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 12/4/24) 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 SEE ALSO aes(2) blowfish(2), des(2), elgamal(2), rsa(2) Page 2 Plan 9 (printed 12/4/24)