Comparing different GCD algorithms

Abstract

© 2020 SERSC. In our paper we analyze effectiveness of several algorithms of the GCD calculation for pairs of large naturals with respect to their speed, number of iterations and possibility of parallelization of the computation procedure. We involve in our investigation the classical Euclidean GCD Algorithm, the k-ary GCD Algorithm by J. Sorenson and the new Approximating k-ary GCD Algorithm, elaborated by S. Ishmukhametov. We outline main advantage sides and shortages of each considered algorithm and their application to practical tasks like computations in finite fields used by cryptographers.