= ipints: genprime, gensafeprime, genstrongprime, DSAprimes, probably_prime : prime number generation     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 This set of functions in IPints (see ipints(2))  helps  Limboapplications generate and test large prime numbers with rela‐tive efficiency.  The numbers are all represented by IPint. Probably_prime uses the Miller-Rabin  test  to  test  n.   Itreturns  true  (non-zero) if P is probably prime.  The proba‐bility of n not being prime is 1/4**nrep.  If  probably_primereturns false (zero), n is certainly not prime. Genprime  returns  a  random prime of length nbits.  Since ituses the Miller-Rabin test,  nrep  is  the  repetition  countpassed to probably_prime. Gensafeprime  returns  a tuple (p, alpha), where p is a primeof length nbits and alpha is a generator of  the  multiplica‐tive  group  of  integers mod p; there is a prime q such thatp-1=2*q. Genstrongprime returns a prime p with the  following  proper‐ties: -      (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  generatingDSA  primes  and  returns a tuple (q, p, seed), where p and qare primes, and q divides p-1.  The random seed used is  alsoreturned, 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 ALSOcrypt-intro(2),   crypt-crypt(2),   crypt-dsagen(2),   crypt-gensk(2), ipints(2)