PRIME(2)                                                 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 accu-
racy)

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 follow-
ing 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-Rabin test, nrep is the repetition count passed to
probably_prime. Gensafegprime generates an n-bit prime p and
a generator alpha of the multiplicative group of integers
mod p; there is a prime q such that p-1=2*q.  Genstrongprime
generates a prime, p, with the following properties:

-    (p-1)/2 is prime.  Therefore p-1 has a large prime fac-
tor, 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

Page 1                       Plan 9             (printed 1/27/22)

PRIME(2)                                                 PRIME(2)

recommended algorithm for DSA primes.  q divides p-1. The
random seed used is also returned, so that skeptics can
later confirm the computation.  Be patient; this is a slow
algorithm.

SOURCE
/sys/src/libsec