Journal of Computations & Modelling

Four Moduli RNS Bases for Efficient Design of Modular Multiplication

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• Abstract

  Residue Number System provides parallel and fast arithmetic operation by replacing large number computation with small moduli without carry propagation between moduli. RNS can be applied in application like public key cryptography in order to achieve more speed and less power consumption. Modular Multiplication is the main operation in this application. Selecting RNS moduli sets (bases) is the most important part in modular multiplication. In this work RNS bases in order to design efficient modular multiplication is presented. The proposed RNS bases in first basis employs the basis and multiplicative inverses with small hamming weight based on the work reported in literature and in second basis, well formed arithmetic unit RNS basis with efficient forward and reverse converter are employed. The proposed RNS bases are suitable for public key cryptography algorithm especially for Elliptic Curve Cryptography (ECC). The results show that combination of these RNS basis has achieved noticeable improvement in hardware complexity and also less time delay.