mp_mulop.cpp deleted file mode 100644 index 0c79cc2ef..000000000 --- a/src/math/mp/mp_mulop.cpp +++ /dev/null @@ -1,77 +0,0 @@ -/* -* Simple O(N^2) Multiplication and Squaring -* (C) 1999-2008 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/internal/mp_madd.h> -#include <botan/internal/mp_asmi.h> -#include <botan/mem_ops.h> - -namespace Botan { - -extern "C" { - -/* -* Simple O(N^2) Multiplication -*/ -void bigint_simple_mul(word z[], const word x[], size_t x_size, - const word y[], size_t y_size) - { - const size_t x_size_8 = x_size - (x_size % 8); - - clear_mem(z, x_size + y_size); - - for(size_t i = 0; i != y_size; ++i) - { - const word y_i = y[i]; - - word carry = 0; - - for(size_t j = 0; j != x_size_8; j += 8) - carry = word8_madd3(z + i + j, x + j, y_i, carry); - - for(size_t j = x_size_8; j != x_size; ++j) - z[i+j] = word_madd3(x[j], y_i, z[i+j], &carry); - - z[x_size+i] = carry; - } - } - -/* -* Simple O(N^2) Squaring -* -* This is exactly the same algorithm as bigint_simple_mul, however -* because C/C++ compilers suck at alias analysis it is good to have -* the version where the compiler knows that x == y -* -* There is an O(n^1.5) squaring algorithm specified in Handbook of -* Applied Cryptography, chapter 14 -* -*/ -void bigint_simple_sqr(word z[], const word x[], size_t x_size) - { - const size_t x_size_8 = x_size - (x_size % 8); - - clear_mem(z, 2*x_size); - - for(size_t i = 0; i != x_size; ++i) - { - const word x_i = x[i]; - word carry = 0; - - for(size_t j = 0; j != x_size_8; j += 8) - carry = word8_madd3(z + i + j, x + j, x_i, carry); - - for(size_t j = x_size_8; j != x_size; ++j) - z[i+j] = word_madd3(x[j], x_i, z[i+j], &carry); - - z[x_size+i] = carry; - } - } - -} - -} diff --git a/src/math/mp/mp_shift.cpp b/src/math/mp/mp_shift.cpp deleted file mode 100644 index 0531658ec..000000000 --- a/src/math/mp/mp_shift.cpp +++ /dev/null @@ -1,138 +0,0 @@ -/* -* MP Shift Algorithms -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/mp_core.h> -#include <botan/mem_ops.h> - -namespace Botan { - -extern "C" { - -/* -* Single Operand Left Shift -*/ -void bigint_shl1(word x[], size_t x_size, size_t word_shift, size_t bit_shift) - { - if(word_shift) - { - for(size_t j = 1; j != x_size + 1; ++j) - x[(x_size - j) + word_shift] = x[x_size - j]; - clear_mem(x, word_shift); - } - - if(bit_shift) - { - word carry = 0; - for(size_t j = word_shift; j != x_size + word_shift + 1; ++j) - { - word temp = x[j]; - x[j] = (temp << bit_shift) | carry; - carry = (temp >> (MP_WORD_BITS - bit_shift)); - } - } - } - -/* -* Single Operand Right Shift -*/ -void bigint_shr1(word x[], size_t x_size, size_t word_shift, size_t bit_shift) - { - if(x_size < word_shift) - { - clear_mem(x, x_size); - return; - } - - if(word_shift) - { - copy_mem(x, x + word_shift, x_size - word_shift); - clear_mem(x + x_size - word_shift, word_shift); - } - - if(bit_shift) - { - word carry = 0; - - size_t top = x_size - word_shift; - - while(top >= 4) - { - word w = x[top-1]; - x[top-1] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - - w = x[top-2]; - x[top-2] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - - w = x[top-3]; - x[top-3] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - - w = x[top-4]; - x[top-4] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - - top -= 4; - } - - while(top) - { - word w = x[top-1]; - x[top-1] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - - top--; - } - } - } - -/* -* Two Operand Left Shift -*/ -void bigint_shl2(word y[], const word x[], size_t x_size, - size_t word_shift, size_t bit_shift) - { - for(size_t j = 0; j != x_size; ++j) - y[j + word_shift] = x[j]; - if(bit_shift) - { - word carry = 0; - for(size_t j = word_shift; j != x_size + word_shift + 1; ++j) - { - word w = y[j]; - y[j] = (w << bit_shift) | carry; - carry = (w >> (MP_WORD_BITS - bit_shift)); - } - } - } - -/* -* Two Operand Right Shift -*/ -void bigint_shr2(word y[], const word x[], size_t x_size, - size_t word_shift, size_t bit_shift) - { - if(x_size < word_shift) return; - - for(size_t j = 0; j != x_size - word_shift; ++j) - y[j] = x[j + word_shift]; - if(bit_shift) - { - word carry = 0; - for(size_t j = x_size - word_shift; j > 0; --j) - { - word w = y[j-1]; - y[j-1] = (w >> bit_shift) | carry; - carry = (w << (MP_WORD_BITS - bit_shift)); - } - } - } - -} - -} diff --git a/src/math/mp/mp_types.h b/src/math/mp/mp_types.h deleted file mode 100644 index 60282fb83..000000000 --- a/src/math/mp/mp_types.h +++ /dev/null @@ -1,46 +0,0 @@ -/* -* Low Level MPI Types -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MPI_TYPES_H__ -#define BOTAN_MPI_TYPES_H__ - -#include <botan/types.h> -#include <botan/mul128.h> - -namespace Botan { - -#if (BOTAN_MP_WORD_BITS == 8) - typedef byte word; - typedef u16bit dword; - #define BOTAN_HAS_MP_DWORD -#elif (BOTAN_MP_WORD_BITS == 16) - typedef u16bit word; - typedef u32bit dword; - #define BOTAN_HAS_MP_DWORD -#elif (BOTAN_MP_WORD_BITS == 32) - typedef u32bit word; - typedef u64bit dword; - #define BOTAN_HAS_MP_DWORD -#elif (BOTAN_MP_WORD_BITS == 64) - typedef u64bit word; - - #if defined(BOTAN_TARGET_HAS_NATIVE_UINT128) - typedef uint128_t dword; - #define BOTAN_HAS_MP_DWORD - #endif - -#else - #error BOTAN_MP_WORD_BITS must be 8, 16, 32, or 64 -#endif - -const word MP_WORD_MASK = ~static_cast<word>(0); -const word MP_WORD_TOP_BIT = static_cast<word>(1) << (8*sizeof(word) - 1); -const word MP_WORD_MAX = MP_WORD_MASK; - -} - -#endif diff --git a/src/math/mp/mp_x86_32/info.txt b/src/math/mp/mp_x86_32/info.txt deleted file mode 100644 index f36abaf62..000000000 --- a/src/math/mp/mp_x86_32/info.txt +++ /dev/null @@ -1,18 +0,0 @@ -load_on dep - -mp_bits 32 - -<header:internal> -mp_madd.h -mp_asmi.h -</header:internal> - -<arch> -x86_32 -</arch> - -<cc> -clang -gcc -icc -</cc> diff --git a/src/math/mp/mp_x86_32/mp_asmi.h b/src/math/mp/mp_x86_32/mp_asmi.h deleted file mode 100644 index 9b858c8d5..000000000 --- a/src/math/mp/mp_x86_32/mp_asmi.h +++ /dev/null @@ -1,240 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_ASM_INTERNAL_H__ -#define BOTAN_MP_ASM_INTERNAL_H__ - -#include <botan/internal/mp_madd.h> - -namespace Botan { - -extern "C" { - -/* -* Helper Macros for x86 Assembly -*/ -#ifndef ASM - #define ASM(x) x "\n\t" -#endif - -#define ADDSUB2_OP(OPERATION, INDEX) \ - ASM("movl 4*" #INDEX "(%[y]), %[carry]") \ - ASM(OPERATION " %[carry], 4*" #INDEX "(%[x])") \ - -#define ADDSUB3_OP(OPERATION, INDEX) \ - ASM("movl 4*" #INDEX "(%[x]), %[carry]") \ - ASM(OPERATION " 4*" #INDEX "(%[y]), %[carry]") \ - ASM("movl %[carry], 4*" #INDEX "(%[z])") \ - -#define LINMUL_OP(WRITE_TO, INDEX) \ - ASM("movl 4*" #INDEX "(%[x]),%%eax") \ - ASM("mull %[y]") \ - ASM("addl %[carry],%%eax") \ - ASM("adcl $0,%%edx") \ - ASM("movl %%edx,%[carry]") \ - ASM("movl %%eax, 4*" #INDEX "(%[" WRITE_TO "])") - -#define MULADD_OP(IGNORED, INDEX) \ - ASM("movl 4*" #INDEX "(%[x]),%%eax") \ - ASM("mull %[y]") \ - ASM("addl %[carry],%%eax") \ - ASM("adcl $0,%%edx") \ - ASM("addl 4*" #INDEX "(%[z]),%%eax") \ - ASM("adcl $0,%%edx") \ - ASM("movl %%edx,%[carry]") \ - ASM("movl %%eax, 4*" #INDEX " (%[z])") - -#define DO_8_TIMES(MACRO, ARG) \ - MACRO(ARG, 0) \ - MACRO(ARG, 1) \ - MACRO(ARG, 2) \ - MACRO(ARG, 3) \ - MACRO(ARG, 4) \ - MACRO(ARG, 5) \ - MACRO(ARG, 6) \ - MACRO(ARG, 7) - -#define ADD_OR_SUBTRACT(CORE_CODE) \ - ASM("rorl %[carry]") \ - CORE_CODE \ - ASM("sbbl %[carry],%[carry]") \ - ASM("negl %[carry]") - -/* -* Word Addition -*/ -inline word word_add(word x, word y, word* carry) - { - asm( - ADD_OR_SUBTRACT(ASM("adcl %[y],%[x]")) - : [x]"=r"(x), [carry]"=r"(*carry) - : "0"(x), [y]"rm"(y), "1"(*carry) - : "cc"); - return x; - } - -/* -* Eight Word Block Addition, Two Argument -*/ -inline word word8_add2(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "adcl")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Addition, Three Argument -*/ -inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "adcl")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Word Subtraction -*/ -inline word word_sub(word x, word y, word* carry) - { - asm( - ADD_OR_SUBTRACT(ASM("sbbl %[y],%[x]")) - : [x]"=r"(x), [carry]"=r"(*carry) - : "0"(x), [y]"rm"(y), "1"(*carry) - : "cc"); - return x; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "sbbl")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2_rev(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbl")) - : [carry]"=r"(carry) - : [x]"r"(y), [y]"r"(x), [z]"r"(x), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Subtraction, Three Argument -*/ -inline word word8_sub3(word z[8], const word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbl")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul2(word x[8], word y, word carry) - { - asm( - DO_8_TIMES(LINMUL_OP, "x") - : [carry]"=r"(carry) - : [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%eax", "%edx"); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul3(word z[8], const word x[8], word y, word carry) - { - asm( - DO_8_TIMES(LINMUL_OP, "z") - : [carry]"=r"(carry) - : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%eax", "%edx"); - return carry; - } - -/* -* Eight Word Block Multiply/Add -*/ -inline word word8_madd3(word z[8], const word x[8], word y, word carry) - { - asm( - DO_8_TIMES(MULADD_OP, "") - : [carry]"=r"(carry) - : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%eax", "%edx"); - return carry; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd(word* w2, word* w1, word* w0, word x, word y) - { - asm( - ASM("mull %[y]") - - ASM("addl %[x],%[w0]") - ASM("adcl %[y],%[w1]") - ASM("adcl $0,%[w2]") - - : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) - : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) - : "cc"); - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd_2(word* w2, word* w1, word* w0, word x, word y) - { - asm( - ASM("mull %[y]") - - ASM("addl %[x],%[w0]") - ASM("adcl %[y],%[w1]") - ASM("adcl $0,%[w2]") - - ASM("addl %[x],%[w0]") - ASM("adcl %[y],%[w1]") - ASM("adcl $0,%[w2]") - - : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) - : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) - : "cc"); - } - -} - -} - -#endif diff --git a/src/math/mp/mp_x86_32/mp_madd.h b/src/math/mp/mp_x86_32/mp_madd.h deleted file mode 100644 index 9d60c721d..000000000 --- a/src/math/mp/mp_x86_32/mp_madd.h +++ /dev/null @@ -1,67 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2008 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_WORD_MULADD_H__ -#define BOTAN_MP_WORD_MULADD_H__ - -#include <botan/mp_types.h> - -#if (BOTAN_MP_WORD_BITS != 32) - #error The mp_x86_32 module requires that BOTAN_MP_WORD_BITS == 32 -#endif - -namespace Botan { - -extern "C" { - -/* -* Helper Macros for x86 Assembly -*/ -#define ASM(x) x "\n\t" - -/* -* Word Multiply -*/ -inline word word_madd2(word a, word b, word* c) - { - asm( - ASM("mull %[b]") - ASM("addl %[c],%[a]") - ASM("adcl $0,%[carry]") - - : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*c) - : "0"(a), "1"(b), [c]"g"(*c) : "cc"); - - return a; - } - -/* -* Word Multiply/Add -*/ -inline word word_madd3(word a, word b, word c, word* d) - { - asm( - ASM("mull %[b]") - - ASM("addl %[c],%[a]") - ASM("adcl $0,%[carry]") - - ASM("addl %[d],%[a]") - ASM("adcl $0,%[carry]") - - : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*d) - : "0"(a), "1"(b), [c]"g"(c), [d]"g"(*d) : "cc"); - - return a; - } - -} - -} - -#endif diff --git a/src/math/mp/mp_x86_32_msvc/info.txt b/src/math/mp/mp_x86_32_msvc/info.txt deleted file mode 100644 index 3029d6a61..000000000 --- a/src/math/mp/mp_x86_32_msvc/info.txt +++ /dev/null @@ -1,16 +0,0 @@ -mp_bits 32 - -load_on dep - -<header:internal> -mp_generic:mp_madd.h -mp_asmi.h -</header:internal> - -<arch> -x86_32 -</arch> - -<cc> -msvc -</cc> diff --git a/src/math/mp/mp_x86_32_msvc/mp_asmi.h b/src/math/mp/mp_x86_32_msvc/mp_asmi.h deleted file mode 100644 index ef149c920..000000000 --- a/src/math/mp/mp_x86_32_msvc/mp_asmi.h +++ /dev/null @@ -1,542 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_ASM_INTERNAL_H__ -#define BOTAN_MP_ASM_INTERNAL_H__ - -#include <botan/internal/mp_madd.h> - -namespace Botan { - -extern "C" { - -/* -* Word Addition -*/ -inline word word_add(word x, word y, word* carry) - { - word z = x + y; - word c1 = (z < x); - z += *carry; - *carry = c1 | (z < *carry); - return z; - } - -/* -* Eight Word Block Addition, Two Argument -*/ -inline word word8_add2(word x[8], const word y[8], word carry) - { - __asm { - mov edx,[x] - mov esi,[y] - xor eax,eax - sub eax,[carry] //force CF=1 iff *carry==1 - mov eax,[esi] - adc [edx],eax - mov eax,[esi+4] - adc [edx+4],eax - mov eax,[esi+8] - adc [edx+8],eax - mov eax,[esi+12] - adc [edx+12],eax - mov eax,[esi+16] - adc [edx+16],eax - mov eax,[esi+20] - adc [edx+20],eax - mov eax,[esi+24] - adc [edx+24],eax - mov eax,[esi+28] - adc [edx+28],eax - sbb eax,eax - neg eax - } - } - -/* -* Eight Word Block Addition, Three Argument -*/ -inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) - { - __asm { - mov edi,[x] - mov esi,[y] - mov ebx,[z] - xor eax,eax - sub