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Journal of Applied Mathematics
Volume 2014, Article ID 107109, 9 pages
http://dx.doi.org/10.1155/2014/107109
Research Article

Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications

School of Computer Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia

Received 15 November 2013; Revised 4 July 2014; Accepted 5 July 2014; Published 24 July 2014

Academic Editor: Jin L. Kuang

Copyright © 2014 Shahram Jahani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Public-key cryptosystems are broadly employed to provide security for digital information. Improving the efficiency of public-key cryptosystem through speeding up calculation and using fewer resources are among the main goals of cryptography research. In this paper, we introduce new symbols extracted from binary representation of integers called Big-ones. We present a modified version of the classical multiplication and squaring algorithms based on the Big-ones to improve the efficiency of big integer multiplication and squaring in number theory based cryptosystems. Compared to the adopted classical and Karatsuba multiplication algorithms for squaring, the proposed squaring algorithm is 2 to 3.7 and 7.9 to 2.5 times faster for squaring 32-bit and 8-Kbit numbers, respectively. The proposed multiplication algorithm is also 2.3 to 3.9 and 7 to 2.4 times faster for multiplying 32-bit and 8-Kbit numbers, respectively. The number theory based cryptosystems, which are operating in the range of 1-Kbit to 4-Kbit integers, are directly benefited from the proposed method since multiplication and squaring are the main operations in most of these systems.