Title: Reviewing and Analyzing Efficient GCD/LCM Algorithms for Cryptographic Design

Issue Number: Vol. 7, No. 1
Year of Publication: March - 2017
Page Numbers: 1-7
Authors: Ibrahim Marouf, Mohamad Musab Asad, Qasem Abu Al-Haija
Journal Name: International Journal of New Computer Architectures and their Applications (IJNCAA)
- Hong Kong
DOI:  http://dx.doi.org/10.17781/P002301


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, Lehmers algorithm, and two LCM algorithms: LCM based Prime Factorizations algorithm and LCM based GCD reduction. It was found that Lehmers 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.