eax,[carry] //force CF=1 iff *carry==1 - mov eax,[edi] - adc eax,[esi] - mov [ebx],eax - - mov eax,[edi+4] - adc eax,[esi+4] - mov [ebx+4],eax - - mov eax,[edi+8] - adc eax,[esi+8] - mov [ebx+8],eax - - mov eax,[edi+12] - adc eax,[esi+12] - mov [ebx+12],eax - - mov eax,[edi+16] - adc eax,[esi+16] - mov [ebx+16],eax - - mov eax,[edi+20] - adc eax,[esi+20] - mov [ebx+20],eax - - mov eax,[edi+24] - adc eax,[esi+24] - mov [ebx+24],eax - - mov eax,[edi+28] - adc eax,[esi+28] - mov [ebx+28],eax - - sbb eax,eax - neg eax - } - } - -/* -* Word Subtraction -*/ -inline word word_sub(word x, word y, word* carry) - { - word t0 = x - y; - word c1 = (t0 > x); - word z = t0 - *carry; - *carry = c1 | (z > t0); - return z; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2(word x[8], const word y[8], word carry) - { - __asm { - mov edi,[x] - mov esi,[y] - xor eax,eax - sub eax,[carry] //force CF=1 iff *carry==1 - mov eax,[edi] - sbb eax,[esi] - mov [edi],eax - mov eax,[edi+4] - sbb eax,[esi+4] - mov [edi+4],eax - mov eax,[edi+8] - sbb eax,[esi+8] - mov [edi+8],eax - mov eax,[edi+12] - sbb eax,[esi+12] - mov [edi+12],eax - mov eax,[edi+16] - sbb eax,[esi+16] - mov [edi+16],eax - mov eax,[edi+20] - sbb eax,[esi+20] - mov [edi+20],eax - mov eax,[edi+24] - sbb eax,[esi+24] - mov [edi+24],eax - mov eax,[edi+28] - sbb eax,[esi+28] - mov [edi+28],eax - sbb eax,eax - neg eax - } - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2_rev(word x[8], const word y[8], word carry) - { - x[0] = word_sub(y[0], x[0], &carry); - x[1] = word_sub(y[1], x[1], &carry); - x[2] = word_sub(y[2], x[2], &carry); - x[3] = word_sub(y[3], x[3], &carry); - x[4] = word_sub(y[4], x[4], &carry); - x[5] = word_sub(y[5], x[5], &carry); - x[6] = word_sub(y[6], x[6], &carry); - x[7] = word_sub(y[7], x[7], &carry); - return carry; - } - - -/* -* Eight Word Block Subtraction, Three Argument -*/ -inline word word8_sub3(word z[8], const word x[8], - const word y[8], word carry) - { - __asm { - mov edi,[x] - mov esi,[y] - xor eax,eax - sub eax,[carry] //force CF=1 iff *carry==1 - mov ebx,[z] - mov eax,[edi] - sbb eax,[esi] - mov [ebx],eax - mov eax,[edi+4] - sbb eax,[esi+4] - mov [ebx+4],eax - mov eax,[edi+8] - sbb eax,[esi+8] - mov [ebx+8],eax - mov eax,[edi+12] - sbb eax,[esi+12] - mov [ebx+12],eax - mov eax,[edi+16] - sbb eax,[esi+16] - mov [ebx+16],eax - mov eax,[edi+20] - sbb eax,[esi+20] - mov [ebx+20],eax - mov eax,[edi+24] - sbb eax,[esi+24] - mov [ebx+24],eax - mov eax,[edi+28] - sbb eax,[esi+28] - mov [ebx+28],eax - sbb eax,eax - neg eax - } - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul2(word x[8], word y, word carry) - { - __asm { - mov esi,[x] - mov eax,[esi] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,[carry] //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi],eax //load a - - mov eax,[esi+4] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+4],eax //load a - - mov eax,[esi+8] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+8],eax //load a - - mov eax,[esi+12] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+12],eax //load a - - mov eax,[esi+16] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+16],eax //load a - - mov eax,[esi+20] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+20],eax //load a - - mov eax,[esi+24] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [esi+24],eax //load a - - mov eax,[esi+28] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov [esi+28],eax //load a - - mov eax,edx //store carry - } - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_muladd(word z[8], const word x[8], - word y, word carry) - { - __asm { - mov esi,[x] - mov ebx,[y] - mov edi,[z] - mov eax,[esi] //load a - mul ebx //edx(hi):eax(lo)=a*b - add eax,[carry] //sum lo carry - adc edx,0 //sum hi carry - add eax,[edi] //sum lo z - adc edx,0 //sum hi z - mov ecx,edx //carry for next block = hi z - mov [edi],eax //save lo z - - mov eax,[esi+4] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+4] - adc edx,0 - mov ecx,edx - mov [edi+4],eax - - mov eax,[esi+8] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+8] - adc edx,0 - mov ecx,edx - mov [edi+8],eax - - mov eax,[esi+12] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+12] - adc edx,0 - mov ecx,edx - mov [edi+12],eax - - mov eax,[esi+16] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+16] - adc edx,0 - mov ecx,edx - mov [edi+16],eax - - mov eax,[esi+20] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+20] - adc edx,0 - mov ecx,edx - mov [edi+20],eax - - mov eax,[esi+24] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+24] - adc edx,0 - mov ecx,edx - mov [edi+24],eax - - mov eax,[esi+28] - mul ebx - add eax,ecx - adc edx,0 - add eax,[edi+28] - adc edx,0 - mov [edi+28],eax - mov eax,edx - } - } - -inline word word8_linmul3(word z[4], const word x[4], word y, word carry) - { - __asm { -#if 0 - //it's slower!!! - mov edx,[z] - mov eax,[x] - movd mm7,[y] - - movd mm0,[eax] - movd mm1,[eax+4] - movd mm2,[eax+8] - pmuludq mm0,mm7 - pmuludq mm1,mm7 - pmuludq mm2,mm7 - - movd mm6,[carry] - paddq mm0,mm6 - movd [edx],mm0 - - psrlq mm0,32 - paddq mm1,mm0 - movd [edx+4],mm1 - - movd mm3,[eax+12] - psrlq mm1,32 - paddq mm2,mm1 - movd [edx+8],mm2 - - pmuludq mm3,mm7 - movd mm4,[eax+16] - psrlq mm2,32 - paddq mm3,mm2 - movd [edx+12],mm3 - - pmuludq mm4,mm7 - movd mm5,[eax+20] - psrlq mm3,32 - paddq mm4,mm3 - movd [edx+16],mm4 - - pmuludq mm5,mm7 - movd mm0,[eax+24] - psrlq mm4,32 - paddq mm5,mm4 - movd [edx+20],mm5 - - pmuludq mm0,mm7 - movd mm1,[eax+28] - psrlq mm5,32 - paddq mm0,mm5 - movd [edx+24],mm0 - - pmuludq mm1,mm7 - psrlq mm0,32 - paddq mm1,mm0 - movd [edx+28],mm1 - psrlq mm1,32 - - movd eax,mm1 - emms -#else - mov edi,[z] - mov esi,[x] - mov eax,[esi] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,[carry] //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi],eax //load a - - mov eax,[esi+4] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+4],eax //load a - - mov eax,[esi+8] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+8],eax //load a - - mov eax,[esi+12] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+12],eax //load a - - mov eax,[esi+16] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+16],eax //load a - - mov eax,[esi+20] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+20],eax //load a - - mov eax,[esi+24] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov ecx,edx //store carry - mov [edi+24],eax //load a - - mov eax,[esi+28] //load a - mul [y] //edx(hi):eax(lo)=a*b - add eax,ecx //sum lo carry - adc edx,0 //sum hi carry - mov [edi+28],eax //load a - mov eax,edx //store carry -#endif - } - } - -/* -* Eight Word Block Multiply/Add -*/ -inline word word8_madd3(word z[8], const word x[8], word y, word carry) - { - z[0] = word_madd3(x[0], y, z[0], &carry); - z[1] = word_madd3(x[1], y, z[1], &carry); - z[2] = word_madd3(x[2], y, z[2], &carry); - z[3] = word_madd3(x[3], y, z[3], &carry); - z[4] = word_madd3(x[4], y, z[4], &carry); - z[5] = word_madd3(x[5], y, z[5], &carry); - z[6] = word_madd3(x[6], y, z[6], &carry); - z[7] = word_madd3(x[7], y, z[7], &carry); - return carry; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd(word* w2, word* w1, word* w0, word a, word b) - { - word carry = *w0; - *w0 = word_madd2(a, b, &carry); - *w1 += carry; - *w2 += (*w1 < carry) ? 1 : 0; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd_2(word* w2, word* w1, word* w0, word a, word b) - { - word carry = 0; - a = word_madd2(a, b, &carry); - b = carry; - - word top = (b >> (BOTAN_MP_WORD_BITS-1)); - b <<= 1; - b |= (a >> (BOTAN_MP_WORD_BITS-1)); - a <<= 1; - - carry = 0; - *w0 = word_add(*w0, a, &carry); - *w1 = word_add(*w1, b, &carry); - *w2 = word_add(*w2, top, &carry); - } - -} - -} - -#endif diff --git a/src/math/mp/mp_x86_64/info.txt b/src/math/mp/mp_x86_64/info.txt deleted file mode 100644 index 75c42ddc1..000000000 --- a/src/math/mp/mp_x86_64/info.txt +++ /dev/null @@ -1,18 +0,0 @@ -load_on dep - -mp_bits 64 - -<header:internal> -mp_madd.h -mp_asmi.h -</header:internal> - -<arch> -x86_64 -</arch> - -<cc> -clang -gcc -icc -</cc> diff --git a/src/math/mp/mp_x86_64/mp_asmi.h b/src/math/mp/mp_x86_64/mp_asmi.h deleted file mode 100644 index b2f1202e3..000000000 --- a/src/math/mp/mp_x86_64/mp_asmi.h +++ /dev/null @@ -1,248 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2010 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_ASM_INTERNAL_H__ -#define BOTAN_MP_ASM_INTERNAL_H__ - -#include <botan/internal/mp_madd.h> - -namespace Botan { - -extern "C" { - -/* -* Helper Macros for x86-64 Assembly -*/ -#ifndef ASM - #define ASM(x) x "\n\t" -#endif - -#define ADDSUB2_OP(OPERATION, INDEX) \ - ASM("movq 8*" #INDEX "(%[y]), %[carry]") \ - ASM(OPERATION " %[carry], 8*" #INDEX "(%[x])") \ - -#define ADDSUB3_OP(OPERATION, INDEX) \ - ASM("movq 8*" #INDEX "(%[x]), %[carry]") \ - ASM(OPERATION " 8*" #INDEX "(%[y]), %[carry]") \ - ASM("movq %[carry], 8*" #INDEX "(%[z])") \ - -#define LINMUL_OP(WRITE_TO, INDEX) \ - ASM("movq 8*" #INDEX "(%[x]),%%rax") \ - ASM("mulq %[y]") \ - ASM("addq %[carry],%%rax") \ - ASM("adcq $0,%%rdx") \ - ASM("movq %%rdx,%[carry]") \ - ASM("movq %%rax, 8*" #INDEX "(%[" WRITE_TO "])") - -#define MULADD_OP(IGNORED, INDEX) \ - ASM("movq 8*" #INDEX "(%[x]),%%rax") \ - ASM("mulq %[y]") \ - ASM("addq %[carry],%%rax") \ - ASM("adcq $0,%%rdx") \ - ASM("addq 8*" #INDEX "(%[z]),%%rax") \ - ASM("adcq $0,%%rdx") \ - ASM("movq %%rdx,%[carry]") \ - ASM("movq %%rax, 8*" #INDEX " (%[z])") - -#define DO_8_TIMES(MACRO, ARG) \ - MACRO(ARG, 0) \ - MACRO(ARG, 1) \ - MACRO(ARG, 2) \ - MACRO(ARG, 3) \ - MACRO(ARG, 4) \ - MACRO(ARG, 5) \ - MACRO(ARG, 6) \ - MACRO(ARG, 7) - -#define ADD_OR_SUBTRACT(CORE_CODE) \ - ASM("rorq %[carry]") \ - CORE_CODE \ - ASM("sbbq %[carry],%[carry]") \ - ASM("negq %[carry]") - -/* -* Word Addition -*/ -inline word word_add(word x, word y, word* carry) - { - asm( - ADD_OR_SUBTRACT(ASM("adcq %[y],%[x]")) - : [x]"=r"(x), [carry]"=r"(*carry) - : "0"(x), [y]"rm"(y), "1"(*carry) - : "cc"); - return x; - } - -/* -* Eight Word Block Addition, Two Argument -*/ -inline word word8_add2(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "adcq")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Addition, Three Argument -*/ -inline word word8_add3(word z[8], const word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "adcq")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Word Subtraction -*/ -inline word word_sub(word x, word y, word* carry) - { - asm( - ADD_OR_SUBTRACT(ASM("sbbq %[y],%[x]")) - : [x]"=r"(x), [carry]"=r"(*carry) - : "0"(x), [y]"rm"(y), "1"(*carry) - : "cc"); - return x; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB2_OP, "sbbq")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Subtraction, Two Argument -*/ -inline word word8_sub2_rev(word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbq")) - : [carry]"=r"(carry) - : [x]"r"(y), [y]"r"(x), [z]"r"(x), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Subtraction, Three Argument -*/ -inline word word8_sub3(word z[8], const word x[8], const word y[8], word carry) - { - asm( - ADD_OR_SUBTRACT(DO_8_TIMES(ADDSUB3_OP, "sbbq")) - : [carry]"=r"(carry) - : [x]"r"(x), [y]"r"(y), [z]"r"(z), "0"(carry) - : "cc", "memory"); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul2(word x[8], word y, word carry) - { - asm( - DO_8_TIMES(LINMUL_OP, "x") - : [carry]"=r"(carry) - : [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%rax", "%rdx"); - return carry; - } - -/* -* Eight Word Block Linear Multiplication -*/ -inline word word8_linmul3(word z[8], const word x[8], word y, word carry) - { - asm( - DO_8_TIMES(LINMUL_OP, "z") - : [carry]"=r"(carry) - : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%rax", "%rdx"); - return carry; - } - -/* -* Eight Word Block Multiply/Add -*/ -inline word word8_madd3(word z[8], const word x[8], word y, word carry) - { - asm( - DO_8_TIMES(MULADD_OP, "") - : [carry]"=r"(carry) - : [z]"r"(z), [x]"r"(x), [y]"rm"(y), "0"(carry) - : "cc", "%rax", "%rdx"); - return carry; - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd(word* w2, word* w1, word* w0, word x, word y) - { - asm( - ASM("mulq %[y]") - - ASM("addq %[x],%[w0]") - ASM("adcq %[y],%[w1]") - ASM("adcq $0,%[w2]") - - : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) - : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) - : "cc"); - } - -/* -* Multiply-Add Accumulator -*/ -inline void word3_muladd_2(word* w2, word* w1, word* w0, word x, word y) - { - asm( - ASM("mulq %[y]") - - ASM("addq %[x],%[w0]") - ASM("adcq %[y],%[w1]") - ASM("adcq $0,%[w2]") - - ASM("addq %[x],%[w0]") - ASM("adcq %[y],%[w1]") - ASM("adcq $0,%[w2]") - - : [w0]"=r"(*w0), [w1]"=r"(*w1), [w2]"=r"(*w2) - : [x]"a"(x), [y]"d"(y), "0"(*w0), "1"(*w1), "2"(*w2) - : "cc"); - } - - -#undef ASM -#undef DO_8_TIMES -#undef ADD_OR_SUBTRACT -#undef ADDSUB2_OP -#undef ADDSUB3_OP -#undef LINMUL_OP -#undef MULADD_OP - -} - -} -#endif diff --git a/src/math/mp/mp_x86_64/mp_madd.h b/src/math/mp/mp_x86_64/mp_madd.h deleted file mode 100644 index 4c0d79931..000000000 --- a/src/math/mp/mp_x86_64/mp_madd.h +++ /dev/null @@ -1,69 +0,0 @@ -/* -* Lowest Level MPI Algorithms -* (C) 1999-2008 Jack Lloyd -* 2006 Luca Piccarreta -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MP_WORD_MULADD_H__ -#define BOTAN_MP_WORD_MULADD_H__ - -#include <botan/mp_types.h> - -#if (BOTAN_MP_WORD_BITS != 64) - #error The mp_x86_64 module requires that BOTAN_MP_WORD_BITS == 64 -#endif - -namespace Botan { - -extern "C" { - -/* -* Helper Macros for x86-64 Assembly -*/ -#define ASM(x) x "\n\t" - -/* -* Word Multiply -*/ -inline word word_madd2(word a, word b, word* c) - { - asm( - ASM("mulq %[b]") - ASM("addq %[c],%[a]") - ASM("adcq $0,%[carry]") - - : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*c) - : "0"(a), "1"(b), [c]"g"(*c) : "cc"); - - return a; - } - -/* -* Word Multiply/Add -*/ -inline word word_madd3(word a, word b, word c, word* d) - { - asm( - ASM("mulq %[b]") - - ASM("addq %[c],%[a]") - ASM("adcq $0,%[carry]") - - ASM("addq %[d],%[a]") - ASM("adcq $0,%[carry]") - - : [a]"=a"(a), [b]"=rm"(b), [carry]"=&d"(*d) - : "0"(a), "1"(b), [c]"g"(c), [d]"g"(*d) : "cc"); - - return a; - } - -#undef ASM - -} - -} - -#endif diff --git a/src/math/numbertheory/def_powm.h b/src/math/numbertheory/def_powm.h deleted file mode 100644 index 6ceee7bb6..000000000 --- a/src/math/numbertheory/def_powm.h +++ /dev/null @@ -1,63 +0,0 @@ -/* -* Modular Exponentiation -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_DEFAULT_MODEXP_H__ -#define BOTAN_DEFAULT_MODEXP_H__ - -#include <botan/pow_mod.h> -#include <botan/reducer.h> -#include <vector> - -namespace Botan { - -/** -* Fixed Window Exponentiator -*/ -class Fixed_Window_Exponentiator : public Modular_Exponentiator - { - public: - void set_exponent(const BigInt&); - void set_base(const BigInt&); - BigInt execute() const; - - Modular_Exponentiator* copy() const - { return new Fixed_Window_Exponentiator(*this); } - - Fixed_Window_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); - private: - Modular_Reducer reducer; - BigInt exp; - size_t window_bits; - std::vector<BigInt> g; - Power_Mod::Usage_Hints hints; - }; - -/** -* Montgomery Exponentiator -*/ -class Montgomery_Exponentiator : public Modular_Exponentiator - { - public: - void set_exponent(const BigInt&); - void set_base(const BigInt&); - BigInt execute() const; - - Modular_Exponentiator* copy() const - { return new Montgomery_Exponentiator(*this); } - - Montgomery_Exponentiator(const BigInt&, Power_Mod::Usage_Hints); - private: - BigInt m_exp, m_modulus, m_R_mod, m_R2_mod; - word m_mod_prime; - size_t m_mod_words, m_exp_bits, m_window_bits; - Power_Mod::Usage_Hints m_hints; - std::vector<BigInt> m_g; - }; - -} - -#endif diff --git a/src/math/numbertheory/dsa_gen.cpp b/src/math/numbertheory/dsa_gen.cpp deleted file mode 100644 index d30a08f1a..000000000 --- a/src/math/numbertheory/dsa_gen.cpp +++ /dev/null @@ -1,134 +0,0 @@ -/* -* DSA Parameter Generation -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> -#include <botan/algo_factory.h> -#include <botan/hash.h> -#include <botan/parsing.h> -#include <algorithm> -#include <memory> - -namespace Botan { - -namespace { - -/* -* Check if this size is allowed by FIPS 186-3 -*/ -bool fips186_3_valid_size(size_t pbits, size_t qbits) - { - if(qbits == 160) - return (pbits == 512 || pbits == 768 || pbits == 1024); - - if(qbits == 224) - return (pbits == 2048); - - if(qbits == 256) - return (pbits == 2048 || pbits == 3072); - - return false; - } - -} - -/* -* Attempt DSA prime generation with given seed -*/ -bool generate_dsa_primes(RandomNumberGenerator& rng, - Algorithm_Factory& af, - BigInt& p, BigInt& q, - size_t pbits, size_t qbits, - const std::vector<byte>& seed_c) - { - if(!fips186_3_valid_size(pbits, qbits)) - throw Invalid_Argument( - "FIPS 186-3 does not allow DSA domain parameters of " + - std::to_string(pbits) + "/" + std::to_string(qbits) + " bits long"); - - if(seed_c.size() * 8 < qbits) - throw Invalid_Argument( - "Generating a DSA parameter set with a " + std::to_string(qbits) + - "long q requires a seed at least as many bits long"); - - std::unique_ptr<HashFunction> hash( - af.make_hash_function("SHA-" + std::to_string(qbits))); - - const size_t HASH_SIZE = hash->output_length(); - - class Seed - { - public: - Seed(const std::vector<byte>& s) : seed(s) {} - - operator std::vector<byte>& () { return seed; } - - Seed& operator++() - { - for(size_t j = seed.size(); j > 0; --j) - if(++seed[j-1]) - break; - return (*this); - } - private: - std::vector<byte> seed; - }; - - Seed seed(seed_c); - - q.binary_decode(hash->process(seed)); - q.set_bit(qbits-1); - q.set_bit(0); - - if(!check_prime(q, rng)) - return false; - - const size_t n = (pbits-1) / (HASH_SIZE * 8), - b = (pbits-1) % (HASH_SIZE * 8); - - BigInt X; - std::vector<byte> V(HASH_SIZE * (n+1)); - - for(size_t j = 0; j != 4096; ++j) - { - for(size_t k = 0; k <= n; ++k) - { - ++seed; - hash->update(seed); - hash->final(&V[HASH_SIZE * (n-k)]); - } - - X.binary_decode(&V[HASH_SIZE - 1 - b/8], - V.size() - (HASH_SIZE - 1 - b/8)); - X.set_bit(pbits-1); - - p = X - (X % (2*q) - 1); - - if(p.bits() == pbits && check_prime(p, rng)) - return true; - } - return false; - } - -/* -* Generate DSA Primes -*/ -std::vector<byte> generate_dsa_primes(RandomNumberGenerator& rng, - Algorithm_Factory& af, - BigInt& p, BigInt& q, - size_t pbits, size_t qbits) - { - while(true) - { - std::vector<byte> seed(qbits / 8); - rng.randomize(&seed[0], seed.size()); - - if(generate_dsa_primes(rng, af, p, q, pbits, qbits, seed)) - return seed; - } - } - -} diff --git a/src/math/numbertheory/info.txt b/src/math/numbertheory/info.txt deleted file mode 100644 index 62386c3bc..000000000 --- a/src/math/numbertheory/info.txt +++ /dev/null @@ -1,35 +0,0 @@ -define BIGINT_MATH 20131128 - -load_on auto - -<header:public> -numthry.h -pow_mod.h -reducer.h -</header:public> - -<header:internal> -def_powm.h -</header:internal> - -<source> -dsa_gen.cpp -jacobi.cpp -make_prm.cpp -mp_numth.cpp -numthry.cpp -pow_mod.cpp -powm_fw.cpp -powm_mnt.cpp -primes.cpp -reducer.cpp -ressol.cpp -</source> - -<requires> -algo_factory -bigint -hash -libstate -rng -</requires> diff --git a/src/math/numbertheory/jacobi.cpp b/src/math/numbertheory/jacobi.cpp deleted file mode 100644 index fcccc80e5..000000000 --- a/src/math/numbertheory/jacobi.cpp +++ /dev/null @@ -1,53 +0,0 @@ -/* -* Jacobi Function -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> - -namespace Botan { - -/* -* Calculate the Jacobi symbol -*/ -s32bit jacobi(const BigInt& a, const BigInt& n) - { - if(a.is_negative()) - throw Invalid_Argument("jacobi: first argument must be non-negative"); - if(n.is_even() || n < 2) - throw Invalid_Argument("jacobi: second argument must be odd and > 1"); - - BigInt x = a, y = n; - s32bit J = 1; - - while(y > 1) - { - x %= y; - if(x > y / 2) - { - x = y - x; - if(y % 4 == 3) - J = -J; - } - if(x.is_zero()) - return 0; - - size_t shifts = low_zero_bits(x); - x >>= shifts; - if(shifts % 2) - { - word y_mod_8 = y % 8; - if(y_mod_8 == 3 || y_mod_8 == 5) - J = -J; - } - - if(x % 4 == 3 && y % 4 == 3) - J = -J; - std::swap(x, y); - } - return J; - } - -} diff --git a/src/math/numbertheory/make_prm.cpp b/src/math/numbertheory/make_prm.cpp deleted file mode 100644 index dc94420ab..000000000 --- a/src/math/numbertheory/make_prm.cpp +++ /dev/null @@ -1,100 +0,0 @@ -/* -* Prime Generation -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> -#include <botan/parsing.h> -#include <algorithm> - -namespace Botan { - -/* -* Generate a random prime -*/ -BigInt random_prime(RandomNumberGenerator& rng, - size_t bits, const BigInt& coprime, - size_t equiv, size_t modulo) - { - if(bits <= 1) - throw Invalid_Argument("random_prime: Can't make a prime of " + - std::to_string(bits) + " bits"); - else if(bits == 2) - return ((rng.next_byte() % 2) ? 2 : 3); - else if(bits == 3) - return ((rng.next_byte() % 2) ? 5 : 7); - else if(bits == 4) - return ((rng.next_byte() % 2) ? 11 : 13); - - if(coprime <= 0) - throw Invalid_Argument("random_prime: coprime must be > 0"); - if(modulo % 2 == 1 || modulo == 0) - throw Invalid_Argument("random_prime: Invalid modulo value"); - if(equiv >= modulo || equiv % 2 == 0) - throw Invalid_Argument("random_prime: equiv must be < modulo, and odd"); - - while(true) - { - BigInt p(rng, bits); - - // Force lowest and two top bits on - p.set_bit(bits - 1); - p.set_bit(bits - 2); - p.set_bit(0); - - if(p % modulo != equiv) - p += (modulo - p % modulo) + equiv; - - const size_t sieve_size = std::min(bits / 2, PRIME_TABLE_SIZE); - secure_vector<u16bit> sieve(sieve_size); - - for(size_t j = 0; j != sieve.size(); ++j) - sieve[j] = p % PRIMES[j]; - - size_t counter = 0; - while(true) - { - if(counter == 4096 || p.bits() > bits) - break; - - bool passes_sieve = true; - ++counter; - p += modulo; - - if(p.bits() > bits) - break; - - for(size_t j = 0; j != sieve.size(); ++j) - { - sieve[j] = (sieve[j] + modulo) % PRIMES[j]; - if(sieve[j] == 0) - passes_sieve = false; - } - - if(!passes_sieve || gcd(p - 1, coprime) != 1) - continue; - if(check_prime(p, rng)) - return p; - } - } - } - -/* -* Generate a random safe prime -*/ -BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) - { - if(bits <= 64) - throw Invalid_Argument("random_safe_prime: Can't make a prime of " + - std::to_string(bits) + " bits"); - - BigInt p; - do - p = (random_prime(rng, bits - 1) << 1) + 1; - while(!check_prime(p, rng)); - return p; - } - -} diff --git a/src/math/numbertheory/mp_numth.cpp b/src/math/numbertheory/mp_numth.cpp deleted file mode 100644 index e6826b9dd..000000000 --- a/src/math/numbertheory/mp_numth.cpp +++ /dev/null @@ -1,74 +0,0 @@ -/* -* Fused and Important MP Algorithms -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> -#include <botan/internal/mp_core.h> -#include <botan/internal/rounding.h> -#include <algorithm> - -namespace Botan { - -/* -* Square a BigInt -*/ -BigInt square(const BigInt& x) - { - const size_t x_sw = x.sig_words(); - - BigInt z(BigInt::Positive, round_up<size_t>(2*x_sw, 16)); - secure_vector<word> workspace(z.size()); - - bigint_sqr(z.mutable_data(), z.size(), - &workspace[0], - x.data(), x.size(), x_sw); - return z; - } - -/* -* Multiply-Add Operation -*/ -BigInt mul_add(const BigInt& a, const BigInt& b, const BigInt& c) - { - if(c.is_negative() || c.is_zero()) - throw Invalid_Argument("mul_add: Third argument must be > 0"); - - BigInt::Sign sign = BigInt::Positive; - if(a.sign() != b.sign()) - sign = BigInt::Negative; - - const size_t a_sw = a.sig_words(); - const size_t b_sw = b.sig_words(); - const size_t c_sw = c.sig_words(); - - BigInt r(sign, std::max(a.size() + b.size(), c_sw) + 1); - secure_vector<word> workspace(r.size()); - - bigint_mul(r.mutable_data(), r.size(), - &workspace[0], - a.data(), a.size(), a_sw, - b.data(), b.size(), b_sw); - - const size_t r_size = std::max(r.sig_words(), c_sw); - bigint_add2(r.mutable_data(), r_size, c.data(), c_sw); - return r; - } - -/* -* Subtract-Multiply Operation -*/ -BigInt sub_mul(const BigInt& a, const BigInt& b, const BigInt& c) - { - if(a.is_negative() || b.is_negative()) - throw Invalid_Argument("sub_mul: First two arguments must be >= 0"); - - BigInt r = a; - r -= b; - r *= c; - return r; - } - -} diff --git a/src/math/numbertheory/numthry.cpp b/src/math/numbertheory/numthry.cpp deleted file mode 100644 index e3c673ea5..000000000 --- a/src/math/numbertheory/numthry.cpp +++ /dev/null @@ -1,409 +0,0 @@ -/* -* Number Theory Functions -* (C) 1999-2011 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> -#include <botan/reducer.h> -#include <botan/internal/bit_ops.h> -#include <botan/internal/mp_core.h> -#include <algorithm> - -namespace Botan { - -namespace { - -/* -* Miller-Rabin Primality Tester -*/ -class MillerRabin_Test - { - public: - bool is_witness(const BigInt& nonce); - MillerRabin_Test(const BigInt& num); - private: - BigInt n, r, n_minus_1; - size_t s; - Fixed_Exponent_Power_Mod pow_mod; - Modular_Reducer reducer; - }; - -/* -* Miller-Rabin Test, as described in Handbook of Applied Cryptography -* section 4.24 -*/ -bool MillerRabin_Test::is_witness(const BigInt& a) - { - if(a < 2 || a >= n_minus_1) - throw Invalid_Argument("Bad size for nonce in Miller-Rabin test"); - - BigInt y = pow_mod(a); - if(y == 1 || y == n_minus_1) - return false; - - for(size_t i = 1; i != s; ++i) - { - y = reducer.square(y); - - if(y == 1) // found a non-trivial square root - return true; - - if(y == n_minus_1) // -1, trivial square root, so give up - return false; - } - - if(y != n_minus_1) // fails Fermat test - return true; - - return false; - } - -/* -* Miller-Rabin Constructor -*/ -MillerRabin_Test::MillerRabin_Test(const BigInt& num) - { - if(num.is_even() || num < 3) - throw Invalid_Argument("MillerRabin_Test: Invalid number for testing"); - - n = num; - n_minus_1 = n - 1; - s = low_zero_bits(n_minus_1); - r = n_minus_1 >> s; - - pow_mod = Fixed_Exponent_Power_Mod(r, n); - reducer = Modular_Reducer(n); - } - -/* -* Miller-Rabin Iterations -*/ -size_t miller_rabin_test_iterations(size_t bits, size_t level) - { - struct mapping { size_t bits; size_t verify_iter; size_t check_iter; }; - - const mapping tests[] = { - { 50, 55, 25 }, - { 100, 38, 22 }, - { 160, 32, 18 }, - { 163, 31, 17 }, - { 168, 30, 16 }, - { 177, 29, 16 }, - { 181, 28, 15 }, - { 185, 27, 15 }, - { 190, 26, 15 }, - { 195, 25, 14 }, - { 201, 24, 14 }, - { 208, 23, 14 }, - { 215, 22, 13 }, - { 222, 21, 13 }, - { 231, 20, 13 }, - { 241, 19, 12 }, - { 252, 18, 12 }, - { 264, 17, 12 }, - { 278, 16, 11 }, - { 294, 15, 10 }, - { 313, 14, 9 }, - { 334, 13, 8 }, - { 360, 12, 8 }, - { 392, 11, 7 }, - { 430, 10, 7 }, - { 479, 9, 6 }, - { 542, 8, 6 }, - { 626, 7, 5 }, - { 746, 6, 4 }, - { 926, 5, 3 }, - { 1232, 4, 2 }, - { 1853, 3, 2 }, - { 0, 0, 0 } - }; - - for(size_t i = 0; tests[i].bits; ++i) - { - if(bits <= tests[i].bits) - { - if(level >= 2) - return tests[i].verify_iter; - else if(level == 1) - return tests[i].check_iter; - else if(level == 0) - return std::max<size_t>(tests[i].check_iter / 4, 1); - } - } - - return level > 0 ? 