Speeding up Euclid's GCD algorithm with no magnitude comparisons

摘要

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.