Comparison of fast modular multiplication architectures in FPGA

Abstract

Modular multiplication is the fundamental operation in most public-key cryptosystem. Therefore, the efficiency of modular multiplication directly affects the efficiency of whole crypto-system. This paper presents implementation and comparison of several recently proposed, highly efficient architectures for modular multiplication on FPGAs: interleaved multiplication, two variants of Montgomery multiplication, Jeong-Burleson multiplication, multiplication based on key size partitioning and complement. Finally, new hardware architecture for time optimal modular multiplication is proposed based on Hamming weight and position of one's in multiplicand.