term% cat index.txt PRIME(2) System Calls Manual PRIME(2)
NAME
genprime, gensafeprime, genstrongprime, DSAprimes, probably_prime,
smallprimetest - prime number generation
SYNOPSIS
#include <u.h>
#include <libc.h>
#include <mp.h>
#include <libsec.h>
int smallprimetest(mpint *p)
int probably_prime(mpint *p, int nrep)
void genprime(mpint *p, int n, int nrep)
void gensafeprime(mpint *p, mpint *alpha, int n, int accuracy)
void genstrongprime(mpint *p, int n, int nrep)
void DSAprimes(mpint *q, mpint *p, uchar seed[SHA1dlen])
DESCRIPTION
Public key algorithms abound in prime numbers. The following routines
generate primes or test numbers for primality.
Smallprimetest checks for divisibility by the first 10000 primes. It
returns 0 if p is not divisible by the primes and -1 if it is.
Probably_prime uses the Miller-Rabin test to test p. It returns non-
zero if P is probably prime. The probability of it not being prime is
1/4**nrep.
Genprime generates a random n bit prime. Since it uses the Miller-Ra‐
bin test, nrep is the repetition count passed to probably_prime. Gen‐
safegprime generates an n-bit prime p and a generator alpha of the mul‐
tiplicative group of integers mod p; there is a prime q such that
p-1=2*q. Genstrongprime generates a prime, p, with the following prop‐
erties:
- (p-1)/2 is prime. Therefore p-1 has a large prime factor, p'.
- p'-1 has a large prime factor
- p+1 has a large prime factor
DSAprimes generates two primes, q and p, using the NIST recommended al‐
gorithm for DSA primes. q divides p-1. The random seed used is also
returned, so that skeptics can later confirm the computation. Be pa‐
tient; this is a slow algorithm.
SOURCE
/sys/src/libsec
SEE ALSO
aes(2) blowfish(2), des(2), elgamal(2), rsa(2)
PRIME(2)