Comparison of scalar point multiplication algorithms in a low resource device

Abstract

Since it was invented, Elliptic Curve Cryptography (ECC) is considered an ideal choice for implementing public key cryptography in resource constrained devices, thanks to its small keys. Scalar point multiplication is the central and the complex operation in the cryptographic computations of ECC that requires a lot of optimizations on execution time and energy consumption especially in low computing power devices such as embedded systems. Thus, many scalar point multiplication algorithms are proposed, each using their own computational techniques and mathematical formulas. In this paper, we have combined the computational techniques with some optimized mathematical formulas and we have implemented them on some Elliptic Curves scalar point multiplication algorithms over finite field. The aim of this work is to identify the most efficient algorithm that combine the best computational technique and the mathematical formulas, and consequently offer less-memory requirements and faster field arithmetic operations. The results show that Montgomery ladder algorithm in co-Z addition with update formula gives better results compared to the other algorithms implemented in this paper.