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/*
* Number Theory Functions
* (C) 1999-2007 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#ifndef BOTAN_NUMBER_THEORY_H_
#define BOTAN_NUMBER_THEORY_H_
#include <botan/bigint.h>
namespace Botan {
class RandomNumberGenerator;
/**
* Fused multiply-add
* @param a an integer
* @param b an integer
* @param c an integer
* @return (a*b)+c
*/
BigInt BOTAN_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) sub_mul(const BigInt& a,
const BigInt& b,
const BigInt& c);
/**
* Fused multiply-subtract
* @param a an integer
* @param b an integer
* @param c an integer
* @return (a*b)-c
*/
BigInt BOTAN_PUBLIC_API(2,0) mul_sub(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_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) lcm(const BigInt& x, const BigInt& y);
/**
* @param x an integer
* @return (x*x)
*/
BigInt BOTAN_PUBLIC_API(2,0) square(const BigInt& x);
/**
* Modular inversion
* @param x a positive integer
* @param modulus a positive integer
* @return y st (x*y) % modulus == 1 or 0 if no such value
* Not const time
*/
BigInt BOTAN_PUBLIC_API(2,0) inverse_mod(const BigInt& x,
const BigInt& modulus);
/**
* Const time modular inversion
* Requires the modulus be odd
*/
BigInt BOTAN_PUBLIC_API(2,0) ct_inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod);
/**
* Return a^-1 * 2^k mod b
* Returns k, between n and 2n
* Not const time
*/
size_t BOTAN_PUBLIC_API(2,0) almost_montgomery_inverse(BigInt& result,
const BigInt& a,
const BigInt& b);
/**
* Call almost_montgomery_inverse and correct the result to a^-1 mod b
*/
BigInt BOTAN_PUBLIC_API(2,0) normalized_montgomery_inverse(const BigInt& a, const BigInt& b);
/**
* 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)
*/
int32_t BOTAN_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) 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_PUBLIC_API(2,0) low_zero_bits(const BigInt& x);
/**
* Check for primality
* @param n a positive integer to test for primality
* @param rng a random number generator
* @param prob chance of false positive is bounded by 1/2**prob
* @param is_random true if n was randomly chosen by us
* @return true if all primality tests passed, otherwise false
*/
bool BOTAN_PUBLIC_API(2,0) is_prime(const BigInt& n,
RandomNumberGenerator& rng,
size_t prob = 56,
bool is_random = false);
inline bool quick_check_prime(const BigInt& n, RandomNumberGenerator& rng)
{ return is_prime(n, rng, 32); }
inline bool check_prime(const BigInt& n, RandomNumberGenerator& rng)
{ return is_prime(n, rng, 56); }
inline bool verify_prime(const BigInt& n, RandomNumberGenerator& rng)
{ return is_prime(n, rng, 80); }
/**
* 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 that (prime - 1) 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
* @param prob use test so false positive is bounded by 1/2**prob
* @return random prime with the specified criteria
*/
BigInt BOTAN_PUBLIC_API(2,0) random_prime(RandomNumberGenerator& rng,
size_t bits,
const BigInt& coprime = 0,
size_t equiv = 1,
size_t equiv_mod = 2,
size_t prob = 128);
/**
* 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_PUBLIC_API(2,0) random_safe_prime(RandomNumberGenerator& rng,
size_t bits);
/**
* Generate DSA parameters using the FIPS 186 kosherizer
* @param rng a random number generator
* @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<uint8_t> BOTAN_PUBLIC_API(2,0)
generate_dsa_primes(RandomNumberGenerator& rng,
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 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
* @param offset optional offset from seed to start searching at
* @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_PUBLIC_API(2,0)
generate_dsa_primes(RandomNumberGenerator& rng,
BigInt& p_out, BigInt& q_out,
size_t pbits, size_t qbits,
const std::vector<uint8_t>& seed,
size_t offset = 0);
/**
* The size of the PRIMES[] array
*/
const size_t PRIME_TABLE_SIZE = 6541;
/**
* A const array of all primes less than 65535
*/
extern const uint16_t BOTAN_PUBLIC_API(2,0) PRIMES[];
}
#endif
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