A parallel implementation for polynomial multiplication modulo a prime

Abstract

We present a parallel implementation in Cilk C of a modular algorithm for multiplying two polynomials in Zq[x] for integer q > 1, for multi-core computers. Our algorithm uses Chinese remaindering. It multiplies modulo primes p1, p2, ... in parallel and uses a parallel FFT for each prime. Our software multiplies two polynomials of degree 109 modulo a 32 bit integer q in 83 seconds on a 20 core computer.