Abstract
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.
Highlights
Elliptic Curve Cryptography (ECC) [1], [2] has gained popularity in the field of public key cryptosystem for its smaller key size, faster processing time and robust security against popular cryptanalytic attacks comparing to other Public Key Cryptography(PKC) systems
EXPERIMENTAL RESULTS AND DISCUSSIONS numerical experiment results of proposed ECC scheme and the scalar multiplication algorithm are decomparison of computational costs of Key generation, ECC encryption and ECC decryption methods of proposed scheme with the conventional ECC scheme are presented in Fig. 6, Fig. 7 and Fig. 8
The experimental results show that the computational cost of the proposed scalar multiplication algorithm is less than that of [18] and [7] which proves the efficiency of the proposed scalar multiplication algorithm
Summary
Elliptic Curve Cryptography (ECC) [1], [2] has gained popularity in the field of public key cryptosystem for its smaller key size, faster processing time and robust security against popular cryptanalytic attacks comparing to other Public Key Cryptography(PKC) systems. These features engrossed the attentions of manufacturers of small processing devices like smart cards, Raspberry computers, wireless devices, pagers, smart phones and tablets [3]. F. Amounas [9] et al proposed an algorithm to generate a data sequence and applied it on ECC encrypted message over the finite field GF(p). Cryptanalysis of ECC went on with the same pace
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