Effective computations of module inverses with the Approximating k-ary GDD Algorithm by Ishmukhametov

Abstract

Finite field calculations are used in modern cryptographic protocols for generating keys, encrypting and decrypting data, and building an electronic digital signature. The module inversing is necessary part of these calculations based on the extended Euclidean algorithm. Ishmukhametov developed a new algorithm for calculating the greatest common divisor of natural numbers called the approximat-ing algorithm which is a variant of the k-ary GCD Algorithm by J. Sorenson. In this paper we develop an extension version of this algorithm.