On the Design of RNS Bases for Modular Multiplication

Modular multiplication is the main and basic operation in public key cryptography algorithms like Elliptic Curve Cryptography (ECC). By using Residue Number System (RNS) in these algorithms, large number computation is replaced by computation over the small moduli without carry propagation between moduli. Moduli selection has an important role in the efficiency of modular multiplication. Therefore in this work the moduli sets for modular multiplication with aims of increasing the efficiency of arithmetic operation and speeding up the RNS to RNS conversions are presented. The proposed moduli sets are suitable for ECC. The results show a noticeable improvement in speed comparing to the state-of-the-art.