diff options
Diffstat (limited to 'old/botan/src/math/numbertheory')
18 files changed, 2427 insertions, 0 deletions
diff --git a/old/botan/src/math/numbertheory/blinding.cpp b/old/botan/src/math/numbertheory/blinding.cpp new file mode 100644 index 0000000..c6a3fd1 --- /dev/null +++ b/old/botan/src/math/numbertheory/blinding.cpp @@ -0,0 +1,49 @@ +/* +* Blinder +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/blinding.h> +#include <botan/numthry.h> + +namespace Botan { + +/* +* Blinder Constructor +*/ +Blinder::Blinder(const BigInt& e, const BigInt& d, const BigInt& n) + { + if(e < 1 || d < 1 || n < 1) + throw Invalid_Argument("Blinder: Arguments too small"); + + reducer = Modular_Reducer(n); + this->e = e; + this->d = d; + } + +/* +* Blind a number +*/ +BigInt Blinder::blind(const BigInt& i) const + { + if(!reducer.initialized()) + return i; + + e = reducer.square(e); + d = reducer.square(d); + return reducer.multiply(i, e); + } + +/* +* Unblind a number +*/ +BigInt Blinder::unblind(const BigInt& i) const + { + if(!reducer.initialized()) + return i; + return reducer.multiply(i, d); + } + +} diff --git a/old/botan/src/math/numbertheory/blinding.h b/old/botan/src/math/numbertheory/blinding.h new file mode 100644 index 0000000..5f7f9e6 --- /dev/null +++ b/old/botan/src/math/numbertheory/blinding.h @@ -0,0 +1,34 @@ +/* +* Blinder +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_BLINDER_H__ +#define BOTAN_BLINDER_H__ + +#include <botan/bigint.h> +#include <botan/reducer.h> + +namespace Botan { + +/* +* Blinding Function Object +*/ +class BOTAN_DLL Blinder + { + public: + BigInt blind(const BigInt&) const; + BigInt unblind(const BigInt&) const; + + Blinder() {} + Blinder(const BigInt&, const BigInt&, const BigInt&); + private: + Modular_Reducer reducer; + mutable BigInt e, d; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/def_powm.h b/old/botan/src/math/numbertheory/def_powm.h new file mode 100644 index 0000000..472c865 --- /dev/null +++ b/old/botan/src/math/numbertheory/def_powm.h @@ -0,0 +1,64 @@ +/* +* 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 BOTAN_DLL 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; + u32bit window_bits; + std::vector<BigInt> g; + Power_Mod::Usage_Hints hints; + }; + +/* +* Montgomery Exponentiator +*/ +class BOTAN_DLL 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 exp, modulus; + BigInt R2, R_mod; + std::vector<BigInt> g; + word mod_prime; + u32bit mod_words, exp_bits, window_bits; + Power_Mod::Usage_Hints hints; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/dsa_gen.cpp b/old/botan/src/math/numbertheory/dsa_gen.cpp new file mode 100644 index 0000000..83646e5 --- /dev/null +++ b/old/botan/src/math/numbertheory/dsa_gen.cpp @@ -0,0 +1,135 @@ +/* +* 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(u32bit pbits, u32bit 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, + u32bit pbits, u32bit qbits, + const MemoryRegion<byte>& seed_c) + { + if(!fips186_3_valid_size(pbits, qbits)) + throw Invalid_Argument( + "FIPS 186-3 does not allow DSA domain parameters of " + + to_string(pbits) + "/" + to_string(qbits) + " bits long"); + + if(seed_c.size() * 8 < qbits) + throw Invalid_Argument( + "Generating a DSA parameter set with a " + to_string(qbits) + + "long q requires a seed at least as many bits long"); + + std::auto_ptr<HashFunction> hash( + af.make_hash_function("SHA-" + to_string(qbits))); + + const u32bit HASH_SIZE = hash->OUTPUT_LENGTH; + + class Seed + { + public: + Seed(const MemoryRegion<byte>& s) : seed(s) {} + + operator MemoryRegion<byte>& () { return seed; } + + Seed& operator++() + { + for(u32bit j = seed.size(); j > 0; --j) + if(++seed[j-1]) + break; + return (*this); + } + private: + SecureVector<byte> seed; + }; + + Seed