There are many methods for RNS implementation. The Bajard method is the fastest RNS implementation until now. One of the goals of this paper is to optimize this method to achieve higher performance for hardware implementation of RSA cryptosystem. Higher performance means increase in processing speed and less area. Proper hardware architectures for this method are proposed. For this purpose the number of multiplications is the criterion of the processing speed and the required memory for saving the constant values indicates the area required for this system. The number of multiplications is reduced by 400/(3k+ 11) percent (k is the number of modulus) in the final improved system and the number of constant values reduced by 50 percent.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of a nonlinear additive functional equation in RNS.

Residue Number System (RNS) is a carry-free and non-weighed integer system. In this paper an improved three-moduli set {2n-1, 2n+1,2pn-1} in reverse converter based on CRT algorithm is proposed. CRT algorithm can perform a better delay and hardware implementation in modules via other algorithms. This moduli is based on p that covers a wide range on modules and supports the whole range of its modules in dynamic range. With growth in moduli, many types of modules have been proposed. By using dynamic range we can solve many problems in Residue Number System (RNS) by just one three moduli. In proposed moduli set of this paper in Residue Number System (RNS), the internal circuit is improved and thus, complexity of circuit, energy consumption and power consumption in our proposed design is improved. These improvements are shown in evaluation in terms of CSA adders, CPA adders and delay.

Background and Objectives: Residue number system (RNS) is considered as a prominent candidate for high-speed arithmetic applications due to its limited carry propagation, fault tolerance, and parallelism in “Addition”, “Subtraction”, and “Multiplication” operations. Whereas, “Comparison”, “Division”, “Scaling”, “Overflow Detection” and “Sign Detection” are considered as complicated operations in residue number systems, which have also received a surge of attention in a multitude of publications. Efficient realization of Comparators facilitates other hard-to-implement operations and extends the spectrum of RNS applications. Such comparators can substitute the straightforward method (i.e. converting the comparison operands to binary and comparing them with wide word binary comparators) to compare RNS numbers. Methods: Dynamic Range Partitioning (DRP) method has shown advantages for comparing unsigned RNS numbers in the 3-moduli sets {2^n,2^n±1} and {2^n,2^n-〖1,2〗^(n+1)-1}, in comparison with other methods. In this paper, we employed DRP components and designed a unified unit that detects the sign of operands and also compares numbers, for the 5-moduli set γ={2^2n,2^n±1,2^n±3}. This unit can be used for comparison of signed and also unsigned RNS numbers in the moduli set γ.Results: Synthesized comparison results reveal 47% (54%) speed-up, 35% (32%) less area consumption, 25% (24%) lower power dissipation, and 60% (65%) less energy for n=8 (16) in comparison to the straightforward signed comparator. Conclusion: According to the results of this study, DRP method for sign detection and comparison operations outperforms other methods in different moduli sets including 5-moduli set γ={2^2n,2^n±1,2^n±3}.

In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of the arithmetic operations. But as a result of using the non-weighted system, the performance of some calculations such as comparison and reverse conversion is extraordinarily difficult as compared with binary representation. We can use the benefits of both representations in the novel system and this scheme has a simple implementation for reverse/forward conversion.