Speeding up Euclid's GCD algorithm with no magnitude comparisons
by Che Wun Chiou, Fu Hua Chou, Yun-Chi Yeh
International Journal of Information and Computer Security (IJICS), Vol. 4, No. 1, 2010

Abstract: Euclid's Greatest Common Divisor (GCD) algorithm is an efficient approach for calculating multiplicative inversions. It relies mainly on a fast modular arithmetic algorithm to run quickly. A traditional modular arithmetic algorithm based on nonrestoring division needs a magnitude comparison for each iteration of shift-and-subtract operation. This process is time consuming, since it requires magnitude comparisons for every computation iteration step. To eradicate this problem, this study develops a new fast Euclidean GCD algorithm without magnitude comparisons. The proposed modular algorithm has an execution time that is about 33% shorter than the conventional modular algorithm.

Online publication date: Fri, 26-Feb-2010

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