Aarti Malik

Abstract

Elliptic Curve Cryptosystems (ECC) have been proposed as an alternative to other established public key cryptosystems such as RSA (Rivest Shamir Adleman). ECC provide more security per bit than other known public key schemes based on the discrete logarithm problem. Smaller key sizes result in faster computations, lower power consumption and memory and bandwidth savings, thus making ECC a fast, flexible and cost-effective solution for providing security in constrained environments. Implementing ECC on reconfigurable platform combines the speed, security and concurrency of hardware along with the flexibility of the software approach.

This work proposes a generic architecture for elliptic curve cryptosystem on a Field Programmable Gate Array (FPGA) that performs an elliptic curve scalar multiplication in 1.16milliseconds for GF (2163), which is considerably faster than most other documented implementations. One of the benefits of the proposed processor architecture is that it is easily reprogrammable to use different algorithms and is adaptable to any field order. Also through reconfiguration the arithmetic unit can be optimized for different area/speed requirements. The mathematics involved uses binary extension field of the form GF (2n) as the underlying field and polynomial basis for the representation of the elements in the field. A significant gain in performance is obtained by using projective coordinates for the points on the curve during the computation process.

Library of Congress Subject Headings

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

Publication Date

2-2005

Document Type

Thesis

Student Type

Graduate

Degree Name

Computer Engineering (MS)

Department, Program, or Center

Computer Engineering (KGCOE)

Advisor

Pratapa Reddy

Advisor/Committee Member

Greg Semeraro

Advisor/Committee Member

Dorin Patru

Comments

Physical copy available from RIT's Wallace Library at Z103 .M35 2005

Campus

RIT – Main Campus

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