Constructing Highly Nonlinear Cryptographic Balanced Boolean Functions on Learning Capabilities of Recurrent Neural Networks

Abstract

This study presents a novel approach to cryptographic algorithm design that harnesses the power of recurrent neural networks. Unlike traditional mathematical-based methods, neural networks offer nonlinear models that excel at capturing chaotic behavior within systems. We employ a recurrent neural network trained on Monte Carlo estimation to predict future states and generate confusion components. The resulting highly nonlinear substitution boxes exhibit exceptional characteristics, with a maximum nonlinearity of 114 and low linear and differential probabilities. To evaluate the efficacy of our methodology, we employ a comprehensive range of traditional and advanced metrics for assessing randomness and cryptanalytics. Comparative analysis against state-of-the-art methods demonstrates that our developed nonlinear confusion component offers remarkable efficiency for block-cipher applications.

Keywords

• Block ciphers
• confusion components
• Monte Carlo estimation
• recurrent neural networks
• substitution boxes