Calculation of Bezout’s coefficients for the k-ary algorithm of finding GCD

Abstract

© 2017, Allerton Press, Inc. Bezout’s equation is a representation of the greatest common divisor d of integers A and B as a linear combination Ax + By = d, where x and y are integers called Bezout’s coefficients. The task of finding Bezout’s coefficients has numerous applications in the number theory and cryptography, for example, for calculation of multiplicative inverse elements in modular arithmetic. Usually Bezout’s coefficients are caclulated using the extended version of the classical Euclidian algorithm. We elaborate a new algorithm for calculating Bezout’s coefficients based on the k-ary GCD algorithm.