2 : 1; // for large inputs - } - -} - -/* -* Return the number of 0 bits at the end of n -*/ -size_t low_zero_bits(const BigInt& n) - { - size_t low_zero = 0; - - if(n.is_positive() && n.is_nonzero()) - { - for(size_t i = 0; i != n.size(); ++i) - { - const word x = n.word_at(i); - - if(x) - { - low_zero += ctz(x); - break; - } - else - low_zero += BOTAN_MP_WORD_BITS; - } - } - - return low_zero; - } - -/* -* Calculate the GCD -*/ -BigInt gcd(const BigInt& a, const BigInt& b) - { - if(a.is_zero() || b.is_zero()) return 0; - if(a == 1 || b == 1) return 1; - - BigInt x = a, y = b; - x.set_sign(BigInt::Positive); - y.set_sign(BigInt::Positive); - size_t shift = std::min(low_zero_bits(x), low_zero_bits(y)); - - x >>= shift; - y >>= shift; - - while(x.is_nonzero()) - { - x >>= low_zero_bits(x); - y >>= low_zero_bits(y); - if(x >= y) { x -= y; x >>= 1; } - else { y -= x; y >>= 1; } - } - - return (y << shift); - } - -/* -* Calculate the LCM -*/ -BigInt lcm(const BigInt& a, const BigInt& b) - { - return ((a * b) / gcd(a, b)); - } - -namespace { - -/* -* If the modulus is odd, then we can avoid computing A and C. This is -* a critical path algorithm in some instances and an odd modulus is -* the common case for crypto, so worth special casing. See note 14.64 -* in Handbook of Applied Cryptography for more details. -*/ -BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) - { - BigInt u = mod, v = n; - BigInt B = 0, D = 1; - - while(u.is_nonzero()) - { - const size_t u_zero_bits = low_zero_bits(u); - u >>= u_zero_bits; - for(size_t i = 0; i != u_zero_bits; ++i) - { - if(B.is_odd()) - { B -= mod; } - B >>= 1; - } - - const size_t v_zero_bits = low_zero_bits(v); - v >>= v_zero_bits; - for(size_t i = 0; i != v_zero_bits; ++i) - { - if(D.is_odd()) - { D -= mod; } - D >>= 1; - } - - if(u >= v) { u -= v; B -= D; } - else { v -= u; D -= B; } - } - - if(v != 1) - return 0; // no modular inverse - - while(D.is_negative()) D += mod; - while(D >= mod) D -= mod; - - return D; - } - -} - -/* -* Find the Modular Inverse -*/ -BigInt inverse_mod(const BigInt& n, const BigInt& mod) - { - if(mod.is_zero()) - throw BigInt::DivideByZero(); - if(mod.is_negative() || n.is_negative()) - throw Invalid_Argument("inverse_mod: arguments must be non-negative"); - - if(n.is_zero() || (n.is_even() && mod.is_even())) - return 0; // fast fail checks - - if(mod.is_odd()) - return inverse_mod_odd_modulus(n, mod); - - BigInt u = mod, v = n; - BigInt A = 1, B = 0, C = 0, D = 1; - - while(u.is_nonzero()) - { - const size_t u_zero_bits = low_zero_bits(u); - u >>= u_zero_bits; - for(size_t i = 0; i != u_zero_bits; ++i) - { - if(A.is_odd() || B.is_odd()) - { A += n; B -= mod; } - A >>= 1; B >>= 1; - } - - const size_t v_zero_bits = low_zero_bits(v); - v >>= v_zero_bits; - for(size_t i = 0; i != v_zero_bits; ++i) - { - if(C.is_odd() || D.is_odd()) - { C += n; D -= mod; } - C >>= 1; D >>= 1; - } - - if(u >= v) { u -= v; A -= C; B -= D; } - else { v -= u; C -= A; D -= B; } - } - - if(v != 1) - return 0; // no modular inverse - - while(D.is_negative()) D += mod; - while(D >= mod) D -= mod; - - return D; - } - -word monty_inverse(word input) - { - word b = input; - word x2 = 1, x1 = 0, y2 = 0, y1 = 1; - - // First iteration, a = n+1 - word q = bigint_divop(1, 0, b); - word r = (MP_WORD_MAX - q*b) + 1; - word x = x2 - q*x1; - word y = y2 - q*y1; - - word a = b; - b = r; - x2 = x1; - x1 = x; - y2 = y1; - y1 = y; - - while(b > 0) - { - q = a / b; - r = a - q*b; - x = x2 - q*x1; - y = y2 - q*y1; - - a = b; - b = r; - x2 = x1; - x1 = x; - y2 = y1; - y1 = y; - } - - // Now invert in addition space - y2 = (MP_WORD_MAX - y2) + 1; - - return y2; - } - -/* -* Modular Exponentiation -*/ -BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) - { - Power_Mod pow_mod(mod); - - /* - * Calling set_base before set_exponent means we end up using a - * minimal window. This makes sense given that here we know that any - * precomputation is wasted. - */ - pow_mod.set_base(base); - pow_mod.set_exponent(exp); - return pow_mod.execute(); - } - -/* -* Test for primaility using Miller-Rabin -*/ -bool primality_test(const BigInt& n, - RandomNumberGenerator& rng, - size_t level) - { - if(n == 2) - return true; - if(n <= 1 || n.is_even()) - return false; - - // Fast path testing for small numbers (<= 65521) - if(n <= PRIMES[PRIME_TABLE_SIZE-1]) - { - const word num = n.word_at(0); - - for(size_t i = 0; PRIMES[i]; ++i) - { - if(num == PRIMES[i]) - return true; - if(num < PRIMES[i]) - return false; - } - - return false; - } - - if(level > 2) - level = 2; - - const size_t PREF_NONCE_BITS = 192; - - const size_t NONCE_BITS = std::min(n.bits() - 2, PREF_NONCE_BITS); - - MillerRabin_Test mr(n); - - const size_t tests = miller_rabin_test_iterations(n.bits(), level); - - BigInt nonce; - for(size_t i = 0; i != tests; ++i) - { - while(nonce < 2 || nonce >= (n-1)) - nonce.randomize(rng, NONCE_BITS); - - if(mr.is_witness(nonce)) - return false; - } - return true; - } - -} diff --git a/src/math/numbertheory/numthry.h b/src/math/numbertheory/numthry.h deleted file mode 100644 index a34d855b2..000000000 --- a/src/math/numbertheory/numthry.h +++ /dev/null @@ -1,237 +0,0 @@ -/* -* Number Theory Functions -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_NUMBER_THEORY_H__ -#define BOTAN_NUMBER_THEORY_H__ - -#include <botan/bigint.h> -#include <botan/pow_mod.h> -#include <botan/rng.h> - -namespace Botan { - -/** -* Fused multiply-add -* @param a an integer -* @param b an integer -* @param c an integer -* @return (a*b)+c -*/ -BigInt BOTAN_DLL mul_add(const BigInt& a, - const BigInt& b, - const BigInt& c); - -/** -* Fused subtract-multiply -* @param a an integer -* @param b an integer -* @param c an integer -* @return (a-b)*c -*/ -BigInt BOTAN_DLL sub_mul(const BigInt& a, - const BigInt& b, - const BigInt& c); - -/** -* Return the absolute value -* @param n an integer -* @return absolute value of n -*/ -inline BigInt abs(const BigInt& n) { return n.abs(); } - -/** -* Compute the greatest common divisor -* @param x a positive integer -* @param y a positive integer -* @return gcd(x,y) -*/ -BigInt BOTAN_DLL gcd(const BigInt& x, const BigInt& y); - -/** -* Least common multiple -* @param x a positive integer -* @param y a positive integer -* @return z, smallest integer such that z % x == 0 and z % y == 0 -*/ -BigInt BOTAN_DLL lcm(const BigInt& x, const BigInt& y); - -/** -* @param x an integer -* @return (x*x) -*/ -BigInt BOTAN_DLL square(const BigInt& x); - -/** -* Modular inversion -* @param x a positive integer -* @param modulus a positive integer -* @return y st (x*y) % modulus == 1 -*/ -BigInt BOTAN_DLL inverse_mod(const BigInt& x, - const BigInt& modulus); - -/** -* Compute the Jacobi symbol. If n is prime, this is equivalent -* to the Legendre symbol. -* @see http://mathworld.wolfram.com/JacobiSymbol.html -* -* @param a is a non-negative integer -* @param n is an odd integer > 1 -* @return (n / m) -*/ -s32bit BOTAN_DLL jacobi(const BigInt& a, - const BigInt& n); - -/** -* Modular exponentation -* @param b an integer base -* @param x a positive exponent -* @param m a positive modulus -* @return (b^x) % m -*/ -BigInt BOTAN_DLL power_mod(const BigInt& b, - const BigInt& x, - const BigInt& m); - -/** -* Compute the square root of x modulo a prime using the -* Shanks-Tonnelli algorithm -* -* @param x the input -* @param p the prime -* @return y such that (y*y)%p == x, or -1 if no such integer -*/ -BigInt BOTAN_DLL ressol(const BigInt& x, const BigInt& p); - -/* -* Compute -input^-1 mod 2^MP_WORD_BITS. Returns zero if input -* is even. If input is odd, input and 2^n are relatively prime -* and an inverse exists. -*/ -word BOTAN_DLL monty_inverse(word input); - -/** -* @param x a positive integer -* @return count of the zero bits in x, or, equivalently, the largest -* value of n such that 2^n divides x evenly. Returns zero if -* n is less than or equal to zero. -*/ -size_t BOTAN_DLL low_zero_bits(const BigInt& x); - -/** -* Primality Testing -* @param n a positive integer to test for primality -* @param rng a random number generator -* @param level how hard to test -* @return true if all primality tests passed, otherwise false -*/ -bool BOTAN_DLL primality_test(const BigInt& n, - RandomNumberGenerator& rng, - size_t level = 1); - -/** -* Quickly check for primality -* @param n a positive integer to test for primality -* @param rng a random number generator -* @return true if all primality tests passed, otherwise false -*/ -inline bool quick_check_prime(const BigInt& n, RandomNumberGenerator& rng) - { return primality_test(n, rng, 0); } - -/** -* Check for primality -* @param n a positive integer to test for primality -* @param rng a random number generator -* @return true if all primality tests passed, otherwise false -*/ -inline bool check_prime(const BigInt& n, RandomNumberGenerator& rng) - { return primality_test(n, rng, 1); } - -/** -* Verify primality - this function is slow but useful if you want to -* ensure that a possibly malicious entity did not provide you with -* something that 'looks like' a prime -* @param n a positive integer to test for primality -* @param rng a random number generator -* @return true if all primality tests passed, otherwise false -*/ -inline bool verify_prime(const BigInt& n, RandomNumberGenerator& rng) - { return primality_test(n, rng, 2); } - -/** -* Randomly generate a prime -* @param rng a random number generator -* @param bits how large the resulting prime should be in bits -* @param coprime a positive integer the result should be coprime to -* @param equiv a non-negative number that the result should be - equivalent to modulo equiv_mod -* @param equiv_mod the modulus equiv should be checked against -* @return random prime with the specified criteria -*/ -BigInt BOTAN_DLL random_prime(RandomNumberGenerator& rng, - size_t bits, const BigInt& coprime = 1, - size_t equiv = 1, size_t equiv_mod = 2); - -/** -* Return a 'safe' prime, of the form p=2*q+1 with q prime -* @param rng a random number generator -* @param bits is how long the resulting prime should be -* @return prime randomly chosen from safe primes of length bits -*/ -BigInt BOTAN_DLL random_safe_prime(RandomNumberGenerator& rng, - size_t bits); - -class Algorithm_Factory; - -/** -* Generate DSA parameters using the FIPS 186 kosherizer -* @param rng a random number generator -* @param af an algorithm factory -* @param p_out where the prime p will be stored -* @param q_out where the prime q will be stored -* @param pbits how long p will be in bits -* @param qbits how long q will be in bits -* @return random seed used to generate this parameter set -*/ -std::vector<byte> BOTAN_DLL -generate_dsa_primes(RandomNumberGenerator& rng, - Algorithm_Factory& af, - BigInt& p_out, BigInt& q_out, - size_t pbits, size_t qbits); - -/** -* Generate DSA parameters using the FIPS 186 kosherizer -* @param rng a random number generator -* @param af an algorithm factory -* @param p_out where the prime p will be stored -* @param q_out where the prime q will be stored -* @param pbits how long p will be in bits -* @param qbits how long q will be in bits -* @param seed the seed used to generate the parameters -* @return true if seed generated a valid DSA parameter set, otherwise - false. p_out and q_out are only valid if true was returned. -*/ -bool BOTAN_DLL -generate_dsa_primes(RandomNumberGenerator& rng, - Algorithm_Factory& af, - BigInt& p_out, BigInt& q_out, - size_t pbits, size_t qbits, - const std::vector<byte>& seed); - -/** -* The size of the PRIMES[] array -*/ -const size_t PRIME_TABLE_SIZE = 6541; - -/** -* A const array of all primes less than 65535 -*/ -extern const u16bit BOTAN_DLL PRIMES[]; - -} - -#endif diff --git a/src/math/numbertheory/pow_mod.cpp b/src/math/numbertheory/pow_mod.cpp deleted file mode 100644 index c7d7fe70e..000000000 --- a/src/math/numbertheory/pow_mod.cpp +++ /dev/null @@ -1,211 +0,0 @@ -/* -* Modular Exponentiation Proxy -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/pow_mod.h> -#include <botan/libstate.h> -#include <botan/engine.h> - -namespace Botan { - -/* -* Power_Mod Constructor -*/ -Power_Mod::Power_Mod(const BigInt& n, Usage_Hints hints) - { - core = nullptr; - set_modulus(n, hints); - } - -/* -* Power_Mod Copy Constructor -*/ -Power_Mod::Power_Mod(const Power_Mod& other) - { - core = nullptr; - if(other.core) - core = other.core->copy(); - } - -/* -* Power_Mod Assignment Operator -*/ -Power_Mod& Power_Mod::operator=(const Power_Mod& other) - { - delete core; - core = nullptr; - if(other.core) - core = other.core->copy(); - return (*this); - } - -/* -* Power_Mod Destructor -*/ -Power_Mod::~Power_Mod() - { - delete core; - } - -/* -* Set the modulus -*/ -void Power_Mod::set_modulus(const BigInt& n, Usage_Hints hints) const - { - delete core; - core = nullptr; - - if(n != 0) - { - Algorithm_Factory::Engine_Iterator i(global_state().algorithm_factory()); - - while(const Engine* engine = i.next()) - { - core = engine->mod_exp(n, hints); - - if(core) - break; - } - - if(!core) - throw Lookup_Error("Power_Mod: Unable to find a working engine"); - } - } - -/* -* Set the base -*/ -void Power_Mod::set_base(const BigInt& b) const - { - if(b.is_zero() || b.is_negative()) - throw Invalid_Argument("Power_Mod::set_base: arg must be > 0"); - - if(!core) - throw Internal_Error("Power_Mod::set_base: core was NULL"); - core->set_base(b); - } - -/* -* Set the exponent -*/ -void Power_Mod::set_exponent(const BigInt& e) const - { - if(e.is_negative()) - throw Invalid_Argument("Power_Mod::set_exponent: arg must be > 0"); - - if(!core) - throw Internal_Error("Power_Mod::set_exponent: core was NULL"); - core->set_exponent(e); - } - -/* -* Compute the result -*/ -BigInt Power_Mod::execute() const - { - if(!core) - throw Internal_Error("Power_Mod::execute: core was NULL"); - return core->execute(); - } - -/* -* Try to choose a good window size -*/ -size_t Power_Mod::window_bits(size_t exp_bits, size_t, - Power_Mod::Usage_Hints hints) - { - static const size_t wsize[][2] = { - { 1434, 7 }, - { 539, 6 }, - { 197, 4 }, - { 70, 3 }, - { 25, 2 }, - { 0, 0 } - }; - - size_t window_bits = 1; - - if(exp_bits) - { - for(size_t j = 0; wsize[j][0]; ++j) - { - if(exp_bits >= wsize[j][0]) - { - window_bits += wsize[j][1]; - break; - } - } - } - - if(hints & Power_Mod::BASE_IS_FIXED) - window_bits += 2; - if(hints & Power_Mod::EXP_IS_LARGE) - ++window_bits; - - return window_bits; - } - -namespace { - -/* -* Choose potentially useful hints -*/ -Power_Mod::Usage_Hints choose_base_hints(const BigInt& b, const BigInt& n) - { - if(b == 2) - return Power_Mod::Usage_Hints(Power_Mod::BASE_IS_2 | - Power_Mod::BASE_IS_SMALL); - - const size_t b_bits = b.bits(); - const size_t n_bits = n.bits(); - - if(b_bits < n_bits / 32) - return Power_Mod::BASE_IS_SMALL; - if(b_bits > n_bits / 4) - return Power_Mod::BASE_IS_LARGE; - - return Power_Mod::NO_HINTS; - } - -/* -* Choose potentially useful hints -*/ -Power_Mod::Usage_Hints choose_exp_hints(const BigInt& e, const BigInt& n) - { - const size_t e_bits = e.bits(); - const size_t n_bits = n.bits(); - - if(e_bits < n_bits / 32) - return Power_Mod::BASE_IS_SMALL; - if(e_bits > n_bits / 4) - return Power_Mod::BASE_IS_LARGE; - return Power_Mod::NO_HINTS; - } - -} - -/* -* Fixed_Exponent_Power_Mod Constructor -*/ -Fixed_Exponent_Power_Mod::Fixed_Exponent_Power_Mod(const BigInt& e, - const BigInt& n, - Usage_Hints hints) : - Power_Mod(n, Usage_Hints(hints | EXP_IS_FIXED | choose_exp_hints(e, n))) - { - set_exponent(e); - } - -/* -* Fixed_Base_Power_Mod Constructor -*/ -Fixed_Base_Power_Mod::Fixed_Base_Power_Mod(const BigInt& b, const BigInt& n, - Usage_Hints hints) : - Power_Mod(n, Usage_Hints(hints | BASE_IS_FIXED | choose_base_hints(b, n))) - { - set_base(b); - } - -} diff --git a/src/math/numbertheory/pow_mod.h b/src/math/numbertheory/pow_mod.h deleted file mode 100644 index b78510793..000000000 --- a/src/math/numbertheory/pow_mod.h +++ /dev/null @@ -1,104 +0,0 @@ -/* -* Modular Exponentiator -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_POWER_MOD_H__ -#define BOTAN_POWER_MOD_H__ - -#include <botan/bigint.h> - -namespace Botan { - -/** -* Modular Exponentiator Interface -*/ -class BOTAN_DLL Modular_Exponentiator - { - public: - virtual void set_base(const BigInt&) = 0; - virtual void set_exponent(const BigInt&) = 0; - virtual BigInt execute() const = 0; - virtual Modular_Exponentiator* copy() const = 0; - virtual ~Modular_Exponentiator() {} - }; - -/** -* Modular Exponentiator Proxy -*/ -class BOTAN_DLL Power_Mod - { - public: - - enum Usage_Hints { - NO_HINTS = 0x0000, - - BASE_IS_FIXED = 0x0001, - BASE_IS_SMALL = 0x0002, - BASE_IS_LARGE = 0x0004, - BASE_IS_2 = 0x0008, - - EXP_IS_FIXED = 0x0100, - EXP_IS_SMALL = 0x0200, - EXP_IS_LARGE = 0x0400 - }; - - /* - * Try to choose a good window size - */ - static size_t window_bits(size_t exp_bits, size_t base_bits, - Power_Mod::Usage_Hints hints); - - void set_modulus(const BigInt&, Usage_Hints = NO_HINTS) const; - void set_base(const BigInt&) const; - void set_exponent(const BigInt&) const; - - BigInt execute() const; - - Power_Mod& operator=(const Power_Mod&); - - Power_Mod(const BigInt& = 0, Usage_Hints = NO_HINTS); - Power_Mod(const Power_Mod&); - virtual ~Power_Mod(); - private: - mutable Modular_Exponentiator* core; - Usage_Hints hints; - }; - -/** -* Fixed Exponent Modular Exponentiator Proxy -*/ -class BOTAN_DLL Fixed_Exponent_Power_Mod : public Power_Mod - { - public: - BigInt operator()(const BigInt& b) const - { set_base(b); return execute(); } - - Fixed_Exponent_Power_Mod() {} - - Fixed_Exponent_Power_Mod(const BigInt& exponent, - const BigInt& modulus, - Usage_Hints hints = NO_HINTS); - }; - -/** -* Fixed Base Modular Exponentiator Proxy -*/ -class BOTAN_DLL Fixed_Base_Power_Mod : public Power_Mod - { - public: - BigInt operator()(const BigInt& e) const - { set_exponent(e); return execute(); } - - Fixed_Base_Power_Mod() {} - - Fixed_Base_Power_Mod(const BigInt& base, - const BigInt& modulus, - Usage_Hints hints = NO_HINTS); - }; - -} - -#endif diff --git a/src/math/numbertheory/powm_fw.cpp b/src/math/numbertheory/powm_fw.cpp deleted file mode 100644 index 16a48a5b0..000000000 --- a/src/math/numbertheory/powm_fw.cpp +++ /dev/null @@ -1,69 +0,0 @@ -/* -* Fixed Window Exponentiation -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/def_powm.h> -#include <botan/numthry.h> -#include <vector> - -namespace Botan { - -/* -* Set the exponent -*/ -void Fixed_Window_Exponentiator::set_exponent(const BigInt& e) - { - exp = e; - } - -/* -* Set the base -*/ -void Fixed_Window_Exponentiator::set_base(const BigInt& base) - { - window_bits = Power_Mod::window_bits(exp.bits(), base.bits(), hints); - - g.resize((1 << window_bits)); - g[0] = 1; - g[1] = base; - - for(size_t i = 2; i != g.size(); ++i) - g[i] = reducer.multiply(g[i-1], g[0]); - } - -/* -* Compute the result -*/ -BigInt Fixed_Window_Exponentiator::execute() const - { - const size_t exp_nibbles = (exp.bits() + window_bits - 1) / window_bits; - - BigInt x = 1; - - for(size_t i = exp_nibbles; i > 0; --i) - { - for(size_t j = 0; j != window_bits; ++j) - x = reducer.square(x); - - const u32bit nibble = exp.get_substring(window_bits*(i-1), window_bits); - - x = reducer.multiply(x, g[nibble]); - } - return x; - } - -/* -* Fixed_Window_Exponentiator Constructor -*/ -Fixed_Window_Exponentiator::Fixed_Window_Exponentiator(const BigInt& n, - Power_Mod::Usage_Hints hints) - { - reducer = Modular_Reducer(n); - this->hints = hints; - window_bits = 0; - } - -} diff --git a/src/math/numbertheory/powm_mnt.cpp b/src/math/numbertheory/powm_mnt.cpp deleted file mode 100644 index a3eac1f83..000000000 --- a/src/math/numbertheory/powm_mnt.cpp +++ /dev/null @@ -1,142 +0,0 @@ -/* -* Montgomery Exponentiation -* (C) 1999-2010,2012 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/internal/def_powm.h> -#include <botan/numthry.h> -#include <botan/internal/mp_core.h> - -namespace Botan { - -/* -* Set the exponent -*/ -void Montgomery_Exponentiator::set_exponent(const BigInt& exp) - { - m_exp = exp; - m_exp_bits = exp.bits(); - } - -/* -* Set the base -*/ -void Montgomery_Exponentiator::set_base(const BigInt& base) - { - m_window_bits = Power_Mod::window_bits(m_exp.bits(), base.bits(), m_hints); - - m_g.resize((1 << m_window_bits)); - - BigInt z(BigInt::Positive, 2 * (m_mod_words + 1)); - secure_vector<word> workspace(z.size()); - - m_g[0] = 1; - - bigint_monty_mul(z.mutable_data(), z.size(), - m_g[0].data(), m_g[0].size(), m_g[0].sig_words(), - m_R2_mod.data(), m_R2_mod.size(), m_R2_mod.sig_words(), - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - m_g[0] = z; - - m_g[1] = (base >= m_modulus) ? (base % m_modulus) : base; - - bigint_monty_mul(z.mutable_data(), z.size(), - m_g[1].data(), m_g[1].size(), m_g[1].sig_words(), - m_R2_mod.data(), m_R2_mod.size(), m_R2_mod.sig_words(), - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - m_g[1] = z; - - const BigInt& x = m_g[1]; - const size_t x_sig = x.sig_words(); - - for(size_t i = 2; i != m_g.size(); ++i) - { - const BigInt& y = m_g[i-1]; - const size_t y_sig = y.sig_words(); - - bigint_monty_mul(z.mutable_data(), z.size(), - x.data(), x.size(), x_sig, - y.data(), y.size(), y_sig, - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - m_g[i] = z; - } - } - -/* -* Compute the result -*/ -BigInt Montgomery_Exponentiator::execute() const - { - const size_t exp_nibbles = (m_exp_bits + m_window_bits - 1) / m_window_bits; - - BigInt x = m_R_mod; - - const size_t z_size = 2*(m_mod_words + 1); - - BigInt z(BigInt::Positive, z_size); - secure_vector<word> workspace(z_size); - - for(size_t i = exp_nibbles; i > 0; --i) - { - for(size_t k = 0; k != m_window_bits; ++k) - { - bigint_monty_sqr(z.mutable_data(), z_size, - x.data(), x.size(), x.sig_words(), - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - x = z; - } - - const u32bit nibble = m_exp.get_substring(m_window_bits*(i-1), m_window_bits); - - const BigInt& y = m_g[nibble]; - - bigint_monty_mul(z.mutable_data(), z_size, - x.data(), x.size(), x.sig_words(), - y.data(), y.size(), y.sig_words(), - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - x = z; - } - - x.grow_to(2*m_mod_words + 1); - - bigint_monty_redc(x.mutable_data(), - m_modulus.data(), m_mod_words, m_mod_prime, - &workspace[0]); - - return x; - } - -/* -* Montgomery_Exponentiator Constructor -*/ -Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod, - Power_Mod::Usage_Hints hints) : - m_modulus(mod), - m_mod_words(m_modulus.sig_words()), - m_window_bits(1), - m_hints(hints) - { - // Montgomery reduction only works for positive odd moduli - if(!m_modulus.is_positive() || m_modulus.is_even()) - throw Invalid_Argument("Montgomery_Exponentiator: invalid modulus"); - - m_mod_prime = monty_inverse(mod.word_at(0)); - - const BigInt r = BigInt::power_of_2(m_mod_words * BOTAN_MP_WORD_BITS); - m_R_mod = r % m_modulus; - m_R2_mod = (m_R_mod * m_R_mod) % m_modulus; - } - -} diff --git a/src/math/numbertheory/primes.cpp b/src/math/numbertheory/primes.cpp deleted file mode 100644 index a0c0f0093..000000000 --- a/src/math/numbertheory/primes.cpp +++ /dev/null @@ -1,609 +0,0 @@ -/* -* Small Primes Table -* (C) 1999-2007 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> - -namespace Botan { - -const u16bit PRIMES[PRIME_TABLE_SIZE+1] = { - 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, - 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, - 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, - 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, - 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, - 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, - 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, - 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, - 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, - 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, - 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, - 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, - 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, - 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, - 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, - 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, - 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, - 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, - 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, - 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, - 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, - 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, - 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, - 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, - 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, - 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, - 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, - 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, - 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, - 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, - 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, - 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, - 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, - 