Information Security Journal: A Global Perspective,  Vol. 18, No. 3, pp. 131 – 138, Taylor & Francis, 2009

Copyright © Taylor & Francis Group, LLC

ISSN: 1939-3555 print / 1939-3547 online

DOI: 10.1080/19393550902926053



Efficient Modular Squaring Algorithms for Hardware Implementation in GF(p)


Lo’ai Tawalbeh1, Saed Swedan1, and Adnan Gutub2


1Computer Engineering Department, Jordan University of Science and Technology

Irbid, Jordan


2Computer Engineering Department, King Fahd University of Petroleum and Minerals

Dhahran, Saudi Arabia





Some of the most popular public key encryption algorithms use exponentiation as their core operation, which can be mostly broken into several modular squaring operations. In this paper, we present GF(p) modular squaring algorithms and efficiently implement them on hardware. We present different algorithms, two for squaring and one for reduction combined with the squaring, to provide a general modular squaring algorithm.

The algorithms are implemented through datapaths that uses redundant Carry-Save Adders, making the computation time independent form the operands precision. The proposed algorithms are compared with each other as well as with the existing modular squaring algorithms. The experimental results are obtained by synthesizing the hardware designs for FPGA Virtex5 chip (xc5vlx50 ff1153 technology), which showed interesting results and

made our ideas very attractive.




cryptography hardware, modular arithmetic, security architecture, design



Author Posting. (c) 'Copyright Holder', 2009.
This is the author's version of the work. It is posted here by permission of 'Copyright Holder' for personal use, not for redistribution.
The definitive version was published in Information Security Journal: A Global Perspective, Volume 18 Issue 3, 2009.
doi:10.1080/19393550902926053 (