Distribution of the absolute indicator of random Boolean functions

TL;DR

This paper investigates the distribution of the absolute indicator in random Boolean functions, revealing its potential to differentiate nonrandom sequences from truly random ones, thus contributing to cryptographic analysis.

Contribution

It provides the first detailed study of the behavior of the absolute indicator of random Boolean functions, expanding understanding of their cryptographic properties.

Findings

Absolute indicator can distinguish nonrandom from random sequences

Distribution of the absolute indicator for random Boolean functions characterized

Enhances tools for cryptographic sequence analysis

Abstract

The absolute indicator is one of the measures used to determine the resistance offered by a Boolean function when used in the design of a symmetric cryptosystem. It was proposed along with the sum of square indicator to evaluate the quality of the diffusion property of block ciphers and hash functions. While the behaviour of the sum of square of random Boolean functions was already known, what remained was the study of the comportment of the absolute indicator of random Boolean functions. As an application, we show that the absolute indicator can distinguish a nonrandom binary sequence from a random one.