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IPINTS-GENPRIME(2)					    IPINTS-GENPRIME(2)

NAME
       ipints:	 genprime,  gensafeprime,  genstrongprime,  DSAprimes,	proba‐
       bly_prime  - prime number generation

SYNOPSIS
       include "ipints.m";
       ipints := load IPints IPints->PATH;
       IPint: import ipints;

       probably_prime: fn(n: ref IPint, nrep: int): int;

       genprime: fn(nbits: int, nrep: int): ref IPint;
       gensafeprime: fn(nbits: int, nrep: int): (ref IPint, ref IPint); # p, alpha
       genstrongprime: fn(nbits: int, nrep: int): ref IPint;
       DSAprimes: fn(): (ref IPint, ref IPint, array of byte);	   # q, p, seed

DESCRIPTION
       This set of functions in IPints (see ipints(2))	helps  Limbo  applica‐
       tions  generate	and test large prime numbers with relative efficiency.
       The numbers are all represented by IPint.

       Probably_prime uses the Miller-Rabin test to test n.  It	 returns  true
       (non-zero)  if  P  is  probably	prime.	The probability of n not being
       prime is 1/4**nrep.  If probably_prime returns false (zero), n is  cer‐
       tainly not prime.

       Genprime	 returns  a  random  prime of length nbits.  Since it uses the
       Miller-Rabin test, nrep	is  the	 repetition  count  passed  to	proba‐
       bly_prime.

       Gensafeprime  returns  a tuple (p, alpha), where p is a prime of length
       nbits and alpha is a generator of the multiplicative group of  integers
       mod p; there is a prime q such that p-1=2*q.

       Genstrongprime returns 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 uses the NIST recommended algorithm for generating DSA primes
       and returns a tuple (q, p, seed), where p  and  q  are  primes,	and  q
       divides	p-1.   The random seed used is also returned, so that sceptics
       can later confirm the computation.

SOURCE
       /libinterp/ipint.c
       /libsec/port/probably_prime.c
       /libsec/port/dsaprimes.c
       /libsec/port/genprime.c
       /libsec/port/gensafeprime.c
       /libsec/port/genstrongprime.c

SEE ALSO
       crypt-intro(2),	 crypt-crypt(2),   crypt-dsagen(2),    crypt-gensk(2),
       ipints(2)

							    IPINTS-GENPRIME(2)
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