Design of a Flexible Schönhage-Strassen FFT Polynomial Multiplier with High- Level Synthesis to Accelerate HE in the Cloud

Homomorphic Encryption (HE) allows for encrypted data to be sent to, stored, 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 a large number of resource intensive arithmetic operations such as high precision, high degree polynomial multiplication. This work aims to accelerate the multi-precision arithmetic operations used in HE with specific focus on an implementation of the Schönhage-Strassen Fast Fourier Transform (FFT)-based multiplication algorithm. It is planned 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. The developed FFT based polynomial multiplier exhibits flexibility in the selection of HE security parameters facilitating its use in a wide range of schemes and applications. The design yields substantial speedup over the polynomial multiplication functions implemented in the Number Theory Library (NTL) utilized by software based HE solutions.