Use of Simple Arithmetic Operations to Construct Efficiently Implementable Boolean functions Possessing High Nonlinearity and Good Resistance to Algebraic Attacks

TL;DR

This paper introduces a new class of Boolean functions constructed using simple arithmetic operations that achieve an optimal balance of low complexity, high nonlinearity, and strong resistance to algebraic attacks, especially for small input sizes.

Contribution

The authors present a novel method combining simple integer and binary field arithmetic to construct Boolean functions with superior cryptographic properties and efficiency.

Findings

Functions outperform existing ones in nonlinearity and algebraic immunity for n ≤ 20.

The approach achieves a better trade-off between complexity and security.

Constructed functions are efficiently implementable with high cryptographic strength.

Abstract

We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions in the family achieving a combination of nonlinearity and (fast) algebraic immunity which is superior to what is achieved by any other efficiently implementable function. The main novelty of our approach is to apply a judicious combination of simple integer and binary field arithmetic to Boolean function construction.