A way to compute a greatest common divisor in the Galois field (GF (2^n ))

Waleed Eltayeb Ahmed

doi:10.24297/jam.v16i0.8167

A way to compute a greatest common divisor in the Galois field (GF (2^n ))

Authors

Waleed Eltayeb Ahmed Al – Imam Mohammed Ibn Saud Islamic University

DOI:

https://doi.org/10.24297/jam.v16i0.8167

Keywords:

Greatest common divisor, multiplicative inverse, irreducible polynomial, extended Euclidean algorithm, Bezout identity

Abstract

This paper presents how the steps that used to determine a multiplicative inverse by method based on the Euclidean algorithm, can be used to find a greatest common divisor for polynomials in the Galois field (2^n ).

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Author Biography

Waleed Eltayeb Ahmed, Al – Imam Mohammed Ibn Saud Islamic University

Mathematics and Statistics Department, Faculty of Science, Al-Imam Mohammad Ibn Saud Islamic University, Saudi Arabia

References

W. Eltayeb Ahmed, Some Techniques to Compute Multiplicative Inverses for Advanced Encryption Standard, Journal of Advances in Mathematics, Vol 16 (2019) ISSN: 2347-1921. https://cirworld.com/index.php/jam

A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, CRC Press, New York, 1997.

John B. Fealenigh , A First Course in Abstract Algebra, 7 th edition, Pearson press , 2002.

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Published

2019-02-28

How to Cite

Ahmed, W. E. (2019). A way to compute a greatest common divisor in the Galois field (GF (2^n )). JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8317–8321. https://doi.org/10.24297/jam.v16i0.8167