seed(seed_c); + + q.binary_decode(hash->process(seed)); + q.set_bit(qbits-1); + q.set_bit(0); + + if(!is_prime(q, rng)) + return false; + + const u32bit n = (pbits-1) / (HASH_SIZE * 8), + b = (pbits-1) % (HASH_SIZE * 8); + + BigInt X; + SecureVector<byte> V(HASH_SIZE * (n+1)); + + for(u32bit j = 0; j != 4096; ++j) + { + for(u32bit 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 && is_prime(p, rng)) + return true; + } + return false; + } + +/* +* Generate DSA Primes +*/ +SecureVector<byte> generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p, BigInt& q, + u32bit pbits, u32bit qbits) + { + SecureVector<byte> seed(qbits/8); + + while(true) + { + rng.randomize(seed, seed.size()); + + if(generate_dsa_primes(rng, af, p, q, pbits, qbits, seed)) + return seed; + } + } + +} diff --git a/old/botan/src/math/numbertheory/info.txt b/old/botan/src/math/numbertheory/info.txt new file mode 100644 index 0000000..1595c73 --- /dev/null +++ b/old/botan/src/math/numbertheory/info.txt @@ -0,0 +1,33 @@ +realname "Math Functions" + +load_on auto + +define BIGINT_MATH + +<add> +blinding.cpp +blinding.h +def_powm.h +dsa_gen.cpp +jacobi.cpp +make_prm.cpp +mp_numth.cpp +numthry.cpp +numthry.h +pow_mod.cpp +pow_mod.h +powm_fw.cpp +powm_mnt.cpp +primes.cpp +reducer.cpp +reducer.h +ressol.cpp +</add> + +<requires> +algo_factory +bigint +hash +libstate +rng +</requires> diff --git a/old/botan/src/math/numbertheory/jacobi.cpp b/old/botan/src/math/numbertheory/jacobi.cpp new file mode 100644 index 0000000..2ad05ff --- /dev/null +++ b/old/botan/src/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; + + u32bit 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/old/botan/src/math/numbertheory/make_prm.cpp b/old/botan/src/math/numbertheory/make_prm.cpp new file mode 100644 index 0000000..b136b6d --- /dev/null +++ b/old/botan/src/math/numbertheory/make_prm.cpp @@ -0,0 +1,97 @@ +/* +* 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, + u32bit bits, const BigInt& coprime, + u32bit equiv, u32bit modulo) + { + if(bits <= 1) + throw Invalid_Argument("random_prime: Can't make a prime of " + + 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); + p.set_bit(bits - 2); + p.set_bit(0); + + if(p % modulo != equiv) + p += (modulo - p % modulo) + equiv; + + const u32bit sieve_size = std::min(bits / 2, PRIME_TABLE_SIZE); + SecureVector<u32bit> sieve(sieve_size); + + for(u32bit j = 0; j != sieve.size(); ++j) + sieve[j] = p % PRIMES[j]; + + u32bit counter = 0; + while(true) + { + if(counter == 4096 || p.bits() > bits) + break; + + bool passes_sieve = true; + ++counter; + p += modulo; + + if(p.bits() > bits) + break; + + for(u32bit 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(passes_mr_tests(rng, p)) + return p; + } + } + } + +/* +* Generate a random safe prime +*/ +BigInt random_safe_prime(RandomNumberGenerator& rng, u32bit bits) + { + if(bits <= 64) + throw Invalid_Argument("random_safe_prime: Can't make a prime of " + + to_string(bits) + " bits"); + + BigInt p; + do + p = (random_prime(rng, bits - 1) << 1) + 1; + while(!is_prime(p, rng)); + return p; + } + +} diff --git a/old/botan/src/math/numbertheory/mp_numth.cpp b/old/botan/src/math/numbertheory/mp_numth.cpp new file mode 100644 index 0000000..45a3984 --- /dev/null +++ b/old/botan/src/math/numbertheory/mp_numth.cpp @@ -0,0 +1,71 @@ +/* +* Fused and Important MP Algorithms +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/mp_core.h> +#include <botan/util.h> +#include <algorithm> + +namespace Botan { + +/* +* Square a BigInt +*/ +BigInt square(const BigInt& x) + { + const u32bit x_sw = x.sig_words(); + + BigInt z(BigInt::Positive, round_up(2*x_sw, 16)); + SecureVector<word> workspace(z.size()); + + bigint_sqr(z.get_reg(), z.size(), workspace, + 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 u32bit a_sw = a.sig_words(); + const u32bit b_sw = b.sig_words(); + const u32bit