Implementation of stream cipher system based on representation of integers in residue number system

Abstract

Residue Number Systems (RNS) based on Chinese Remainder Theorem (CRT) permits the representation of large integers in terms of combinations of smaller ones. The set of all integers from 0 to M-1 with RNS representation and component wise modular addition and multiplication constitutes direct sum of smaller commutative rings. Encryption and decryption algorithm based on the properties of direct sum of smaller rings offers distinct advantages over decimal or fixed radix arithmetic. In this paper representation of integer using RNS, is successfully utilized in additive, multiplicative and affine stream cipher systems. The property of the cipher system based on RNS number system allow speeding up the encryption / decryption algorithm, reduce the time complexity and provides immunity to side channel, algebraic, and known plain text attacks. In this paper, the characteristics of additive, multiplicative and affine stream cipher systems, the key generation, and encryption and decryption based on RNS number system representation are discussed. �2010 IEEE.