CCE Theses and Dissertations

Date of Award

2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Computer Science (CISD)

Department

Graduate School of Computer and Information Sciences

Advisor

Wei Li

Committee Member

James Cannady

Committee Member

Junping Sun

Keywords

Elliptic Curve, Performance Counter, Performance Evaluation, Program Profiling, Projective Transformation, Scalar Point Multiplication

Abstract

For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was founded on the practical solution that obtaining realistic performance figures should be based on more precise computational cost metrics and specific computing platforms. As part of that solution, an empirical performance benchmark comparison between two approaches implementing projective Elliptic-curve scalar point-multiplication will be presented to provide the selection of, and subsequently ways to improve scalar point-multiplication technology executing in a 64-bit x86 runtime environment.

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