prime(3) - Plan 9 from User Space

| PRIME(3) | PRIME(3)
| 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-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 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 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
| `/usr/lib/plan9/src/libsec`
SEE ALSO
| aes(3) blowfish(3), des(3), elgamal(3), rsa(3),