International Association
for Cryptologic Research

Recognizing the importance of fast and resource-efficient polynomial multiplication in homomorphic encryption, in this paper, we introduce a novel method that enables integer multiplier-less Number Theoretic Transform (NTT) for computing polynomial multiplication. First, we use a Fermat number as an auxiliary modulus of NTT. However, this approach of using Fermat number scales poorly with the degree of polynomial. Hence, we propose a transformation of a large-degree univariate polynomial into small-degree multi-variable polynomials. After that, we compute these NTTs on small-degree polynomials with Fermat number as modulus. We design an accelerator architecture customized for the novel multivariate NTT and use it for benchmarking practical homomorphic encryption applications. The accelerator can achieve a 1,200× speed-up compared to software implementations. We further discuss the potential and limitations of the proposed polynomial multiplication method in the context of homomorphic encryption.