Rapid Prototyping and Performance Analysis of Elliptic Curve Cryptographic Algorithms using Java and Maple

A. Burnett and T. Dowling (Ireland)

Keywords

Software Evaluation, Software Reuse, Rapid PrototypingModel, Performance Analysis, Security, Elliptic CurveCryptography

Abstract

Elliptic Curve Cryptography is an increasingly popular method of public key cryptography. It is important that these systems are made as secure as possible to known attacks. The determination of the number of points on a given elliptic curve is central to establishing whether it is an appropriately secure curve to use. This paper describes the design, implementation and evolution of an algorithm of Schoof [1] used to perform this task in Java. We also examine the use of the Maple [2] programming environ ment as a rapid prototyping model to facilitate the debug ging and testing of Java. Maple is particularly suitable due to the complicated mathematical algebraic constructs re quired for this system. Finally, we will consider the per formance analysis of the algorithm on the two platforms as well as how various optimizations improve performance.

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