c_sw = c.sig_words(); + + BigInt r(sign, std::max(a.size() + b.size(), c_sw) + 1); + SecureVector<word> workspace(r.size()); + + bigint_mul(r.get_reg(), r.size(), workspace, + a.data(), a.size(), a_sw, + b.data(), b.size(), b_sw); + const u32bit r_size = std::max(r.sig_words(), c_sw); + bigint_add2(r.get_reg(), 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/old/botan/src/math/numbertheory/numthry.cpp b/old/botan/src/math/numbertheory/numthry.cpp new file mode 100644 index 0000000..4486813 --- /dev/null +++ b/old/botan/src/math/numbertheory/numthry.cpp @@ -0,0 +1,346 @@ +/* +* Number Theory Functions +* (C) 1999-2009 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/numthry.h> +#include <botan/bit_ops.h> +#include <algorithm> + +namespace Botan { + +namespace { + +/* +* Miller-Rabin Iterations +*/ +u32bit miller_rabin_test_iterations(u32bit bits, bool verify) + { + struct mapping { u32bit bits; u32bit verify_iter; u32bit check_iter; }; + + static 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(u32bit i = 0; tests[i].bits; ++i) + { + if(bits <= tests[i].bits) + { + if(verify) + return tests[i].verify_iter; + else + return tests[i].check_iter; + } + } + return 2; + } + +} + +/* +* Return the number of 0 bits at the end of n +*/ +u32bit low_zero_bits(const BigInt& n) + { + if(n.is_negative() || n.is_zero()) return 0; + + u32bit low_zero = 0; + + if(n.is_positive() && n.is_nonzero()) + { + for(u32bit i = 0; i != n.size(); ++i) + { + word x = n[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); + u32bit 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)); + } + +/* +* 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; + + BigInt x = mod, y = n, u = mod, v = n; + BigInt A = 1, B = 0, C = 0, D = 1; + + while(u.is_nonzero()) + { + u32bit zero_bits = low_zero_bits(u); + u >>= zero_bits; + for(u32bit i = 0; i != zero_bits; ++i) + { + if(A.is_odd() || B.is_odd()) + { A += y; B -= x; } + A >>= 1; B >>= 1; + } + + zero_bits = low_zero_bits(v); + v >>= zero_bits; + for(u32bit i = 0; i != zero_bits; ++i) + { + if(C.is_odd() || D.is_odd()) + { C += y; D -= x; } + 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; + + while(D.is_negative()) D += mod; + while(D >= mod) D -= mod; + + return D; + } + +/* +* Modular Exponentiation +*/ +BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) + { + Power_Mod pow_mod(mod); + pow_mod.set_base(base); + pow_mod.set_exponent(exp); + return pow_mod.execute(); + } + +/* +* Do simple tests of primality +*/ +s32bit simple_primality_tests(const BigInt& n) + { + const s32bit NOT_PRIME = -1, UNKNOWN = 0, PRIME = 1; + + if(n == 2) + return PRIME; + if(n <= 1 || n.is_even()) + return NOT_PRIME; + + if(n <= PRIMES[PRIME_TABLE_SIZE-1]) + { + const word num = n.word_at(0); + for(u32bit i = 0; PRIMES[i]; ++i) + { + if(num == PRIMES[i]) return PRIME; + if(num < PRIMES[i]) return NOT_PRIME; + } + return NOT_PRIME; + } + + u32bit check_first = std::min(n.bits() / 32, PRIME_PRODUCTS_TABLE_SIZE); + for(u32bit i = 0; i != check_first; ++i) + if(gcd(n, PRIME_PRODUCTS[i]) != 1) + return NOT_PRIME; + + return UNKNOWN; + } + +/* +* Fast check of primality +*/ +bool check_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 0); + } + +/* +* Test for primality +*/ +bool is_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 1); + } + +/* +* Verify primality +*/ +bool verify_prime(const BigInt& n, RandomNumberGenerator& rng) + { + return run_primality_tests(rng, n, 2); + } + +/* +* Verify primality +*/ +bool run_primality_tests(RandomNumberGenerator& rng, + const BigInt& n, u32bit level) + { + s32bit simple_tests = simple_primality_tests(n); + if(simple_tests) return (simple_tests == 1) ? true : false; + return passes_mr_tests(rng, n, level); + } + +/* +* Test for primaility using Miller-Rabin +*/ +bool