Design of a Flexible Schoenhage-Strassen FFT Polynomial Multiplier with High-Level Synthesis

Homomorphic Encryption (HE) is a promising field because it allows for encrypted data to be sent to and operated on by untrusted parties without the risk of privacy compromise. The benefits and applications of HE are far reaching, especially in regard to cloud computing. However, current HE solutions require resource intensive arithmetic operations such as high precision, high degree polynomial multiplication resulting in a minimum computational complexity of O(n log(n)) on standard CPUs though application of the Fast Fourier Transform (FFT). These operations result in poor overall performance for HE schemes in software and would benefit greatly from hardware acceleration. This work aims to accelerate the multi-precision arithmetic operations used in HE with specific focus on an implementation of the Schönhage-Strassen FFT based multiplication algorithm. It is to be incorporated into a larger HE library of arithmetic functions tuned for High Level Synthesis (HLS) that enables flexible solutions for hardware/software systems on reconfigurable cloud resources. Although this project was inspired by HE, it could be incorporated within a generic mathematical library and support other domains. The developed FFT based polynomial multiplier exhibits flexibility in the selection of security parameters facilitating its use in a wide range of HE schemes and applications. The design also displayed substantial speedup over the polynomial multiplication functions implemented in the Number Theory Library (NTL) utilized by software based HE solutions