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, - 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, - 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, - 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, - 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, - 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, - 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, - 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, - 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, - 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, - 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, - 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, - 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, - 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, - 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, - 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, - 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, - 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, - 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, - 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, - 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, - 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, - 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, - 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, - 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, - 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, - 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, - 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, - 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, - 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, - 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, - 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, - 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, - 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, - 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, - 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, - 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, - 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, - 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, - 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, - 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, - 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, - 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, - 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, - 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, - 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, - 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, - 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, - 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, - 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, - 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, - 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, - 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, - 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, - 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, - 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, - 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, - 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, - 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, - 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, - 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, - 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, - 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, - 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, - 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, - 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, - 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, - 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, - 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, - 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, - 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, - 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, - 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, - 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, - 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, - 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, - 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, - 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, - 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, -10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, -10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, -10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, -10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, -10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, -10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, -10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, -10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, -10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, -10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, -11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, -11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, -11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, -11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, -11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, -11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, -11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, -11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, -11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, -12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, -12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, -12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, -12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, -12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, -12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, -12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, -12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, -12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, -12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, -13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, -13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, -13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, -13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, -13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, -13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, -13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, -13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, -13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, -13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, -14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, -14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, -14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, -14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, -14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, -14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, -14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, -14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, -14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, -15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, -15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, -15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, -15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, -15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, -15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, -15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, -15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, -15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, -15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, -16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, -16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, -16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, -16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, -16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, -16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, -16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, -16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, -16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, -17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, -17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, -17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, -17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, -17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, -17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, -17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, -17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, -17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, -18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, -18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, -18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, -18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, -18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, -18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, -18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, -18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, -18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, -19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, -19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, -19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, -19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, -19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, -19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, -19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, -19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, -19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, -20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, -20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, -20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, -20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, -20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, -20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, -20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, -20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, -20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, -21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, -21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, -21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, -21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, -21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, -21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, -21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, -21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, -21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, -22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, -22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, -22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, -22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, -22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, -22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, -22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, -22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, -22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, -23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, -23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, -23189, 23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, -23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, -23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, -23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, -23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, -23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, -23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, -23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 24043, -24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, -24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, -24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, -24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, -24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, -24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, -24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, -24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, -25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, -25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, -25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, -25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, -25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, -25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, -25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, -25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, -25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, -26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, -26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, -26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, -26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, -26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, -26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, -26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, -26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, -26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, -26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, -27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 