A method for constructing post-quantum EDS algorithms with small signature and public key sizes based on finite noncommutative associative algebras with two hidden groups

This paper presents a novel methodology for constructing post-quantum digital signature algorithms based on finite noncommutative associative algebras. The proposed approach enhances signature randomization by leveraging the algebraic interaction of two hidden noncommutative groups and chaotic mappings, resulting in both compact key representations and increased cryptographic robustness. A core contribution is the implementation of evolutionary algorithms for the automated design of multiplication tables, ensuring associativity and optimized performance. One-time exponent parameters b and n are generated using logistic mappings to introduce chaos, thereby impeding statistical cryptanalysis even in scenarios involving bulk signature analysis. Experimental evaluation confirms the exponential complexity of attack models under optimized parameters, while also validating efficient real-world implementation using Python and NumPy. This work is the first to systematically apply evolutionary search to the generation of algebraic structures for digital signatures, demonstrating practical post-quantum security and computational feasibility.