Implementation of Arithmetic Unit for RNS Using 2n + 3 as Base

Abstract

Choice of a good modulo base number is an important factor in strength of Modular arithmetic used in Cryptography, Digital signal processing (DSP) and in other areas and therefore needs special attention. Existing literature abundantly describes operations with 2n ± 1 as modulo base. The numbers 2n ± 3 are also prime and offer a set of new base numbers for modular arithmetic. In this paper, implementation of modulo 2n + 3 addition based on shifting and distributive law are described. Modulo operation is performed till the final residue is less than 2n + 3. The results are compared with 2n − 3 architectures described in recent literature. The proposed method avoids mapping of bits reported in the earlier work and hence provides an improved architecture for implementation of modular operations.