GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm

Department Of Mathematics, Umaru Ali Shinkafi Polytechnic Sokoto ,Ibrahim A A

doi:10.47191/ijmcr/v9i9.02

Department Of Mathematics, Umaru Ali Shinkafi Polytechnic Sokoto , Ibrahim A A

Open Access

https://doi.org/10.47191/ijmcr/v9i9.02

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Abstract

Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing some cryptographic architectures that could be used in design of strong encryption schemes.

Highlights

24 September 2021 the use of extended Euclidean algorithm in computing the greatest common divisor of Aunu binary polynomials of cardinality seven
The system was later improved to compute the gcd of polynomials using extended Euclidean algorithm
This paper reports a new technique of computing the gcd of Aunu binary polynomials of cardinality seven using extended Euclidean algorithm where each class of the polynomials is permutated up to the number of its succeeding classes by pairing

Summary

INTRODUCTION

The use of modern means of communication for by Liouville in 1846, [1]. Finite fields are widely used in modern cryptographic the business of the day due to the advent of information and designs and architecture of both symmetric and asymmetric communication technologies. All of them worked for some special fields: polynomials of Aunu permutation pattern satisfying some where is a prime. The system was later improved to compute the gcd of polynomials using extended Euclidean algorithm. La theorie des mumbres marked the beginning of finite field “GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm”. This paper reports a new technique of computing the gcd of Aunu binary polynomials of cardinality seven using extended Euclidean algorithm where each class of the polynomials is permutated up to the number of its succeeding classes by pairing. C. The Extended Euclidean Algorithm (EEA) computes the greatest common divisor of two polynomials and establishes an equation relating them. And computation of the gcd of each pair of the polynomial was carried out using extended Euclidean algorithm. Section one covers introduction part of the paper, section two gives some definitions of basic terms as used in the paper, section three reports the methodology of the paper i.e extended Euclidean algorithm, section four presents the major findings of the paper and section five gives conclusion of the paper

Aunu Polynomials

RESULTS

Compute the gcd of and

CONCLUSION