Elliptic Curves Cryptosystem Based Electronic Cash Scheme with Parameter Optimization

Abstract

Proper selection of secret parameters is essential to the security and feasibility of e-cash (electronic cash) scheme. In the paper, we presented an improved e-cash scheme with parameter optimization based on ECC (Elliptic Curves Cryptosystem). In the scheme, the secret parameters are generated with bionic optimization algorithm by a successive adaptive optimizing process. With the optimized secret parameters, the dishonest users and the outer adversaries can not attack e-cash with polynomial algorithms, so the scheme effectively prevents generalized ecash forgery and coalition attack. And the optimizing algorithm can be executed in advance without any influence to the efficiency of e-cash scheme. Besides, the algorithms of the scheme make full use of the superiority of ECC, such as high efficiency, short key length and etc. The optimization designing strategy of the scheme not only reinforces the security and feasibility of e-cash but also greatly improves the efficiency of e-cash for software and hardware application.

Network Security Using ECC with Biometric

“…That means cryptographer elliptic curve is in the form y 2 mod p = (x 3 + ax + b) mod p where 4a 3 + 27b 2 ≠ 0 and p is a prime number and a, b is the parameter of the curve, here variables and coefficient are all restricted to elements of a finite field. There are two families of elliptic curve are used in cryptography application [8,9,10]. In Elliptic curves defined over GF (2 m ), the variables and co-efficient all take on values in GF (2 m ) and in calculation performed over GF (2 m ).…”

“…If we want to add two points of elliptic curve then we have to follow given below rule. For this and all arithmetic operation there are some rules which are as follows [8,9,10].…”

“…Elliptic curve Diffie-Hellman algorithm is the Diffie-Hellman algorithm for the elliptic curve [3,8]. The original Diffie-Hellman algorithm is based on the multiplicative group modulo p, while the elliptic curve Diffie-Hellman (ECDH) protocol is based on the additive elliptic curve group.…”