RobinJadoul / pm1

Pollard's p - 1, in rust, with python bindings

Pollard's p - 1 algorithm for factorization

Written in rust, using pyo3 to provide python bindings and primesieve for fast prime enumeration. libprimesieve.so and primesieve.hpp are required for compilation and running, and assumed to be present on the machine.

The pm1 function provides a factorization with a slightly unusual interface, see below, and pm1base is the same thing, but where you can specify the base a of the exponentiation pow(a, M, n). Additionally pm1_factorbase allows you to specify a a custom factor base for the algorithm, rather than the default choice of primes below 2^n.

The interface provided by pm1 and pm1base will compute $x = a^{M_1 \cdot M_2} \mod n$ and test whether $\gcd(x, n)$ reveals a factor of $n$. Here, $M_0 = \prod_{p \le B_1} p^{\mathrm{exp}}$ and $M_1 = \prod_{B_1 \le p \le B_2} p$. This choice was made for the cases where small prime factors are more likely to have multiple occurences. More control can be achieved with the python bindings and repeated use of the pm1_factorbase approach. The classical extension of a second bound between under which only a single prime factor can be tolerated is currently not implemented.

A rust-driven CLI tool is provided that can perform the pm1base functionality. If you want to compile the CLI only, without python bindings being involved, use the --no-default-features flag for cargo.