Faster Scalar Multiplication Algorithm to Implement a Secured Elliptic Curve Cryptography System

Elliptic Curve Cryptography provides similar strength of protection comparing other public key cryptosystems but requires significantly smaller key size. This paper proposes a new faster scalar multiplication algorithm aiming at a more secured Elliptic Curve Cryptography scheme. This paper also proposes a novel Elliptic Curve Cryptography scheme where maximum length random sequence generation method is utilized as data mapping technique on elliptic curve over a finite field. The proposed scheme is tested on various bits length of prime field and key sizes. The numerical experiments demonstrate that the proposed scheme reduces the computation time compared to conventional scheme and shows very high strength against cryptanalytic attack particularly random walk attack. Keywords—Cryptography; Elliptic curve cryptography; Scalar multiplication; Random walk; Elliptic curve discrete logarithm problem