Faster arithmetic for number-theoretic transforms

TL;DR

This paper presents optimized arithmetic techniques to enhance the efficiency of number-theoretic transforms over prime fields, significantly outperforming existing libraries through reduced modular reductions.

Contribution

The paper introduces a redundant representation method to decrease modular reductions, improving the speed of FFT computations over prime fields.

Findings

Significant performance improvements over NTL library

Reduction in the number of modular reductions needed

Effective optimization of basic arithmetic operations

Abstract

We show how to improve the efficiency of the computation of fast Fourier transforms over F_p where p is a word-sized prime. Our main technique is optimisation of the basic arithmetic, in effect decreasing the total number of reductions modulo p, by making use of a redundant representation for integers modulo p. We give performance results showing a significant improvement over Shoup's NTL library.