Exploring the Advantages and Challenges of Fermat NTT in FHE Acceleration

Recognizing the importance of a fast and resource-efficient polynomial multiplication in homomorphic encryption, in this paper, we design a multiplier-less number theoretic transform using a Fermat number as an auxiliary modulus. To make this algorithm scalable with the degree of polynomial, we apply a univariate to multivariate polynomial ring transformation. We develop an accelerator architecture for fully homomorphic encryption using these algorithmic techniques for efficient multivariate polynomial multiplication. For practical homomorphic encryption application benchmarks, the hardware accelerator achieves a 1,200 \(\times \) speed-up compared to software implementations. Finally, we conclude the paper by discussing the advantages and limitations of the proposed polynomial multiplication method.