A Pure Combinational Logic Gate Based Forward Converter for New Five Moduli Set RNS

Choosing a proper moduli set for Residue Number System based building blocks greatly affects the performance of the whole system. The prevalent issue is that as the number of moduli increases the speed of the residue arithmetic units increases, whereas the forward converters (Binary to Residue converters) and Reverse converters (Residue to Binary converters) become slower and more complex. Different moduli sets with efficient converter are proposed by researchers. One of the most well formed special moduli set is {2ⁿ - 1, 2ⁿ, 2ⁿ + 1}. However some applications like cryptography algorithms require a very large dynamic range which cannot be achieved efficiently using the special moduli sets that consists of three or four moduli. When the required dynamic range is very large, these moduli have to be large, which results in lower performance of the arithmetic units in each modulo channel. In that case, the best solution is to use many small moduli (five or more) to represent the large dynamic range efficiently. In this paper a new novel five moduli set {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2ⁿ⁺¹ - 1, 2^n-1 - 1} for even n with its forward conversion circuits are proposed. The proposed moduli set have a dynamic range that can represent up to 5n - 1 bits while keeping the moduli small enough and the converters efficient.