Algorithms for computing the permutation resemblance of functions over finite groups

TL;DR

This paper introduces linear integer programming methods to compute permutation resemblance of functions over finite groups, providing algorithms and bounds that enhance understanding of how functions approximate permutations.

Contribution

It presents a novel linear integer programming approach for calculating permutation resemblance and extends it to find permutations with minimal differential uniformity.

Findings

Linear integer programming effectively computes permutation resemblance.

An algorithm constructs feasible solutions and establishes upper bounds.

Generalization to functions on finite groups with minimal differential uniformity.

Abstract

Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing feasible solutions to this integer program, and use it to prove an upper bound for permutation resemblance for some special functions. Additionally, we present a generalization of the linear integer program that takes a function on a finite group and determines a permutation with the lowest differential uniformity among those most resembling it.