Alternative Redundant Residue Number System Construction with Redundant Residue Representations

Residue number system (RNS) is a number representation system that represents a large integer with several smaller integers. Due to its ability to perform addition and multiplication in parallel, RNS is widely used in signal processing, communication, and cryptography. To extend the ability of RNS, redundant residue number system (RRNS), which has abilities to detect and correct errors, is proposed to be used in fault tolerant applications. Currently, there are two major ways to construct RRNS from RNS. This paper proposes an alternative way to do the construction by using redundant residue representations. Our proposed RRNS can perform certain operations more efficiently, for example, backward conversion and error detection, and can also perform a complex RNS operation, namely, comparing the values between two RRNS representations. However, it would have more costs to perform addition and multiplication on our RRNS. We also compare our work to the two previous works, and discuss their advantages and drawbacks. Further investigations are required to improve the performance of the proposed RRNS.