Abstract
The multiplicative polynomial inverses of all elemental polynomials exist under each of all irreducible polynomials over the finite field GF(p m) where p is a prime integer and both p and m ≥ 2. For GF(28), the Extended Euclidean Algorithm (EEA) successfully finds multiplicative inverses of all the 255 elemental polynomials under each of 30 irreducible polynomials. However, for GF(73), the same algorithm cannot find multiplicative inverses of all the 342 elemental polynomials under each of its 112 monic irreducible polynomials. A simple algebraic method proposed in the paper finds all the 112 monic irreducible polynomials over GF(73) along with the multiplicative inverses of all the 342 elemental polynomials under each of the 112 irreducible polynomials.
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Acknowledgments
We express our gratitude toward UGC, New Delhi, for providing financial support to the first author. We are also indeed thankful to the Head of the Department of Radio Physics and Electronics, University of Calcutta, for providing necessary infrastructural facilities to undertake research activities.
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Zaman, J.K.M.S.U., Ghosh, R. (2015). Multiplicative Polynomial Inverse Over GF(73): Crisis of EEA and Its Solution. In: Chaki, R., Saeed, K., Choudhury, S., Chaki, N. (eds) Applied Computation and Security Systems. Advances in Intelligent Systems and Computing, vol 305. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1988-0_6
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DOI: https://doi.org/10.1007/978-81-322-1988-0_6
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