Effective Reverse Converter for General Three Moduli Set{(2^n)-1,(2^n)+1,(2^(pn+1))-1}

Abstract

Abstract-Residue number system is a non-weighted integer number system which uses the residues of division of ordinary numbers by some modules for representing that ordinary numbers. In this paper, the general three moduli set }2 n -1,2 n +1,2 pn+1 -1} based on CRT algorithm is proposed in which -p‖ is an even number greater than zero. The special case of this set for p=2 which is }2 n -1,2 n +1,2 2n+1 -1{ is also described in this paper. Since the dynamic range of this set is odd, some difficult problems in RNS can be easily solved based on this set using parity checking. The proposed reverse converter is better in speed and hardware in comparison to reverse converters in similar dynamic range. Moreover, from the complexity point of view, the internal arithmetic circuits of this moduli set is improved and is less complex than the other sets in similar dynamic range.

A Multi-Layered Data Encryption and Decryption Scheme Based on Genetic Algorithm and Residual Numbers

“…Each ϑ i is within the range 0 ≤ ϑ i ≤ m i , [27], such that a positive integer, X , in the interval [0, M ) can be uniquely represented. The MRC technique makes use of mod-m i instead of mod-M as in the case of the CRT thereby reducing the complexity of the architecture.…”