Arithmetic Units for RNS Moduli {2n-3} and {2n+3} Operations

A new moduli set {2ⁿ - 1, 2ⁿ + 3, 2ⁿ + 1, 2ⁿ - 3} has recently been proposed to represent numbers in Residue Number Systems (RNS), increasing the number of channels. With this, the processing time can be reduced by simultaneously exploiting the carry-free characteristic of the modular arithmetic and improving the parallelism. In this paper, hardware structures for addition and multiplication operation in RNS for the moduli {2ⁿ - 3} and {2ⁿ + 3} are proposed and analyzed. In order to evaluate the performance of the proposed units they were implemented on an ASIC technology. The obtained experimental results suggest that the performance of the moduli {2ⁿ ± 3} are acceptable but demand more area resource and impose a larger delay than the typically used {2ⁿ ± 1} arithmetic units. Addition units require at least 42% more area for a performance identical to the {2ⁿ + 1} modulo adder. The multiplication units require up to 37% more area and impose a delay 25% higher. This paper also suggests that more balanced moduli sets should be developed in order to achieve more efficient RNS.