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 .TH PRIME 3 .SH NAME genprime, gensafeprime, genstrongprime, DSAprimes, probably_prime, smallprimetest \- prime number generation .SH SYNOPSIS .B #include .br .B #include .br .B #include .br .B #include .PP .B int smallprimetest(mpint *p) .PP .B int probably_prime(mpint *p, int nrep) .PP .B void genprime(mpint *p, int n, int nrep) .PP .B void gensafeprime(mpint *p, mpint *alpha, int n, int accuracy) .PP .B void genstrongprime(mpint *p, int n, int nrep) .PP .B void DSAprimes(mpint *q, mpint *p, uchar seed[SHA1dlen]) .SH DESCRIPTION .PP Public key algorithms abound in prime numbers. The following routines generate primes or test numbers for primality. .PP .I Smallprimetest checks for divisibility by the first 10000 primes. It returns 0 if .I p is not divisible by the primes and \-1 if it is. .PP .I Probably_prime uses the Miller-Rabin test to test .IR p . It returns non-zero if .I P is probably prime. The probability of it not being prime is 1/4**\fInrep\fR. .PP .I Genprime generates a random .I n bit prime. Since it uses the Miller-Rabin test, .I nrep is the repetition count passed to .IR probably_prime . .I Gensafegprime generates an .IR n -bit prime .I p and a generator .I alpha of the multiplicative group of integers mod \fIp\fR; there is a prime \fIq\fR such that \fIp-1=2*q\fR. .I Genstrongprime generates a prime, .IR p , with the following properties: .IP \- (\fIp\fR-1)/2 is prime. Therefore .IR p -1 has a large prime factor, .IR p '. .IP \- .IR p '-1 has a large prime factor .IP \- .IR p +1 has a large prime factor .PP .I DSAprimes generates two primes, .I q and .IR p, using the NIST recommended algorithm for DSA primes. .I q divides .IR p -1. The random seed used is also returned, so that skeptics can later confirm the computation. Be patient; this is a slow algorithm. .SH SOURCE .B \*9/src/libsec .SH SEE ALSO .IR aes (3) .IR blowfish (3), .IR des (3), .IR elgamal (3), .IR rsa (3),