2009•Unpublished venueRequires access

The Research of Generating Secure Elliptic Curve over GF(p)

Aiqin Hou, Baojian Gao, Jun Wang

Abstract

Generating a secure elliptic curve is complicated and there are only a few algorithms for some special elliptic curves at present. In this paper an algorithm of generating an elliptic curve over prime field GF (p) with a prime number order is discussed. Another algorithm of generating an elliptic curve with an order which equals to the product of two prime numbers is proposed.

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Available abstract

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