NegaBent, No Regrets: Evolving Spectrally Flat Boolean Functions

2026-01-31

AI Summary

This study addresses the efficient construction of Boolean functions with flat nega-Hadamard spectra, particularly those simultaneously possessing bent and negabent properties. To overcome the limitations of conventional algebraic approaches, the work proposes a novel paradigm by systematically introducing evolutionary algorithms—specifically genetic programming—into this domain. A fitness function tailored to the nega-Hadamard transform is designed to guide the automated evolution of Boolean functions satisfying the desired spectral properties. Experimental results demonstrate the successful generation of both negabent and bent-negabent functions across multiple dimensions, confirming the effectiveness and generality of the proposed method. This approach establishes a new computational framework for constructing Boolean functions with prescribed cryptographic criteria.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Negabent Boolean functions are defined by having a flat magnitude spectrum under the nega-Hadamard transform. They exist in both even and odd dimensions, and the subclass of functions that are simultaneously bent and negabent (bent-negabent) has attracted interest due to the combined optimal periodic and negaperiodic spectral properties. In this work, we investigate how evolutionary algorithms can be used to evolve (bent-)negabent Boolean functions. Our experimental results indicate that evolutionary algorithms, especially genetic programming, are a suitable approach for evolving negabent Boolean functions, and we successfully evolve such functions in all dimensions we consider.

Problem

• Negabent
• Boolean functions
• Bent-negabent
• Spectral flatness
• Nega-Hadamard transform

Innovation

• negabent
• bent-negabent
• evolutionary algorithms
• genetic programming
• spectrally flat