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 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.