Efficient Implementation of RNS Montgomery Multiplication Using Balanced RNS Bases

Point multiplication is the most important part of elliptic curve cryptography which consumes remarkable time of implementation. Therefore efficiency enhancement of entire system is depending on efficiency of this part. Increasing the efficiency of the modular multiplication improve overall performance of the cryptographic system as it frequency used in some application such as Elliptic Curve Cryptography. By applying Residue Number System (RNS) to Montgomery multiplication as a method for modular multiplication, delay of modular multiplication will be reduced. Appropriate RNS moduli sets replace time consuming operation of multiplication by smaller operations. In this paper two balanced moduli set with proper dynamic range is presented and the efficiency of conversion from RNS to RNS which is the most time consuming part of the Montgomery modular multiplication will be increased.