A new left-to-right scalar multiplication algorithm using a new recoding technique

Abstract

Elliptic Curve Cryptosystem (ECC) is a well-known cryptosystem for securing the communications. The most important operation in ECC is scalar multiplication. The integer representation plays an important role in the performance of this operation. This paper presents and evaluates a novel recoding technique which reduces the average Hamming weight of integers. The Left-to-Right (L2R) scalar multiplication is modified to utilize this new integer representation. Our analysis shows that the computation cost (the number of required point addition/subtraction operation) in the proposed L2R scalar multiplication algorithm is effectively reduced in comparison with other modified L2R binary scalar multiplication algorithms. © 2014 SERSC.