In this paper, we focus on a class of Boolean permutations of an optimal algebraic degree. Firstly, we construct a class of Boolean permutations. We put forward a method to propose the inverse of a given Boolean permutation. It is shown that a Boolean permutation has an optimal algebraic degree if and only if its inverse has an optimal algebraic degree. Secondly, we present the inverse of the constructed Boolean permutation, and show the inverse permutation has the largest algebraic degree. Finally, we show that the constructed Boolean permutations can achieve optimum algebraic degree by selecting an appropriate initial vector and illustrate it with examples.
Zhang, Fengrong; Hu, Yupu; Xie, Min; Gao, Juntao; and Wang, Qichun
"Constructions of Cryptographically Significant Boolean Permutations,"
Applied Mathematics & Information Sciences: Vol. 06:
1, Article 17.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol06/iss1/17