A New Moduli Set {3n - 1,3n+1,3n + 2,3n - 2} in Residue Number System

Residue Number System (RNS) is non weighted system. This system is a useful tool for Digital Signal Processing (DSP) since it can support parallel, carry-free, high-speed, low power and secure arithmetic. One of the most important considerations when designing RNS systems is the choice of the moduli set. This is due to the fact that the system´s speed, its dynamic range, as well as its hardware complexity depend on both the forms and the number of the chosen moduli. Researchers have considered many moduli sets to be the basis of a RNS processor: {2ⁿ-1,2ⁿ,2ⁿ⁺¹}, {2ⁿ,2ⁿ-1,2^n-1-1} , {rⁿ-2,rⁿ-1,rⁿ}, {r^a,r^b -1,r^c +1} and many others. In this paper a new moduli set {3ⁿ - 1, 3ⁿ + 1, 3ⁿ + 2, 3ⁿ - 2} is introduced. Comparisons demonstrate that we have achieved a significant improvement in terms of speed, security, dynamic range and simple of selection moduli.