passes_mr_tests(RandomNumberGenerator& rng, + const BigInt& n, u32bit level) + { + const u32bit PREF_NONCE_BITS = 40; + + if(level > 2) + level = 2; + + MillerRabin_Test mr(n); + + if(!mr.passes_test(2)) + return false; + + if(level == 0) + return true; + + const u32bit NONCE_BITS = std::min(n.bits() - 1, PREF_NONCE_BITS); + + const bool verify = (level == 2); + + u32bit tests = miller_rabin_test_iterations(n.bits(), verify); + + BigInt nonce; + for(u32bit i = 0; i != tests; ++i) + { + if(!verify && PRIMES[i] < (n-1)) + nonce = PRIMES[i]; + else + { + while(nonce < 2 || nonce >= (n-1)) + nonce.randomize(rng, NONCE_BITS); + } + + if(!mr.passes_test(nonce)) + return false; + } + return true; + } + +/* +* Miller-Rabin Test +*/ +bool MillerRabin_Test::passes_test(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 true; + + for(u32bit i = 1; i != s; ++i) + { + y = reducer.square(y); + + if(y == 1) + return false; + if(y == n_minus_1) + 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); + } + +} diff --git a/old/botan/src/math/numbertheory/numthry.h b/old/botan/src/math/numbertheory/numthry.h new file mode 100644 index 0000000..e4c0437 --- /dev/null +++ b/old/botan/src/math/numbertheory/numthry.h @@ -0,0 +1,120 @@ +/* +* 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/reducer.h> +#include <botan/pow_mod.h> +#include <botan/rng.h> + +namespace Botan { + +/* +* Fused Arithmetic Operations +*/ +BigInt BOTAN_DLL mul_add(const BigInt&, const BigInt&, const BigInt&); +BigInt BOTAN_DLL sub_mul(const BigInt&, const BigInt&, const BigInt&); + +/* +* Number Theory Functions +*/ +inline BigInt abs(const BigInt& n) { return n.abs(); } + +void BOTAN_DLL divide(const BigInt&, const BigInt&, BigInt&, BigInt&); + +BigInt BOTAN_DLL gcd(const BigInt&, const BigInt&); +BigInt BOTAN_DLL lcm(const BigInt&, const BigInt&); + +BigInt BOTAN_DLL square(const BigInt&); +BigInt BOTAN_DLL inverse_mod(const BigInt&, const BigInt&); +s32bit BOTAN_DLL jacobi(const BigInt&, const BigInt&); + +BigInt BOTAN_DLL power_mod(const BigInt&, const BigInt&, const BigInt&); + +/* +* Compute the square root of x modulo a prime +* using the Shanks-Tonnelli algorithm +*/ +BigInt ressol(const BigInt& x, const BigInt& p); + +/* +* Utility Functions +*/ +u32bit BOTAN_DLL low_zero_bits(const BigInt&); + +/* +* Primality Testing +*/ +bool BOTAN_DLL check_prime(const BigInt&, RandomNumberGenerator&); +bool BOTAN_DLL is_prime(const BigInt&, RandomNumberGenerator&); +bool BOTAN_DLL verify_prime(const BigInt&, RandomNumberGenerator&); + +s32bit BOTAN_DLL simple_primality_tests(const BigInt&); + +bool BOTAN_DLL passes_mr_tests(RandomNumberGenerator&, + const BigInt&, u32bit = 1); + +bool BOTAN_DLL run_primality_tests(RandomNumberGenerator&, + const BigInt&, u32bit = 1); + +/* +* Random Number Generation +*/ +BigInt BOTAN_DLL random_prime(RandomNumberGenerator&, + u32bit bits, const BigInt& coprime = 1, + u32bit equiv = 1, u32bit equiv_mod = 2); + +BigInt BOTAN_DLL random_safe_prime(RandomNumberGenerator&, + u32bit); + +/* +* DSA Parameter Generation +*/ +class Algorithm_Factory; + +SecureVector<byte> BOTAN_DLL +generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p, BigInt& q, + u32bit pbits, u32bit qbits); + +bool BOTAN_DLL +generate_dsa_primes(RandomNumberGenerator& rng, + Algorithm_Factory& af, + BigInt& p_out, BigInt& q_out, + u32bit p_bits, u32bit q_bits, + const MemoryRegion<byte>& seed); + +/* +* Prime Numbers +*/ +const u32bit PRIME_TABLE_SIZE = 6541; +const u32bit PRIME_PRODUCTS_TABLE_SIZE = 256; + +extern const u16bit BOTAN_DLL PRIMES[]; +extern const u64bit PRIME_PRODUCTS[]; + +/* +* Miller-Rabin Primality Tester +*/ +class BOTAN_DLL MillerRabin_Test + { + public: + bool passes_test(const BigInt&); + MillerRabin_Test(const BigInt&); + private: + BigInt n, r, n_minus_1; + u32bit s; + Fixed_Exponent_Power_Mod