A Highly Unified Reconfigurable Multicore Architecture to Speed Up NTT/INTT for Homomorphic Polynomial Multiplication

Abstract

The ring learning with error (RLWE)-based fully homomorphic encryption (FHE) scheme has become one of the most promising FHE schemes. However, its performance is limited by the homomorphic multiplication, especially the polynomial multiplication which occupies major computing resources. Therefore, efficient implementation of polynomial multiplication is crucial for high-performance FHE applications. In this article, we present an area-efficient and highly unified reconfigurable multicore number theoretic transform (NTT)/inverse NTT (INTT) architecture (named MCNA), which employs NTT and INTT for polynomial multiplier with a variable number of reconfigurable processing elements. To reduce latency, MCNA merges the preprocessing and postprocessing into the constant-geometry NTT and INTT, respectively. Also, a reconfigurable modular multiplier based on digital signal processor (DSP) is proposed to speed up the modular multiplication. In order to avoid designing independent memory access pattern for INTT, a unified read/write structure of NTT/INTT is presented. Furthermore, a novel memory access pattern named “cyclic-sharing” is proposed to reduce 25% memory capacity. MCNA is evaluated on a Xilinx Virtex-7 field-programmable gate array (FPGA) platform. Running at 250-MHz clock frequency, the throughput of MCNA for NTT/INTT achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.78\times \sim 9.32\times $ </tex-math></inline-formula> improvements in comparison to prior works, while the area efficiency of lookup table (LUT) and flip-flop (FF) is improved by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.25\times \sim 4.79\times $ </tex-math></inline-formula> . For polynomial multiplication, the throughput of MCNA achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.73\times \sim 7.69\times $ </tex-math></inline-formula> enhancements, as well as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.13\times \sim 14.8\times $ </tex-math></inline-formula> area efficiency improvements.