Low space-complexity digit-serial dual basis systolic multiplier over Galois field GF(2m) using Hankel matrix and Karatsuba algorithm

• Published in: IET information security Vol. 7; no. 2; pp. 75 - 86
• Main Authors: Yan Hua, Ying, Lin, Jim-Min, Wun Chiou, Che, Lee, Chiou-Yng, Huan Liu, Yong
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.06.2013; IET; John Wiley & Sons, Inc
• Subjects: Algebra; Algorithms; Applied sciences; Balancing; Complexity; Computation; computational complexity; cryptographic computations; Cryptography; cut set method; elliptic curve cryptosystem; Exact sciences and technology; Field theory and polynomials; finite field arithmetic operation; Galois field GF(2m); Galois fields; Hand held; Hankel matrices; Hankel matrix; Information, signal and communications theory; Karatsuba algorithm; low space complexity digit serial dual basis systolic multiplier; Mathematical analysis; Mathematics; Multipliers; public key cryptography; Sciences and techniques of general use; Signal and communications theory; Telecommunications and information theory; low space complexity digit serial dual basis systolic multiplier; Hankel matrix; cut set method; public key cryptography; Galois field GF(2m); elliptic curve cryptosystem; Hankel matrices; Galois fields; Karatsuba algorithm; finite field arithmetic operation; cryptographic computations; computational complexity; Finite field; Space complexity; Galois algebra; Standardization; Multiplier; Public key cryptography; Elliptic curve; Arithmetic operation; Computational complexity; Time complexity; Mobile computing
• ISSN: 1751-8709; 1751-8717; 1751-8717
• DOI: 10.1049/iet-ifs.2012.0227

Multiplication is one important finite field arithmetic operation in cryptographic computations. Dual basis multipliers over Galois field GF(2m) have been widely applied in this kind of computations because of its advantage of small chip area. Nevertheless, up to date, there are only few methods that can keep balance of low space complexity and low time complexity at the same time. In order to achieve such an efficient aim, this study presents a novel digit-serial dual basis multiplier that is different from existing ones with a modified cut-set method using Karatsuba algorithm as well as Hankel matrix. As a result, the proposed multiplier can save much space and thus be particularly suitable for some hand held devices equipped with only limited resources. The proposed digit-serial dual basis multiplier saves 55% space complexity as compared with existing similar studies with National Institute of Standards and Technology (NIST) suggested values for elliptic curve cryptosystem.