3.9 Number theory

This library provides operations from number theory that frequently arise in cryptographic applications, complementing the existing built-ins and GMP bindings:

[det]crypto_modular_inverse(+X, +M, -Y)

Compute the modular multiplicative inverse of the integer X. Y is unified with an integer such that X*Y is congruent to 1 modulo M.

[det]crypto_generate_prime(+N, -P, +Options)

Generate a prime P with at least N bits. Options is a list of options. Currently, the only supported option is:

safe(Boolean)

If Boolean is true (default is false), then a safe prime is generated. This means that P is of the form 2*Q + 1 where Q is also prime.

[semidet]crypto_is_prime(+P, +Options)

True iff P passes a probabilistic primality test. Options is a list of options. Currently, the only supported option is:

iterations(N)

N is the number of iterations that are performed. If this option is not specified, a number of iterations is used such that the probability of a false positive is at most 2^(-80).