Algorithm for Clustering the Moduli of RNS for the Application of Optimization of Time Complexity in Standard Cipher System

Abstract

Residue number system (RNS) has emerged as a knocking field of research due to its high speed, fault tolerant, carry free and parallel characteristics. Due to these features it has got important role in high performance computing especially with reduced delay. There are various algorithms have been found as a result of the research with respect to RNS. Additionally, since RNS reduces word length due to the modular operations, its computations are faster compared to binary computations. But the major challenges are the selection of moduli sets for the forward (decimal to residue numbers) and reverse (residue numbers to decimal) conversion. RNS performance is purely depending on how efficiently an algorithm computes / chooses the moduli sets [1]-[6]. This paper proposes new method for selecting the moduli sets and its usage in cryptographic applications based on Schonhage modular factorization. The paper proposes six moduli sets {6qk1, 6qk+1, 6qk+3, 6qk+5, 6qk+7, 6qk+11} for the RNS conversions but the Schonhage moduli sets are expressed as the exponents that creates a large gap between the moduli’s computed. Hence, a new method is proposed to for computing moduli sets that helps in representing all the decomposed values approximately in the same range.