Implementing Modular FFTs in FPGAs -- A Basic Block for Lattice-Based Cryptography

Modular FFTs are essential primitives in many application fields. This paper explores the improvements that can be obtained through the use of an FPGA device for implementing modular FFTs. Although the architectural study presented in this paper is generic, the implementation has been particularized for the field of Lattice-based Cryptography, which uses modular FFTs. We present three main FPGA implementation variants for a modular FFT and perform a thorough scalability analysis for the parameters set proposed in the literature so far for the SWIFFT(X) hash function (an FFT of order 64 on Z₂₅₇).