2009•Jisuanji gongchengRequires access

Secure Elliptic Curve Generating Algorithm over GF(p)

Aiqin Hou, Xin Xiao-long, Shiyong Yang

Abstract

This paper analyzes the elliptic curves over prime field GF(p), while p is greater than 3.It discusses an algorithm to generate an elliptic curve with a prime order.On basis of this, the problems for generating an elliptic curve with an order which equals to the product of two prime numbers are studied.A secure elliptic curve generating algorithm over GF(p) is proposed.It gives some examples for producing an elliptic curve and all the points on this elliptic curve under these two circumstances.Simulation experimental results show this algorithm is effective and feasible.

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Available abstract

Key concepts: Tripling-oriented Doche–Icart–Kohel curve, Schoof's algorithm, Hessian form of an elliptic curve, Elliptic curve point multiplication, Elliptic curve, Jacobian curve, Elliptic curve cryptography, Prime (order theory)