PRIME(3)

📦 version 0_git20260208, in alpine 3.24, arch rolling, nixos 26.05, nixpkgs unstable

💅 PRIME(3) — like, the prime(3) page from your Library Functions Manual, bestie

okay so first things first, this is section 3 of the Library Functions Manual, and it's all about prime numbers. yes, those primes. the big ones. the cryptographic ones. grab a strawberry 🍓 and let's go.

✨ NAME ✨

genprime, gensafeprime, genstrongprime, DSAprimes, probably_prime, smallprimetest — prime number generation, babes. that's the whole vibe. 🔥

🌸 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])

like, look at all those includes. u.h, libc.h, mp.h, libsec.h — you need them all, no skipping. 👑

🦋 DESCRIPTION 🦋

Public key algorithms abound in prime numbers, like genuinely obsessed with them. so the following routines either generate primes or test numbers for primality. that's it. that's the whole job. 💅

🌈 the vibes, function by function

🎀 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. quick little vibe check, lowkey. ✨

💜 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. so like, crank up nrep if you want to be sure sure. ngl that's the whole deal. 😭

🌸 genprime

generates a random n bit prime. since it uses the Miller-Rabin test, nrep is the repetition count passed to probably_prime. easy. 🫶

⭐ gensafeprime

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. safe prime behavior, we love to see it. 👑

🔥 genstrongprime

generates a prime, p, with the following properties, and yes you're getting all three:

  • (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

strong prime said "i have layers" and honestly? iconic. 💀

🧚 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. transparency slay. 💖

⚠️ ok bestie listen: Be patient; this is a slow algorithm. like, actually slow. go make a snack, hydrate, come back. 🍓

🐚 SOURCE 🐚

/src/libsec

👀 SEE ALSO 👀

aes(3), blowfish(3), des(3), elgamal(3), rsa(3)

and that's the page!! 🎀 it's PRIME(3) from the Library Functions Manual, section 3, straight outta /src/libsec — stay cryptographic, bestie, mwah 💅💖✨

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