pow_mod; + Modular_Reducer reducer; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/pow_mod.cpp b/old/botan/src/math/numbertheory/pow_mod.cpp new file mode 100644 index 0000000..fd9b8e9 --- /dev/null +++ b/old/botan/src/math/numbertheory/pow_mod.cpp @@ -0,0 +1,157 @@ +/* +* Modular Exponentiation Proxy +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/pow_mod.h> +#include <botan/pk_engine.h> + +namespace Botan { + +/* +* Power_Mod Constructor +*/ +Power_Mod::Power_Mod(const BigInt& n, Usage_Hints hints) + { + core = 0; + set_modulus(n, hints); + } + +/* +* Power_Mod Copy Constructor +*/ +Power_Mod::Power_Mod(const Power_Mod& other) + { + core = 0; + if(other.core) + core = other.core->copy(); + } + +/* +* Power_Mod Assignment Operator +*/ +Power_Mod& Power_Mod::operator=(const Power_Mod& other) + { + delete core; + core = 0; + 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 = ((n == 0) ? 0 : Engine_Core::mod_exp(n, hints)); + } + +/* +* 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(); + } + +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 u32bit b_bits = b.bits(); + const u32bit 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 u32bit e_bits = e.bits(); + const u32bit 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/old/botan/src/math/numbertheory/pow_mod.h b/old/botan/src/math/numbertheory/pow_mod.h new file mode 100644 index 0000000..6952dcd --- /dev/null +++ b/old/botan/src/math/numbertheory/pow_mod.h @@ -0,0 +1,93 @@ +/* +* 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 + }; + + 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&); + ~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&, const BigInt&, + Usage_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&, const BigInt&, + Usage_Hints = NO_HINTS); + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/powm_fw.cpp b/old/botan/src/math/numbertheory/powm_fw.cpp new file mode 100644 index 0000000..b764ee7 --- /dev/null +++ b/old/botan/src/math/numbertheory/powm_fw.cpp @@ -0,0 +1,104 @@ +/* +* Fixed Window Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/def_powm.h> +#include <botan/numthry.h> +#include <vector> + +namespace Botan { + +namespace { + +/* +* Try to choose a good window size +*/ +u32bit choose_window_bits(u32bit exp_bits, u32bit, + Power_Mod::Usage_Hints hints) + { + static const u32bit wsize[][2] = { + { 2048, 7 }, { 1024, 6 }, { 256, 5 }, { 128, 4 }, { 64, 3 }, { 0, 0 } + }; + + u32bit window_bits = 3; + + if(exp_bits) + { + for(u32bit j = 0; wsize[j][0]; ++j) + { + if(exp_bits >= wsize[j][0]) + { + window_bits += wsize[j][1]; + break; + } + } + } + + if(hints & Power_Mod::EXP_IS_FIXED) + window_bits += 2; + if(hints & Power_Mod::EXP_IS_LARGE) + window_bits += 2; + if(hints & Power_Mod::BASE_IS_FIXED) + ++window_bits; + + return window_bits; + } + +} + +/* +* 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 = choose_window_bits(exp.bits(), base.bits(), hints); + + g.resize((1 << window_bits) - 1); + g[0] = base; + for(u32bit j = 1; j != g.size(); ++j) + g[j] = reducer.multiply(g[j-1], g[0]); + } + +/* +* Compute the result +*/ +BigInt Fixed_Window_Exponentiator::execute() const + { + const u32bit exp_nibbles = (exp.bits() + window_bits - 1) / window_bits; + + BigInt x = 1; + for(u32bit j = exp_nibbles; j > 0; --j) + { + for(u32bit k = 0; k != window_bits; ++k) + x = reducer.square(x); + + u32bit nibble = exp.get_substring(window_bits*(j-1), window_bits); + if(nibble) + x = reducer.multiply(x, g[nibble-1]); + } + 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/old/botan/src/math/numbertheory/powm_mnt.cpp b/old/botan/src/math/numbertheory/powm_mnt.cpp new file mode 100644 index 0000000..e6d8cc3 --- /dev/null +++ b/old/botan/src/math/numbertheory/powm_mnt.cpp @@ -0,0 +1,180 @@ +/* +* Montgomery Exponentiation +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/def_powm.h> +#include <botan/numthry.h> +#include <botan/mp_core.h> + +namespace Botan { + +namespace { + +/* +* Try to choose a good window size +*/ +u32bit choose_window_bits(u32bit exp_bits, u32bit, + Power_Mod::Usage_Hints hints) + { + static const u32bit wsize[][2] = { + { 2048, 4 }, { 1024, 3 }, { 256, 2 }, { 128, 1 }, { 0, 0 } + }; + + u32bit window_bits = 1; + + if(exp_bits) + { + for(u32bit 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; + } + +/* +* Montgomery Reduction +*/ +inline void montgomery_reduce(BigInt& out, MemoryRegion<word>& z_buf, + const BigInt& x_bn, u32bit x_size, word u) + { + const word* x = x_bn.data(); + word* z = z_buf.begin(); + u32bit z_size = z_buf.size(); + + bigint_monty_redc(z, z_size, x, x_size, u); + + out.get_reg().set(z + x_size, x_size + 1); + } + +} + +/* +* Set the exponent +*/ +void Montgomery_Exponentiator::set_exponent(const BigInt& exp) + { + this->exp = exp; + exp_bits = exp.bits(); + } + +/* +* Set the base +*/ +void Montgomery_Exponentiator::set_base(const BigInt& base) + { + window_bits = choose_window_bits(exp.bits(), base.bits(), hints); + + g.resize((1 << window_bits) - 1); + + SecureVector<word> z(2 * (mod_words + 1)); + SecureVector<word> workspace(z.size()); + + g[0] = (base >= modulus) ? (base % modulus) : base; + bigint_mul(z.begin(), z.size(), workspace, + g[0].data(), g[0].size(), g[0].sig_words(), + R2.data(), R2.size(), R2.sig_words()); + + montgomery_reduce(g[0], z, modulus, mod_words, mod_prime); + + const BigInt& x = g[0]; + const u32bit x_sig = x.sig_words(); + + for(u32bit j = 1; j != g.size(); ++j) + { + const BigInt& y = g[j-1]; + const u32bit y_sig = y.sig_words(); + + z.clear(); + bigint_mul(z.begin(), z.size(), workspace, + x.data(), x.size(), x_sig, + y.data(), y.size(), y_sig); + + montgomery_reduce(g[j], z, modulus, mod_words, mod_prime); + } + } + +/* +* Compute the result +*/ +BigInt Montgomery_Exponentiator::execute() const + { + const u32bit exp_nibbles = (exp_bits + window_bits - 1) / window_bits; + + BigInt x = R_mod; + SecureVector<word> z(2 * (mod_words + 1)); + SecureVector<word> workspace(2 * (mod_words + 1)); + + for(u32bit j = exp_nibbles; j > 0; --j) + { + for(u32bit k = 0; k != window_bits; ++k) + { + z.clear(); + bigint_sqr(z.begin(), z.size(), workspace, + x.data(), x.size(), x.sig_words()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + } + + u32bit nibble = exp.get_substring(window_bits*(j-1), window_bits); + if(nibble) + { + const BigInt& y = g[nibble-1]; + + z.clear(); + bigint_mul(z.begin(), z.size(), workspace, + x.data(), x.size(), x.sig_words(), + y.data(), y.size(), y.sig_words()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + } + } + + z.clear(); + z.copy(x.data(), x.size()); + + montgomery_reduce(x, z, modulus, mod_words, mod_prime); + return x; + } + +/* +* Montgomery_Exponentiator Constructor +*/ +Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod, + Power_Mod::Usage_Hints hints) + { + if(!mod.is_positive()) + throw Exception("Montgomery_Exponentiator: modulus must be positive"); + if(mod.is_even()) + throw Exception("Montgomery_Exponentiator: modulus must be odd"); + + window_bits = 0; + this->hints = hints; + modulus = mod; + + mod_words = modulus.sig_words(); + + BigInt mod_prime_bn(BigInt::Power2, MP_WORD_BITS); + mod_prime = (mod_prime_bn - inverse_mod(modulus, mod_prime_bn)).word_at(0); + + R_mod = BigInt(BigInt::Power2, MP_WORD_BITS * mod_words); + R_mod %= modulus; + + R2 = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words); + R2 %= modulus; + } + +} diff --git a/old/botan/src/math/numbertheory/primes.cpp b/old/botan/src/math/numbertheory/primes.cpp new file mode 100644 index 0000000..a9c8ab5 --- /dev/null +++ b/old/botan/src/math/numbertheory/primes.cpp @@ -0,0 +1,676 @@ +/* +* 