Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications

Jahani, Shahram and Samsudin, Azman and Subramanian, Kumbakonam Govindarajan (2014) Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications. Journal of Applied Mathematics, 2014 (107109). pp. 1-9. ISSN 1110-757X

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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 themain 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 classicalmultiplication and squaring algorithms based on the Big-ones to improve the efficiency of big integermultiplication 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.

Item Type:	Article
Subjects:	Q Science > QA Mathematics > QA75.5-76.95 Electronic computers. Computer science
Divisions:	Pusat Pengajian Sains Komputer (School of Computer Sciences) > Article Zoom Profil Pakar (Expert Profile) > Azman Samsudin (Computer Sciences)
Depositing User:	Mr Noorazilan Noordin
Date Deposited:	14 Feb 2018 07:06
Last Modified:	14 Feb 2018 07:06
URI:	http://eprints.usm.my/id/eprint/38934

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