The software implementations of cryptographic algorithms are considered to be very slow, when there are requirements of multi-precision arithmetic operations on very long integers. These arithmetic operations may include addition, subtraction, multiplication, division and exponentiation. Several research papers have been published providing different solutions to make these operations faster. Digital Signature Algorithm (DSA) is a cryptographic application that requires multi-precision arithmetic operations. These arithmetic operations are mostly based upon modular multiplication and exponentiation on integers of the size of 1024 bits. The use of such numbers is an essential part of providing high security against the cryptanalytic attacks on the authenticated messages. When these operations are implemented in software, performance in terms of speed becomes very low. The major focus of the thesis is the study of various arithmetic operations for public key cryptography and selecting the fast multi-precision arithmetic algorithms for hardware implementation. These selected algorithms are implemented in hardware and software for performance comparison and they are used to implement Digital Signature Algorithm for performance analysis.

Library of Congress Subject Headings

Cryptography--Data processing; Digital signatures; Public key cryptography; Data encryption (Computer science)

Publication Date


Document Type


Student Type


Degree Name

Computer Engineering (MS)

Department, Program, or Center

Computer Engineering (KGCOE)


Marcin Lukowiak

Advisor/Committee Member

Stanislaw Radziszowski

Advisor/Committee Member

Muhammad Shaaban


Physical copy available from RIT's Wallace Library at Z103 .J36 2005


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