Nested Method for Optimizing Elliptic Curve Scalar Multiplication

Abstract

The algebraic curve that attracted considerable interest in recent years is called Elliptic Curve (EC). This is due to the computational complexity of its arithmetic over a finite field. The complexity of its arithmetic operations granted EC highly interest for many applications, especially in Cryptography. The scalar multiplication plays an important role in the performance of the elliptic curve cryptosystem (ECC). This paper focused on optimizing the performance of this important operation, which is called elliptic curve scalar multiplication (ECSM). As known from previous works, this operation can be sped up using one of the most important representations called Mutual Opposite Form (MOF). Based on this representation, we proposed an algorithm to improve the performance of ECSM. The efficiency of the proposed algorithm is enhanced in terms of computation time compared to the existing standard ECSM methods.

Keywords

• elliptic curve scalar multiplication
• binary method
• mutual opposite form