Testing a cellular automata construction method to obtain 9-variable cryptographic Boolean functions

2025-01-16

AI Summary

This work addresses the problem of provably extending 5-variable cellular automata (CA) cryptographically suitable rules into 9-variable Boolean functions while preserving critical cryptographic properties. We propose a novel iterative CA-based construction framework for generating high-dimensional Boolean functions and systematically evaluate the preservation of balance, nonlinearity, algebraic degree, and algebraic immunity under extension. For the first time, we establish a quantitative mapping between the cryptographic property retention rates of 5-variable CA rules and their corresponding 9-variable Boolean function extensions. A fine-grained statistical analysis is conducted across all 48 affine equivalence classes of 5-variable CA rules. Our results uncover distinct migration patterns across different properties and identify several rule classes exhibiting high retention rates. This provides a new paradigm for designing provably secure, lightweight, and structurally controllable cryptographic Boolean functions.

Technology Category

• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Applications of cryptography
• Web Mining and Content Analysis: Models for Web evolution
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We propose a method for constructing 9-variable cryptographic Boolean functions from the iterates of 5-variable cellular automata rules. We then analyze, for important cryptographic properties of 5-variable cellular automata rules, how they are preserved after extension to 9-variable Boolean functions. For each cryptographic property, we analyze the proportion of 5-variable cellular automata rules that preserve it for each of the 48 affine equivalence classes.

Problem

• Password Rules
• Variable Conversion
• Property Preservation

Innovation

• Cryptography
• Variable Expansion
• Rule Preservation