FPGA Implementation of Modular Multiplier in Residue Number System

Abstract

This work presents a description of a highperformance hardware implementation of a Montgomery modular multiplier using a residue number system (RNS). An RNS can be considered as self-defense against simple power analysis (SPA) and differential power analysis (DPA) attacks, and can be used for public-key cryptography, such as the Rivest, Shamir and Adleman (RSA) cryptosystem and elliptic curve cryptosystems (ECC). Various kinds of security are required for Big Data analysis. The proposed RNS-based modular multiplier is suitable for public-key cryptography that can be used for Big Data security. It is implemented on field-programmable gate-array (FPGA) technology and optimized by trying different variants of the Montgomery Algorithm on it. The proposed RNS-based modular multiplication takes only 22 ns on the Xilinx Virtex-II FPGA. In addition, it needs relatively few resources on the FPGA, needing only 68 slices.