Some Results Concerning Cryptographically Significant Permutation Polynomial

Abstract:

The function $x^{2^{n-1}-1}+ax^5 (n$ odd, $a\in\mathbb{F}_{2^n}$) is differentially 4-uniform and is never bijective. Using Hermite’s Criterion, prove some necessary conditions that $x^{2^{n-1}-1}+ax^5+L(x), L(x)$ being a permutation polynomial.

• Periodical: Applied Mechanics and Materials (Volumes 263-266)
• Pages: 3073-3075
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.263-266.3073
• Online since: December 2012
• Authors: Luo Zhong Gong
• Keywords: Hermites Criterion, Inverse Function, Permutation Polynomial, S-Box

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