On acceleration of the k-ary GCD Algorithm

Abstract

In our paper we analyze a method of acceleration of the k-ary Algorithm of finding the greatest common divisor for long natural numbers. The k-ary GCD algorithm was invented in 1990 by J. Sorenson. We show that a small modification of Sorenson’s Algorithm gives a sufficient acceleration of its work. This is useful for applications using the GCD operation like calculations in finite fields, generation of Cryptography keys etc.