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, 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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 }; + +const u64bit PRIME_PRODUCTS[PRIME_PRODUCTS_TABLE_SIZE] = { +(u64bit) 0xFF658BDE2F2A43DFULL, (u64bit) 0xFEEB94CD535119EDULL, (u64bit) 0xFA921839EC24DDD5ULL, (u64bit) 0xFDDA766C77E1E605ULL, +(u64bit) 0xFF3024B0EB4EE333ULL, (u64bit) 0xFEEE350BBC92F4DFULL, (u64bit) 0xFFC724B7D011D01BULL, (u64bit) 0xFEED34B826C33B05ULL, +(u64bit) 0xFE69D8DE3F85C6E3ULL, (u64bit) 0xFE3B48909250918FULL, (u64bit) 0xFF8EC0CE9C632429ULL, (u64bit) 0xFFD92A5C78226D6BULL, +(u64bit) 0xFFB4BFB0C65133CFULL, (u64bit) 0xFE77113704902C57ULL, (u64bit) 0xFF8A21D222EA81FDULL, (u64bit) 0xFEDA1299661CF5ABULL, +(u64bit) 0xFF4CE86187737D0DULL, (u64bit) 0xFFD26443A07F519DULL, (u64bit) 0xFFA817B7191D7967ULL, (u64bit) 0xFF00EDC142868873ULL, +(u64bit) 0xFFB9C6D7F7A239B7ULL, (u64bit) 0xFFE76D3481E98E39ULL, (u64bit) 0xFF76D5432584120DULL, (u64bit) 0xFFAA499F071EC705ULL, +(u64bit) 0xFEB5198F05722E59ULL, (u64bit) 0xFF7E0431CA41107FULL, (u64bit) 0xFFCFD52FEDDC928FULL, (u64bit) 0xFE0EA42537BC6ABFULL, +(u64bit) 0xFF64937896876925ULL, (u64bit) 0xFC6FC87E811607D3ULL, (u64bit) 0xFFBF600E6CDD0F4FULL, (u64bit) 0xFF022700FE658243ULL, +(u64bit) 0xFF2E21166779D6B9ULL, (u64bit) 0xFFC224624C665C33ULL, (u64bit) 0xFF1372F41FF177ADULL, (u64bit) 0xFF31E57E972D0C13ULL, +(u64bit) 0xFFA891F866404D23ULL, (u64bit) 0xFF7BF13EF716E9A3ULL, (u64bit) 0xFE51CAFD9466E733ULL, (u64bit) 0xFDA1CF55F6D6336FULL, +(u64bit) 0xFFAF6C040ED0950FULL, (u64bit) 0xFFAA1725F40BA269ULL, (u64bit) 0xFEC593BC3570BEEBULL, (u64bit) 0xFEE05B35B426F413ULL, +(u64bit) 0xFFCA5209A08890F9ULL, (u64bit) 0xFFED8AF70EB0CC89ULL, (u64bit) 0xFF3F98E3E27860A5ULL, (u64bit) 0xFF92FECD017FF9F7ULL, +(u64bit) 0xFEFA655B2609018FULL, (u64bit) 0xFFFC51D15AAC7B77ULL, (u64bit) 0xFEF5007E71420DB1ULL, (u64bit) 0xFFEC4784141332D1ULL, +(u64bit) 0xFE8384ED4E1D21CDULL, (u64bit) 0xFFD3FF614D3ECC47ULL, (u64bit) 0xFFDE5166FD540313ULL, (u64bit) 0xFF5320ECED04B26FULL, +(u64bit) 0xFF223980F122FF75ULL, (u64bit) 0xFF19C1F27CB1B4A5ULL, (u64bit) 0xFF0F1DFC9DA9523BULL, (u64bit) 0xFF82DE7B387F5427ULL, +(u64bit) 0xFF9A026BA87314E3ULL, (u64bit) 0xFFAC7FF3ACE64E77ULL, (u64bit) 0xFF808EB2FD5873C3ULL, (u64bit) 0xFE983ED5BB363301ULL, +(u64bit) 0xFF714856DB2CFE95ULL, (u64bit) 0xFF84E1510CF3EB9FULL, (u64bit) 0xFF29D04C1DA0B115ULL, (u64bit) 0xFFBCF3BF9433552FULL, +(u64bit) 0xFF32203D58A4C473ULL, (u64bit) 0xFFF00910A15021C3ULL, (u64bit) 0xFDE93041F28240ADULL, (u64bit) 0xFFC518BCD81C03C5ULL, +(u64bit) 0xFEF504CD8BB9CBDDULL, (u64bit) 0xFEB8FFBFFF116A6BULL, (u64bit) 0xFF7642E0785ADA23ULL, (u64bit) 0xFFECF068800FD50DULL, +(u64bit) 0xFFD703577CA247A7ULL, (u64bit) 0xFF54C0ECAD2C9691ULL, (u64bit) 0xFFC031706B8C72F5ULL, (u64bit) 0xFFE59E5CA58BBDF5ULL, +(u64bit) 0xFFF31FAFFD3B331DULL, (u64bit) 0xFF64DDF32349FF6DULL, (u64bit) 0xFFE38309D0BD4A51ULL, (u64bit) 0xFF8C934F76B3C737ULL, +(u64bit) 0xFFDC80B4BAEAFC1FULL, (u64bit) 0xFFCC1FE4C856FBD9ULL, (u64bit) 0xFFDB5976DDF601FDULL, (u64bit) 0xFFD3DD25F424433DULL, +(u64bit) 0xFFC00FA367E746C7ULL, (u64bit) 0xFFE08BF011CC854FULL, (u64bit) 0xFFC3F21982468F6DULL, (u64bit) 0xFFDA6C52478A76DFULL, +(u64bit) 0xFFC67D95AADED363ULL, (u64bit) 0xFFD605D18C3AFC65ULL, (u64bit) 0xFFE828C9D698F1DFULL, (u64bit) 0xFFBE5098D83B7737ULL, +(u64bit) 0xFF79EB34474ABFB9ULL, (u64bit) 0xFFD27AEED0786363ULL, (u64bit) 0xFFD0FE27B77C271FULL, (u64bit) 0xFFFBB6563BD065EFULL, +(u64bit) 0xFFF3638F8635E1EBULL, (u64bit) 0xFFBE862C22C9F065ULL, (u64bit) 0xFF44712D8488A01DULL, (u64bit) 0xFF7EEC97F9913111ULL, +(u64bit) 0xFFC23CC78CB12AB1ULL, (u64bit) 0xFFF390FE85F81D3DULL, (u64bit) 0xFFE8EA21A0FB9931ULL, (u64bit) 0xFFB9D42D17A93385ULL, +(u64bit) 0xFFCDB63AB21E904DULL, (u64bit) 0xFF5EB7F2210D33DFULL, (u64bit) 0xFFE6F6C7BB60C9DFULL, (u64bit) 