Reviewing and Analyzing Efficient GCD/LCM Algorithms for Cryptographic Design

In this paper, we provide a practical review with numerical example and complexity analysis for greatest common divisor (GCD) and Least Common Multiple (LCM) algorithms that are commonly used in the computing coprocessors design such as Cryptoprocessor design. The paper discusses four common GCD alg...

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Bibliographic Details
Published inInternational journal of new computer architectures and their applications Vol. 7; no. 1; pp. 1 - 7
Main Author Marouf, Ibrahim
Format Journal Article
LanguageEnglish
Published The Society of Digital Information and Wireless Communications 2017
Subjects
Algorithms
Applied research
Cryptography
Methods
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ISSN2220-9085
2220-9085
DOI10.17781/P002301

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Summary:In this paper, we provide a practical review with numerical example and complexity analysis for greatest common divisor (GCD) and Least Common Multiple (LCM) algorithms that are commonly used in the computing coprocessors design such as Cryptoprocessor design. The paper discusses four common GCD algorithms: Dijkstra's algorithm, Euclidian algorithm, Binary GCD algorithm, Lehmer's algorithm, and two LCM algorithms: LCM based Prime Factorizations algorithm and LCM based GCD reduction. It was found that Lehmer's algorithm can be used efficiently to compute GCD and LCM with time complexity of O (n/log(n)) which enhances the linear time (O (n)) complexity of well-known Euclidian algorithm.
ISSN:2220-9085
2220-9085
DOI:10.17781/P002301