A random number generator for generating large prime numbers, suitable for cryptography.
glass_pumpkin
is a cryptographically-secure, random number generator, useful for generating large prime numbers.
This library was inspired by pumpkin except its meant to be used with rust stable.
It also lowers the 512-bit restriction to 128 bits so these can be generated and used for elliptic curve prime fields.
It exposes the prime testing functions as well.
This crate uses num-bigint instead of ramp
. I have found
num-bigint
to be just as fast as ramp
for generating primes. On average a prime is generated in less
than 200ms and safe primes about 10 seconds on modern hardware.
Add the following to your Cargo.toml
file:
glass-pumpkin = "0.3"
extern crate glass_pumpkin;
use glass_pumpkin::prime;
fn main() {
let p = prime::new(1024);
let q = prime::new(1024);
let n = p * q;
println!("{}", n);
}
You can also supply OsRng
and generate primes from that.
extern crate glass_pumpkin;
extern crate rand;
use glass_pumpkin::prime;
use rand::rngs::OsRng;
use rand::thread_rng;
fn main() {
let mut rng = OsRng::new().unwrap();
let p = prime::from_rng(1024, &mut rng);
let q = prime::from_rng(1024, &mut rng);
let n = p * q;
println!("{}", n);
}
Primes
are generated similarly to OpenSSL except it applies some recommendations from the Prime and Prejudice paper and uses
the Baliilie-PSW method:
- Generate a random odd number of a given bit-length.
- Divide the candidate by the first 2048 prime numbers. This helps to eliminate certain cases that pass Miller-Rabin but are not prime.
- Test the candidate with Fermat's Theorem.
- Runs log2(bitlength) + 5 Miller-Rabin tests with one of them using generator
2
. - Run lucas test.
Safe primes require (n-1)/2 also be prime.
You can use this crate to check numbers for primality.
extern crate glass_pumpkin;
extern crate num_bigint;
use glass_pumpkin::prime;
use glass_pumpkin::safe_prime;
use num_bigint::BigUint;
fn main() {
if prime::check(&BigUint::from(5)) {
println!("is prime");
}
if safe_prime::check(&BigUint::from(7)) {
println!("is safe prime");
}
}
Stronger prime checking that uses the Baillie-PSW method is an option
by using the strong_check
methods available in the prime
and safe_prime
modules. Primes generated by this crate will pass the Baillie-PSW
test when using cryptographically secure random number generators. For now,
prime::new()
and safe_prime::new()
will continue to use generation
method as describe earlier.