Further results on differentially 4-uniform permutations over $\F_{2^{2m}}$

Abstract

In this paper, we present several new constructions of differentially 4-uniform permutations over $\F_{2^{2m}}$ by modifying the values of the inverse function on some subsets of $\F_{2^{2m}}$. The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of cryptographic substitution boxes.

15 pages. This paper has been accepted for publication in SCIENCE CHINA Mathematics