0xFFAD4CA8DC26D699ULL, +(u64bit) 0xFF7BE75BD21DCA51ULL, (u64bit) 0xFEF89CE23CB61789ULL, (u64bit) 0xFF40ECA3CCA22CE5ULL, (u64bit) 0xF52BDF080F7ABA6FULL, +(u64bit) 0xEC8F38C8B28E0493ULL, (u64bit) 0xE68E732A2ABED62FULL, (u64bit) 0xE21A13779E0CCDC7ULL, (u64bit) 0xD823C075C325191BULL, +(u64bit) 0xD1B284C91EED248BULL, (u64bit) 0xCBA5A08068E8C1F7ULL, (u64bit) 0xC483EE5A2228985DULL, (u64bit) 0xBCAEE9F787AC75EBULL, +(u64bit) 0xB782DAB1B77D3E09ULL, (u64bit) 0xB0D77226F15E387BULL, (u64bit) 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0x2E53167EC64B703BULL, (u64bit) 0x1264ED670CD61961ULL, +(u64bit) 0x071F216A9AB74E2DULL, (u64bit) 0xEE26503C1266CE55ULL, (u64bit) 0x4C6004C7E404E4B5ULL, (u64bit) 0xCB649E41ECE95F85ULL +}; + +} diff --git a/old/botan/src/math/numbertheory/reducer.cpp b/old/botan/src/math/numbertheory/reducer.cpp new file mode 100644 index 0000000..fbd675e --- /dev/null +++ b/old/botan/src/math/numbertheory/reducer.cpp @@ -0,0 +1,97 @@ +/* +* Modular Reducer +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#include <botan/reducer.h> +#include <botan/numthry.h> +#include <botan/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); + mod2_words = modulus_2.sig_words(); + + mu = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words) / modulus; + mu_words = mu.sig_words(); + } + +/* +* Barrett Reduction +*/ +BigInt Modular_Reducer::reduce(const BigInt& x) const + { + if(mod_words == 0) + throw Invalid_State("Modular_Reducer: Never initalized"); + + BigInt t1 = x; + t1.set_sign(BigInt::Positive); + + if(t1 < modulus) + { + if(x.is_negative() && t1.is_nonzero()) + return modulus - t1; + return x; + } + + if(t1 >= modulus_2) + return (x % modulus); + + 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)); + + t1 = t2 - t1; + + if(t1.is_negative()) + { + BigInt b_to_k1(BigInt::Power2, MP_WORD_BITS * (mod_words+1)); + t1 += b_to_k1; + } + + while(t1 >= modulus) + t1 -= modulus; + + if(x.is_negative() && t1.is_nonzero()) + t1 = modulus - t1; + + return t1; + } + +/* +* Multiply, followed by a reduction +*/ +BigInt Modular_Reducer::multiply(const BigInt& x, const BigInt& y) const + { + return reduce(x * y); + } + +/* +* Square, followed by a reduction +*/ +BigInt Modular_Reducer::square(const BigInt& x) const + { + return reduce(Botan::square(x)); + } + +} diff --git a/old/botan/src/math/numbertheory/reducer.h b/old/botan/src/math/numbertheory/reducer.h new file mode 100644 index 0000000..d234e07 --- /dev/null +++ b/old/botan/src/math/numbertheory/reducer.h @@ -0,0 +1,36 @@ +/* +* Modular Reducer +* (C) 1999-2007 Jack Lloyd +* +* Distributed under the terms of the Botan license +*/ + +#ifndef BOTAN_MODARITH_H__ +#define BOTAN_MODARITH_H__ + +#include <botan/bigint.h> + +namespace Botan { + +/* +* Modular Reducer +*/ +class BOTAN_DLL Modular_Reducer + { + public: + BigInt multiply(const BigInt&, const BigInt&) const; + BigInt square(const BigInt&) const; + BigInt reduce(const BigInt&) const; + + bool initialized() const { return (mod_words != 0); } + + Modular_Reducer() { mod_words = 0; } + Modular_Reducer(const BigInt&); + private: + BigInt modulus, modulus_2, mu; + u32bit mod_words, mod2_words, mu_words; + }; + +} + +#endif diff --git a/old/botan/src/math/numbertheory/ressol.cpp b/old/botan/src/math/numbertheory/ressol.cpp new file mode 100644 index 0000000..d51acb8 --- /dev/null +++ b/old/botan/src/math/numbertheory/ressol.cpp @@ -0,0 +1,82 @@ +/* +* 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); + + u32bit 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; + + u32bit i = 0; + while(q != 1) + { + q = mod_p.square(q); + ++i; + } + u32bit t = s; + + if(t <= i) + return -BigInt(1); + + c = power_mod(c, BigInt(BigInt::Power2, t-i-1), p); + r = mod_p.multiply(r, c); + c = mod_p.square(c); + n = mod_p.multiply(n, c); + s = i; + } + + return r; + } + +} |