- License
- Botan is released under the Simplified BSD License (see LICENSE.md)
Number Theory Functions
BigInt mulAdd()(auto ref const BigInt a, auto ref const BigInt b, auto ref const BigInt c);
- Parameters
BigInt a an integer BigInt b an integer BigInt c an integer - Returns
- (a*b)+c
Fused multiply-add
BigInt subMul()(auto ref const BigInt a, auto ref const BigInt b, auto ref const BigInt c);
- Parameters
BigInt a an integer BigInt b an integer BigInt c an integer - Returns
- (a-b)*c
Fused subtract-multiply
BigInt abs()(auto ref const BigInt n);
- Parameters
BigInt n an integer - Returns
- absolute value of n
Return the absolute value
BigInt gcd()(auto ref const BigInt a, auto ref const BigInt b);
- Parameters
BigInt a positive integer x BigInt b positive integer y - Returns
- gcd(x,y)
Compute the greatest common divisor
BigInt lcm()(auto ref const BigInt a, auto ref const BigInt b);
- Parameters
BigInt a a positive integer x BigInt b a positive integer y - Returns
- z, smallest integer such that z % x == 0 and z % y == 0
Least common multiple
BigInt square()(auto ref const BigInt x);
- Parameters
BigInt x an integer - Returns
- (x*x)
BigInt inverseMod()(auto ref const BigInt n, auto ref const BigInt mod);
- Parameters
BigInt n a positive integer x BigInt mod a positive integer modulus - Returns
- y st (x*y) % modulus == 1
Modular inversion
int jacobi()(auto ref const BigInt a, auto ref const BigInt n);
- Parameters
BigInt a is a non-negative integer BigInt n is an odd integer > 1 - Returns
- (n / m)
Compute the Jacobi symbol. If n is prime, this is equivalent to the Legendre symbol. @see http://mathworld.wolfram.com/JacobiSymbol.html
BigInt powerMod()(auto ref const BigInt base, auto ref const BigInt exp, auto ref const BigInt mod);
- Parameters
BigInt base an integer base b BigInt exp a positive exponent x BigInt mod a positive modulus m - Returns
- (b^x) % m
Modular exponentation
BigInt ressol()(auto ref const BigInt a, auto ref const BigInt p);
- Parameters
BigInt a the input x BigInt p the prime p - Returns
- y such that (y*y)%p == x, or -1 if no such integer
Compute the square root of x modulo a prime using the Shanks-Tonnelli algorithm
size_t lowZeroBits()(auto ref const BigInt n);
- Parameters
BigInt n a positive integer x - Returns
- 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.
bool isPrime()(auto ref const BigInt n, RandomNumberGenerator rng, size_t prob = 56, bool is_random = false);
- Parameters
BigInt n a positive integer to test for primality RandomNumberGenerator rng a random number generator size_t prob chance of false positive is bounded by 1/2**prob bool is_random true if n was randomly chosen by us - Returns
- true if all primality tests passed, otherwise false
Check for primality using Miller-Rabin
BigInt randomPrime()(RandomNumberGenerator rng, size_t bits, ref const BigInt coprime, size_t equiv = 1, size_t modulo = 2);
BigInt randomPrime()(RandomNumberGenerator rng, size_t bits, const BigInt coprime = 1, size_t equiv = 1, size_t modulo = 2);
- Parameters
RandomNumberGenerator rng a random number generator size_t bits how large the resulting prime should be in bits BigInt coprime a positive integer the result should be coprime to size_t equiv a non-negative number that the result should be equivalent to modulo equiv_mod size_t modulo the modulus equiv should be checked against - Returns
- random prime with the specified criteria
Randomly generate a prime
BigInt randomSafePrime(RandomNumberGenerator rng, size_t bits);
- Parameters
RandomNumberGenerator rng a random number generator size_t bits is how long the resulting prime should be - Returns
- prime randomly chosen from safe primes of length bits
Return a random 'safe' prime, of the form p=2*q+1 with q prime
Vector!ubyte generateDsaPrimes(RandomNumberGenerator rng, AlgorithmFactory af, ref BigInt p_out, ref BigInt q_out, size_t pbits, size_t qbits);
- Parameters
RandomNumberGenerator rng a random number generator AlgorithmFactory af an algorithm factory BigInt p_out where the prime p will be stored BigInt q_out where the prime q will be stored size_t pbits how long p will be in bits size_t qbits how long q will be in bits - Returns
- random seed used to generate this parameter set
Generate DSA parameters using the FIPS 186 kosherizer
bool generateDsaPrimes()(RandomNumberGenerator rng, AlgorithmFactory af, ref BigInt p_out, ref BigInt q_out, size_t pbits, size_t qbits, auto ref const Vector!ubyte seed_c);
- Parameters
RandomNumberGenerator rng a random number generator AlgorithmFactory af an algorithm factory BigInt p_out where the prime p will be stored BigInt q_out where the prime q will be stored size_t pbits how long p will be in bits size_t qbits how long q will be in bits Vector!ubyte seed_c the seed used to generate the parameters - Returns
- true if seed generated a valid DSA parameter set, otherwise false. p_out and q_out are only valid if true was returned.
Generate DSA parameters using the FIPS 186 kosherizer