/************************************************* * Number Theory Functions Header File * * (C) 1999-2007 Jack Lloyd * *************************************************/ #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); /************************************************* * 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