Faster arithmetic for number-theoretic transforms

We show how to improve the efficiency of the computation of fast Fourier transforms over FpFp 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 Shoupʼs NTL library.