Efficient implementation of elliptic curve cryptography.

Date of Award


Publication Type

Master Thesis

Degree Name



Electrical and Computer Engineering


Engineering, Electronics and Electrical.



Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.


Elliptic Curve Cryptosystems (ECC) were introduced in 1985 by Neal Koblitz and Victor Miller. Small key size made elliptic curve attractive for public key cryptosystem implementation. This thesis introduces solutions of efficient implementation of ECC in algorithmic level and in computation level. In algorithmic level, a fast parallel elliptic curve scalar multiplication algorithm based on a dual-processor hardware system is developed. The method has an average computation time of n3 Elliptic Curve Point Addition on an n-bit scalar. The improvement is n Elliptic Curve Point Doubling compared to conventional methods. When a proper coordinate system and binary representation for the scalar k is used the average execution time will be as low as n Elliptic Curve Point Doubling, which makes this method about two times faster than conventional single processor multipliers using the same coordinate system. In computation level, a high performance elliptic curve processor (ECP) architecture is presented. The processor uses parallelism in finite field calculation to achieve high speed execution of scalar multiplication algorithm. The architecture relies on compile-time detection rather than of run-time detection of parallelism which results in less hardware. Implemented on FPGA, the proposed processor operates at 66MHz in GF(2 167) and performs scalar multiplication in 100muSec, which is considerably faster than recent implementations.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .A57. Source: Masters Abstracts International, Volume: 44-03, page: 1446. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005.