A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree

TL;DR

This paper introduces a highly nonlinear permutation with differential uniformity of four, suitable for cryptographic use, demonstrating its resistance to differential and linear cryptanalysis similar to the inverse function in AES.

Contribution

It presents a new permutation with low differential uniformity and high nonlinearity, expanding options for cryptographic S-box design.

Findings

Permutation has differential uniformity of four

Permutation is highly nonlinear

Suitable for cryptographic applications

Abstract

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially-4 uniform function called the inverse function. Any function used in a symmetric cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that it is resistant to Matsui's linear attack. In this article we demonstrate that a highly nonlinear permutation discovered by Hans Dobbertin has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.