27239, 27241, -27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361, 27367, -27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, -27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, -27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, -27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, -27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, -27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, -28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, -28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, -28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, -28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, -28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, -28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, -28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, -28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, -28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, -29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, -29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, -29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, -29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, -29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, -29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, -29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, -29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, -30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, -30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, -30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, -30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, -30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, -30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, -30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, -30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, -30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, -31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, -31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, -31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, -31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, -31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, -31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723, -31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, -31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, -32009, 32027, 32029, 32051, 32057, 32059, 32063, 32069, 32077, 32083, 32089, -32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, -32213, 32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, -32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, -32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, -32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, -32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, -32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, -32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, -32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 33029, 33037, 33049, -33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, -33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, -33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, -33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, -33521, 33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, -33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, -33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, -33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, -33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 34039, -34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, -34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297, -34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, -34403, 34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, -34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, -34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, -34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, -34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, -34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 35089, -35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, -35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317, 35323, -35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, -35447, 35449, 35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, -35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, -35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, -35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, -35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, -36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, -36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, -36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389, 36433, -36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, -36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, -36643, 36653, 36671, 36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, -36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, -36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, -36931, 36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, -37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, -37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, -37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, -37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517, -37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, -37607, 37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, -37747, 37781, 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, -37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, -37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, -38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261, -38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, -38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, -38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, -38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, -38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, -38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, -38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, -39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, -39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, -39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, -39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, -39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, -39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, -39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, -39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, -40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, -40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, -40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, -40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, -40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, -40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, -40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, -40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993, -41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, -41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, -41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, -41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411, 41413, 41443, -41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, -41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641, 41647, -41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, -41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, -41897, 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, -41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083, -42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197, -42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 42293, 42299, 42307, -42323, 42331, 42337, 42349, 42359, 42373, 42379, 42391, 42397, 42403, 42407, -42409, 42433, 42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, -42491, 42499, 42509, 42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, -42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701, 42703, 42709, 42719, -42727, 42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, -42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, -42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, -43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, -43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, -43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481, 43487, -43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, -43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, -43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, -43889, 43891, 43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, -43991, 43997, 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, -44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, -44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, -44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 44453, -44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 44543, 44549, -44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, -44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, -44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, -44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, -45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, -45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, -45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, -45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, -45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, -45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, -45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, -45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, -46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, -46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, -46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, -46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, -46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, -46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, -46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, -46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017, -47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, -47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, -47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, -47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, -47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, -47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, -47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, -47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, -47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, -48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, -48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, -48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, -48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, -48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, -48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, -48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, -48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, -49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, -49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, -49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, -49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, -49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, -49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, -49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, -49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, -49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, -50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, -50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, -50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 50383, -50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, -50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, -50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789, -50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, -50929, 50951, 50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 51047, -51059, 51061, 51071, 51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, -51197, 51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, -51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, -51421, 