Abstract

This thesis presents a performance evaluation of a 384-bit NIST elliptic curve over prime fields on a 32-bit ARM946E microprocessor running at 100-MHz. While adhering to the constraints of an embedded system, the following items were investigated to decrease computation time: the importance of the underlying finite arithmetic, the use of hardware accelerators, the use of memory options, and the use of available processor features. The elliptic curve implementation utilized existing finite arithmetic C code to interface to an AiMEC Montgomery Exponentiator Core. The exponentiator core supports modular addition, modular multiplication, and exponentiation. The finite arithmetic C code also contained functions to perform operations which are not performed by the exponentiator such as non-modular multiplication, non-modular addition, and modular subtraction. Multiple enhancements were made to the finite field arithmetic. These provided a 22% time reduction in execution time of the 384-bit elliptic curve multiplication. Enhancements included writing assembly functions, adding checks prior to performing a modular reduction, utilizing the exponentiator core only when modulus reduction was necessary, using multiplication if more than two additions are required and placing the finite arithmetic into its own library and using ARM mode. Other optimizations investigated including: cache usage, compiler options (speed vs. size), and Thumb instruction set vs. ARM instruction set provided minimal reduction, 3.6%, in the execution time.

Library of Congress Subject Headings

Curves, Elliptic; Cryptography--Data processing

Publication Date

4-1-2008

Document Type

Thesis

Department, Program, or Center

Computer Engineering (KGCOE)

Advisor

Lukowiak, Marcin

Advisor/Committee Member

Kudithipudi, Dhireesha

Advisor/Committee Member

Kurdziel, Mike

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA567.2.E44 V36 2008

Campus

RIT – Main Campus

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