Point Choosing Algorithm of Elliptic Curve Cryptography
Lu Chen¹, Zhou Qinwu¹, BianZhengzhong¹, Wang Bingkang², Hao Wei³
(1. Xi'an Jiaotong University, Xi'an 710049, China; 2. Xijing Hospital;3. Northwest Electricity Power Professional University)

Abstract: An elliptic curve is defined over a finite field GF(p)for a given set of operation rules. An elliptic curve cryptosystem (ECC) is thus built. Defined are the characters of quadratic remainder while the arithmetic is provided for choosing X coordinate of base point G. According to the different properties of the prime p, two methods of calculating Y coordinate of base point G are proven mathematically. The algorithm has been realized on PC by assembly language. Hence the problem of how to choose a base point and how to code data into a point over an elliptic curve is resolved completely.
Keywords: elliptic curves discretelogarithm;elliptic curve domain parameter;point group; base point;quadratic remainder;quadratic congruence equation