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, -51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, -51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713, -51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817, 51827, 51829, -51839, 51853, 51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 51941, -51949, 51971, 51973, 51977, 51991, 52009, 52021, 52027, 52051, 52057, 52067, -52069, 52081, 52103, 52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, -52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, -52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, -52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, -52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, -52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, -52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, -52957, 52963, 52967, 52973, 52981, 52999, 53003, 53017, 53047, 53051, 53069, -53077, 53087, 53089, 53093, 53101, 53113, 53117, 53129, 53147, 53149, 53161, -53171, 53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, -53281, 53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381, 53401, 53407, -53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, -53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, -53653, 53657, 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, -53783, 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891, -53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 54001, -54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, -54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 54287, 54293, -54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, -54409, 54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, -54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, -54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, -54721, 54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, -54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, -54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, -55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, -55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 55339, 55343, -55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, -55511, 55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621, 55631, -55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691, 55697, 55711, 55717, -55721, 55733, 55763, 55787, 55793, 55799, 55807, 55813, 55817, 55819, 55823, -55829, 55837, 55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921, 55927, -55931, 55933, 55949, 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053, -56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149, 56167, 56171, -56179, 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267, 56269, 56299, -56311, 56333, 56359, 56369, 56377, 56383, 56393, 56401, 56417, 56431, 56437, -56443, 56453, 56467, 56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519, -56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629, 56633, -56659, 56663, 56671, 56681, 56687, 56701, 56711, 56713, 56731, 56737, 56747, -56767, 56773, 56779, 56783, 56807, 56809, 56813, 56821, 56827, 56843, 56857, -56873, 56891, 56893, 56897, 56909, 56911, 56921, 56923, 56929, 56941, 56951, -56957, 56963, 56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073, -57077, 57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149, 57163, 57173, -57179, 57191, 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269, 57271, -57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389, -57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503, 57527, 57529, 57557, -57559, 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667, 57679, -57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737, 57751, 57773, 57781, -57787, 57791, 57793, 57803, 57809, 57829, 57839, 57847, 57853, 57859, 57881, -57899, 57901, 57917, 57923, 57943, 57947, 57973, 57977, 57991, 58013, 58027, -58031, 58043, 58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129, -58147, 58151, 58153, 58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, -58229, 58231, 58237, 58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367, -58369, 58379, 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441, 58451, -58453, 58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, -58603, 58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711, 58727, -58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831, 58889, 58897, 58901, -58907, 58909, 58913, 58921, 58937, 58943, 58963, 58967, 58979, 58991, 58997, -59009, 59011, 59021, 59023, 59029, 59051, 59053, 59063, 59069, 59077, 59083, -59093, 59107, 59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197, -59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333, -59341, 59351, 59357, 59359, 59369, 59377, 59387, 59393, 59399, 59407, 59417, -59419, 59441, 59443, 59447, 59453, 59467, 59471, 59473, 59497, 59509, 59513, -59539, 59557, 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, -59659, 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743, 59747, -59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863, 59879, 59887, 59921, -59929, 59951, 59957, 59971, 59981, 59999, 60013, 60017, 60029, 60037, 60041, -60077, 60083, 60089, 60091, 60101, 60103, 60107, 60127, 60133, 60139, 60149, -60161, 60167, 60169, 60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289, -60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397, 60413, 60427, -60443, 60449, 60457, 60493, 60497, 60509, 60521, 60527, 60539, 60589, 60601, -60607, 60611, 60617, 60623, 60631, 60637, 60647, 60649, 60659, 60661, 60679, -60689, 60703, 60719, 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779, -60793, 60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913, 60917, -60919, 60923, 60937, 60943, 60953, 60961, 61001, 61007, 61027, 61031, 61043, -61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151, 61153, 61169, 61211, -61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 61333, 61339, 61343, -61357, 61363, 61379, 61381, 61403, 61409, 61417, 61441, 61463, 61469, 61471, -61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553, 61559, 61561, -61583, 61603, 61609, 61613, 61627, 61631, 61637, 61643, 61651, 61657, 61667, -61673, 61681, 61687, 61703, 61717, 61723, 61729, 61751, 61757, 61781, 61813, -61819, 61837, 61843, 61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, -61967, 61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047, 62053, -62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, -62189, 62191, 62201, 62207, 62213, 62219, 62233, 62273, 62297, 62299, 62303, -62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417, 62423, 62459, 62467, -62473, 62477, 62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581, -62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 62659, 62683, 62687, -62701, 62723, 62731, 62743, 62753, 62761, 62773, 62791, 62801, 62819, 62827, -62851, 62861, 62869, 62873, 62897, 62903, 62921, 62927, 62929, 62939, 62969, -62971, 62981, 62983, 62987, 62989, 63029, 63031, 63059, 63067, 63073, 63079, -63097, 63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211, 63241, -63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353, -63361, 63367, 63377, 63389, 63391, 63397, 63409, 63419, 63421, 63439, 63443, -63463, 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, -63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649, -63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719, 63727, 63737, -63743, 63761, 63773, 63781, 63793, 63799, 63803, 63809, 63823, 63839, 63841, -63853, 63857, 63863, 63901, 63907, 63913, 63929, 63949, 63977, 63997, 64007, -64013, 64019, 64033, 64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, -64153, 64157, 64171, 64187, 64189, 64217, 64223, 64231, 64237, 64271, 64279, -64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381, 64399, 64403, 64433, -64439, 64451, 64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579, -64591, 64601, 64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667, 64679, -64693, 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849, -64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 64937, 64951, -64969, 64997, 65003, 65011, 65027, 65029, 65033, 65053, 65063, 65071, 65089, -65099, 65101, 65111, 65119, 65123, 65129, 65141, 65147, 65167, 65171, 65173, -65179, 65183, 65203, 65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, -65323, 65327, 65353, 65357, 65371, 65381, 65393, 65407, 65413, 65419, 65423, -65437, 65447, 65449, 65479, 65497, 65519, 65521, 0 }; - -} diff --git a/src/math/numbertheory/reducer.cpp b/src/math/numbertheory/reducer.cpp deleted file mode 100644 index 8e8951c46..000000000 --- a/src/math/numbertheory/reducer.cpp +++ /dev/null @@ -1,81 +0,0 @@ -/* -* Modular Reducer -* (C) 1999-2011 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/reducer.h> -#include <botan/internal/mp_core.h> - -namespace Botan { - -/* -* Modular_Reducer Constructor -*/ -Modular_Reducer::Modular_Reducer(const BigInt& mod) - { - if(mod <= 0) - throw Invalid_Argument("Modular_Reducer: modulus must be positive"); - - modulus = mod; - mod_words = modulus.sig_words(); - - modulus_2 = Botan::square(modulus); - - mu = BigInt::power_of_2(2 * MP_WORD_BITS * mod_words) / modulus; - } - -/* -* Barrett Reduction -*/ -BigInt Modular_Reducer::reduce(const BigInt& x) const - { - if(mod_words == 0) - throw Invalid_State("Modular_Reducer: Never initalized"); - - if(x.cmp(modulus, false) < 0) - { - if(x.is_negative()) - return x + modulus; // make positive - return x; - } - else if(x.cmp(modulus_2, false) < 0) - { - BigInt t1 = x; - t1.set_sign(BigInt::Positive); - t1 >>= (MP_WORD_BITS * (mod_words - 1)); - t1 *= mu; - - t1 >>= (MP_WORD_BITS * (mod_words + 1)); - t1 *= modulus; - - t1.mask_bits(MP_WORD_BITS * (mod_words + 1)); - - BigInt t2 = x; - t2.set_sign(BigInt::Positive); - t2.mask_bits(MP_WORD_BITS * (mod_words + 1)); - - t2 -= t1; - - if(t2.is_negative()) - { - t2 += BigInt::power_of_2(MP_WORD_BITS * (mod_words + 1)); - } - - while(t2 >= modulus) - t2 -= modulus; - - if(x.is_positive()) - return t2; - else - return (modulus - t2); - } - else - { - // too big, fall back to normal division - return (x % modulus); - } - } - -} diff --git a/src/math/numbertheory/reducer.h b/src/math/numbertheory/reducer.h deleted file mode 100644 index 76712074c..000000000 --- a/src/math/numbertheory/reducer.h +++ /dev/null @@ -1,61 +0,0 @@ -/* -* Modular Reducer -* (C) 1999-2010 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#ifndef BOTAN_MODULAR_REDUCER_H__ -#define BOTAN_MODULAR_REDUCER_H__ - -#include <botan/numthry.h> - -namespace Botan { - -/** -* Modular Reducer (using Barrett's technique) -*/ -class BOTAN_DLL Modular_Reducer - { - public: - const BigInt& get_modulus() const { return modulus; } - - BigInt reduce(const BigInt& x) const; - - /** - * Multiply mod p - * @param x - * @param y - * @return (x * y) % p - */ - BigInt multiply(const BigInt& x, const BigInt& y) const - { return reduce(x * y); } - - /** - * Square mod p - * @param x - * @return (x * x) % p - */ - BigInt square(const BigInt& x) const - { return reduce(Botan::square(x)); } - - /** - * Cube mod p - * @param x - * @return (x * x * x) % p - */ - BigInt cube(const BigInt& x) const - { return multiply(x, this->square(x)); } - - bool initialized() const { return (mod_words != 0); } - - Modular_Reducer() { mod_words = 0; } - Modular_Reducer(const BigInt& mod); - private: - BigInt modulus, modulus_2, mu; - size_t mod_words; - }; - -} - -#endif diff --git a/src/math/numbertheory/ressol.cpp b/src/math/numbertheory/ressol.cpp deleted file mode 100644 index 9c48187f4..000000000 --- a/src/math/numbertheory/ressol.cpp +++ /dev/null @@ -1,81 +0,0 @@ -/* -* Shanks-Tonnelli (RESSOL) -* (C) 2007-2008 Falko Strenzke, FlexSecure GmbH -* (C) 2008 Jack Lloyd -* -* Distributed under the terms of the Botan license -*/ - -#include <botan/numthry.h> -#include <botan/reducer.h> - -namespace Botan { - -/* -* Shanks-Tonnelli algorithm -*/ -BigInt ressol(const BigInt& a, const BigInt& p) - { - if(a < 0) - throw Invalid_Argument("ressol(): a to solve for must be positive"); - if(p <= 1) - throw Invalid_Argument("ressol(): prime must be > 1"); - - if(a == 0) - return 0; - if(p == 2) - return a; - - if(jacobi(a, p) != 1) // not a quadratic residue - return -BigInt(1); - - if(p % 4 == 3) - return power_mod(a, ((p+1) >> 2), p); - - size_t s = low_zero_bits(p - 1); - BigInt q = p >> s; - - q -= 1; - q >>= 1; - - Modular_Reducer mod_p(p); - - BigInt r = power_mod(a, q, p); - BigInt n = mod_p.multiply(a, mod_p.square(r)); - r = mod_p.multiply(r, a); - - if(n == 1) - return r; - - // find random non quadratic residue z - BigInt z = 2; - while(jacobi(z, p) == 1) // while z quadratic residue - ++z; - - BigInt c = power_mod(z, (q << 1) + 1, p); - - while(n > 1) - { - q = n; - - size_t i = 0; - while(q != 1) - { - q = mod_p.square(q); - ++i; - } - - if(s <= i) - return -BigInt(1); - - c = power_mod(c, BigInt::power_of_2(s-i-1), p); - r = mod_p.multiply(r, c); - c = mod_p.square(c); - n = mod_p.multiply(n, c); - s = i; - } - - return r; - } - -} |