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authorlloyd <[email protected]>2014-01-01 21:20:55 +0000
committerlloyd <[email protected]>2014-01-01 21:20:55 +0000
commit197dc467dec28a04c3b2f30da7cef122dfbb13e9 (patch)
treecdbd3ddaec051c72f0a757db461973d90c37b97a /lib/math/numbertheory
parent62faac373c07cfe10bc8c309e89ebdd30d8e5eaa (diff)
Shuffle things around. Add NIST X.509 test to build.
Diffstat (limited to 'lib/math/numbertheory')
-rw-r--r--lib/math/numbertheory/def_powm.h63
-rw-r--r--lib/math/numbertheory/dsa_gen.cpp134
-rw-r--r--lib/math/numbertheory/info.txt35
-rw-r--r--lib/math/numbertheory/jacobi.cpp53
-rw-r--r--lib/math/numbertheory/make_prm.cpp100
-rw-r--r--lib/math/numbertheory/mp_numth.cpp74
-rw-r--r--lib/math/numbertheory/numthry.cpp409
-rw-r--r--lib/math/numbertheory/numthry.h237
-rw-r--r--lib/math/numbertheory/pow_mod.cpp211
-rw-r--r--lib/math/numbertheory/pow_mod.h104
-rw-r--r--lib/math/numbertheory/powm_fw.cpp69
-rw-r--r--lib/math/numbertheory/powm_mnt.cpp142
-rw-r--r--lib/math/numbertheory/primes.cpp609
-rw-r--r--lib/math/numbertheory/reducer.cpp81
-rw-r--r--lib/math/numbertheory/reducer.h61
-rw-r--r--lib/math/numbertheory/ressol.cpp81
16 files changed, 2463 insertions, 0 deletions
diff --git a/lib/math/numbertheory/def_powm.h b/lib/math/numbertheory/def_powm.h
new file mode 100644
index 000000000..6ceee7bb6
--- /dev/null
+++ b/lib/math/numbertheory/def_powm.h
@@ -0,0 +1,63 @@
+/*
+* 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/lib/math/numbertheory/dsa_gen.cpp b/lib/math/numbertheory/dsa_gen.cpp
new file mode 100644
index 000000000..d30a08f1a
--- /dev/null
+++ b/lib/math/numbertheory/dsa_gen.cpp
@@ -0,0 +1,134 @@
+/*
+* 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/lib/math/numbertheory/info.txt b/lib/math/numbertheory/info.txt
new file mode 100644
index 000000000..62386c3bc
--- /dev/null
+++ b/lib/math/numbertheory/info.txt
@@ -0,0 +1,35 @@
+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/lib/math/numbertheory/jacobi.cpp b/lib/math/numbertheory/jacobi.cpp
new file mode 100644
index 000000000..fcccc80e5
--- /dev/null
+++ b/lib/math/numbertheory/jacobi.cpp
@@ -0,0 +1,53 @@
+/*
+* 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/lib/math/numbertheory/make_prm.cpp b/lib/math/numbertheory/make_prm.cpp
new file mode 100644
index 000000000..dc94420ab
--- /dev/null
+++ b/lib/math/numbertheory/make_prm.cpp
@@ -0,0 +1,100 @@
+/*
+* 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/lib/math/numbertheory/mp_numth.cpp b/lib/math/numbertheory/mp_numth.cpp
new file mode 100644
index 000000000..e6826b9dd
--- /dev/null
+++ b/lib/math/numbertheory/mp_numth.cpp
@@ -0,0 +1,74 @@
+/*
+* 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/lib/math/numbertheory/numthry.cpp b/lib/math/numbertheory/numthry.cpp
new file mode 100644
index 000000000..e3c673ea5
--- /dev/null
+++ b/lib/math/numbertheory/numthry.cpp
@@ -0,0 +1,409 @@
+/*
+* 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/lib/math/numbertheory/numthry.h b/lib/math/numbertheory/numthry.h
new file mode 100644
index 000000000..a34d855b2
--- /dev/null
+++ b/lib/math/numbertheory/numthry.h
@@ -0,0 +1,237 @@
+/*
+* 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/lib/math/numbertheory/pow_mod.cpp b/lib/math/numbertheory/pow_mod.cpp
new file mode 100644
index 000000000..c7d7fe70e
--- /dev/null
+++ b/lib/math/numbertheory/pow_mod.cpp
@@ -0,0 +1,211 @@
+/*
+* 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/lib/math/numbertheory/pow_mod.h b/lib/math/numbertheory/pow_mod.h
new file mode 100644
index 000000000..b78510793
--- /dev/null
+++ b/lib/math/numbertheory/pow_mod.h
@@ -0,0 +1,104 @@
+/*
+* 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/lib/math/numbertheory/powm_fw.cpp b/lib/math/numbertheory/powm_fw.cpp
new file mode 100644
index 000000000..16a48a5b0
--- /dev/null
+++ b/lib/math/numbertheory/powm_fw.cpp
@@ -0,0 +1,69 @@
+/*
+* 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/lib/math/numbertheory/powm_mnt.cpp b/lib/math/numbertheory/powm_mnt.cpp
new file mode 100644
index 000000000..a3eac1f83
--- /dev/null
+++ b/lib/math/numbertheory/powm_mnt.cpp
@@ -0,0 +1,142 @@
+/*
+* 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/lib/math/numbertheory/primes.cpp b/lib/math/numbertheory/primes.cpp
new file mode 100644
index 000000000..a0c0f0093
--- /dev/null
+++ b/lib/math/numbertheory/primes.cpp
@@ -0,0 +1,609 @@
+/*
+* 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,
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+65437, 65447, 65449, 65479, 65497, 65519, 65521, 0 };
+
+}
diff --git a/lib/math/numbertheory/reducer.cpp b/lib/math/numbertheory/reducer.cpp
new file mode 100644
index 000000000..8e8951c46
--- /dev/null
+++ b/lib/math/numbertheory/reducer.cpp
@@ -0,0 +1,81 @@
+/*
+* 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/lib/math/numbertheory/reducer.h b/lib/math/numbertheory/reducer.h
new file mode 100644
index 000000000..76712074c
--- /dev/null
+++ b/lib/math/numbertheory/reducer.h
@@ -0,0 +1,61 @@
+/*
+* 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/lib/math/numbertheory/ressol.cpp b/lib/math/numbertheory/ressol.cpp
new file mode 100644
index 000000000..9c48187f4
--- /dev/null
+++ b/lib/math/numbertheory/ressol.cpp
@@ -0,0 +1,81 @@
+/*
+* 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;
+ }
+
+}
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