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Diminution of Extended Euclidean Algorithm for Finding Multiplicative Inverse in Galois Field
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This manuscript deals with the theorem on diminution of the Extended Euclidean Algorithm for finding the multiplicative inverse of non-zero elemental polynomials of Galois field with respect to a monic irreducible polynomial over , where is a prime and is any positive integer. This method became successful in finding the multiplicative inverse of all those non-zero polynomials for which the Extended Euclidean Algorithm fails. We find the inverse of all 342 non-zero elemental polynomials of using an irreducible polynomial We also used Cayley Hamilton’s theorem for finding the multiplicative inverse of the non-zero elemental polynomials of a finite field.
Title: Diminution of Extended Euclidean Algorithm for Finding Multiplicative Inverse in Galois Field
Description:
This manuscript deals with the theorem on diminution of the Extended Euclidean Algorithm for finding the multiplicative inverse of non-zero elemental polynomials of Galois field with respect to a monic irreducible polynomial over , where is a prime and is any positive integer.
This method became successful in finding the multiplicative inverse of all those non-zero polynomials for which the Extended Euclidean Algorithm fails.
We find the inverse of all 342 non-zero elemental polynomials of using an irreducible polynomial We also used Cayley Hamilton’s theorem for finding the multiplicative inverse of the non-zero elemental polynomials of a finite field.
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