Journal of Global Research in Computer Sciences

Journal of Global Research in Computer Sciences

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ISSN: 2229-371X

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A NOVEL HIGH DYNAMIC RANGE 5-MODULUS SET {2^(2n+1), 2^2n+1,2^n+12^(n/2)+1,2^(n/2)-1} WHIT EFFICIENT REVERSE CONVERTER AND REVIEW IMPROVING MODULAR MULTIPLICATION'S DYNAMIC RANGE WITH THIS MODULUS SET

Ramin Aliabadian*1, Mehdi Hosseinzadeh*2, Mehdi Golsorkhtabaramiri 2
  1. Department of Computer Engineering, Islamic Azad University Arak Branch, Arak, Iran
  2. Department of Computer Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran
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Abstract

In last years, many modulus sets in the Residue Number System (RNS) for increasing Dynamic Range (DR) and parallelism are presented. Hence, for reach these purposes a new 5-Moduli Set for even n, and its efficient reverse converter design are introduced in this paper. This modulus set contains pair-wise relatively prime, and it offers the maximum feasible DR. New CRT-I and MRC are used to obtain a high-performance memory-less reverse converter for this modulus set. Also, we review improving the modular multiplication with this modulus set, and its dynamic range compared with other modulus sets

INTRODUCTION
The Residue Number System (RNS) is a valid method for the implementation of fast arithmetic and fault tolerant computing. The RNS with its carry-free operations, parallelism and enhanced fault tolerance properties has been used in computer arithmetic since the 1950s [1]. These characteristics make it very useful in some applications consisting of digital signal processing, fault tolerant systems, image processing systems and cryptography. Different modulus sets have been suggested for the RNS that have different properties with regards to the reverse conversion (Residue to Binary or R/B), Dynamic Range (DR) and arithmetic operations. The moduli of the forms, and are very popular according to their easy arithmetic operations [2]. RNS has achieved more attention by researcher in recent years for its ability to do fast arithmetic operation like addition, subtraction and multiplication [3]. Modular multiplication is the most important aspect of public key cryptography algorithms like RSA and elliptic curve cryptography. RNS is the best way to speed up these applications because of its carry free nature. Efficiency of modular multiplication in RNS is depending on choosing of modulus set. The first step for designing an RNS system is the modulus set selection. The modulus set comprises of a set of pair-wise relatively prime integer numbers.
The dynamic range of an RNS system is defined in terms of the product of the module, and it denotes the interval of integers which can be represented in RNS uniquely. The proper selection of a modulus set has an important role in the design of the RNS systems because the speed of RNS arithmetic unit and the complexity of residue to binary converter is affected of the form and number of the modulus image
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