FHNTT: a flexible Number Theoretic Transform design based on hybrid-radix butterfly

Emerging technologies, such as cloud computing and artificial intelligence, significantly arouse concern about data security and privacy. Homomorphic encryption (HE) is a promising invention, which enables computation on encrypted data without decrypting it so as to ensure data security and privacy. Nevertheless, computation within homomorphic encryption involves time-consuming operations, e.g., Number Theoretic Transform (NTT). The tremendous computation overhead is the critical obstacle in deploying HE applications widely. Besides, in order to meet the performance and security requirements of different applications, it is pivotal to design parametric NTT architecture. In this paper, we propose a flexible and parametric NTT accelerating scheme based on hybrid-radix butterfly, named FHNTT. Specifically, we construct high radix butterfly units and divide the computation of them into several stages such that every stage can be performed pipelined. The number of required twiddle factors declines with the increase of radix value. In addition, we adopt address offset strategy to reduce memory consumption. We implement FHNTT on FPGA due to its fine-grained parallel computing capabilities and customized architecture. Empirical results show that FHNTT has an improved performance compared with other NTT architectures and supports a wide range of parameters. Concretely, FHNTT achieves up to 1.99 × to 2.78 × improvement in latency over other FPGA implementations and the memory utilization rate is up to 94%. Moreover, the flexibility makes FHNTT applicable to multiple use cases.