aboutsummaryrefslogtreecommitdiffstats
path: root/src/math/numbertheory
diff options
context:
space:
mode:
authorlloyd <[email protected]>2014-01-01 21:20:55 +0000
committerlloyd <[email protected]>2014-01-01 21:20:55 +0000
commit197dc467dec28a04c3b2f30da7cef122dfbb13e9 (patch)
treecdbd3ddaec051c72f0a757db461973d90c37b97a /src/math/numbertheory
parent62faac373c07cfe10bc8c309e89ebdd30d8e5eaa (diff)
Shuffle things around. Add NIST X.509 test to build.
Diffstat (limited to 'src/math/numbertheory')
-rw-r--r--src/math/numbertheory/def_powm.h63
-rw-r--r--src/math/numbertheory/dsa_gen.cpp134
-rw-r--r--src/math/numbertheory/info.txt35
-rw-r--r--src/math/numbertheory/jacobi.cpp53
-rw-r--r--src/math/numbertheory/make_prm.cpp100
-rw-r--r--src/math/numbertheory/mp_numth.cpp74
-rw-r--r--src/math/numbertheory/numthry.cpp409
-rw-r--r--src/math/numbertheory/numthry.h237
-rw-r--r--src/math/numbertheory/pow_mod.cpp211
-rw-r--r--src/math/numbertheory/pow_mod.h104
-rw-r--r--src/math/numbertheory/powm_fw.cpp69
-rw-r--r--src/math/numbertheory/powm_mnt.cpp142
-rw-r--r--src/math/numbertheory/primes.cpp609
-rw-r--r--src/math/numbertheory/reducer.cpp81
-rw-r--r--src/math/numbertheory/reducer.h61
-rw-r--r--src/math/numbertheory/ressol.cpp81
16 files changed, 0 insertions, 2463 deletions
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;
- }
-
-}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-17 17:26:22 +0000