Analysis of the k-ary Euclid for tuples of integers

Abstract

In our paper we discuss the k-ary Euclid Algorithm for counting the great common divisor (GCD) of two or more integers and suggest some improvements. This gives us a possibility to parallelize and speed up the calculating of GCD, which has a variety of applications in the Number Theory, Modular Arithmetic and the Cryptography Algorithms such as RSA, ElGamal encryption system and others.