A Multifunctional Unit For Reverse Conversion and Sign Detection Based on The 5-Moduli Set

Abstract

The high dynamic range residue number system (RNS) five-moduli { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } has been recently introduced as an arithmetically balanced five-moduli set for computation-intensive applications on wide operands such as asymmetric cryptography algorithms. The previous dedicated design of RNS components for this moduli set is just an unsigned reverse converter. In order to utilize of the moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } in applications handling with signed numbers, two important components are needed: Sign Detector and Signed Reverse Converter. However, having both of these components results in high hardware requirements which makes RNS impractical. This paper overcomes to this problem by designing a unified unit which can perform both signed reverse conversion as well as sign detection through the reuse of hardware. To the authors knowledge, this is the first attempt to design sign detector for a moduli set including 2n±3 moduli. In order to achieve a hardware-amenable design, we first improved the performance of the previous unsigned reverse converter for the moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 }. Then, we extract a sign detection method from the structure of the reverse converter. Finally, we make the unsigned reverse converter to sign converter through the use of the extracted sign signal from the reverse converter. The experimental results shown that the proposed multifunctional unit has relatively the same performance in terms of area, delay and power-consumption than the previous unsigned reverse converter for the set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } while it can perform two complex signed operations.