Computing the modular inverses is as simple as computing the GCDs

Authors:
Chao-Liang Liu;Gwoboa Horng;Hsin-Yu Liu
Affiliations:
Department of Information Science and Applications, Asia University, 500, Liufeng Road, Wufeng, Taichung 41354, Taiwan, ROC;Department of Computer Science, National Chung-Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan, ROC;Department of Computer Science, National Chung-Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan, ROC
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

In 1997, Calvez, Azou, and Vilbe proposed a variation on Euclidean algorithm, which can calculate the greatest common divisors (GCDs) and inverses for polynomials. Inspired by their work, we propose a variation on the Euclidean algorithm, which uses only simple modulo operators, to compute the modular inverses. This variant only modifies the initial values and the termination condition of the Euclidean algorithm. Therefore, computing the modular inverses is as simple as computing the GCDs.