The Simulation of 256-bit Elliptic Curve Cryptosystem

Abstract

Elliptic Curve Cryptosystem have recently come into strong consideration, particularly by standards developers, as alternatives to established standard cryptosystem such as the RSA public key. Elliptic Curve Cryptosystem is "the next generation" of public-key cryptography, providing greater strength, higher speed, and smaller keys than established systems. An elliptic curve operation involves a sequence of elliptic curve additions, and each addition consists of several arithmetic operations in the finite field. The premise is that an elliptic curve 256-bit cryptosystem offers better security than of 1024-bit RSA. The opportunity to conveniently generate Elliptic Curve Cryptosystem using commercial Mathematical Software has now become feasible. The purpose of this paper is to show how the powerful computer algebra system Maple V can be used to explore and visualize Elliptic Curve Cryptosystem. The paper begins with some general background of Elliptic Curve Cryptosystem. Cryptographic operations tend to be highly CPU intensive, particularly public key operations. Then this paper discusses the simulation on Elliptic Curve Cryptosystem for 256-bit key length.