Key Generation in Cryptography Using Elliptic-Curve Cryptography and Genetic Algorithm †

Abstract

Elliptic-curve cryptography (ECC) has become a robust cryptographic technique that ensures secure data transmission with comparatively small key sizes. In this context, this research introduces a novel approach to ECC-key-pair generation by utilizing genetic algorithms (GAs). GAs have proven effective in solving optimization problems by mimicking the principles of natural selection and genetics. The proposed genetic algorithm-based ECC-key generation process involves several stages: chromosome initialization, fitness evaluation, selection, uniform crossover, and mutation. Chromosomes representing points on an elliptic curve are initialized randomly, evaluated for their proximity to a predefined target point using a fitness function, and subjected to tournament selection to determine parents for the next generation. Uniform crossover and mutation operators then create offspring, inheriting traits from their parents while introducing diversity. The generated ECC-key pair comprises private and public keys derived from the GA-driven process. The private key is chosen randomly within the constraints of the elliptic curve’s parameters, while the public key is generated through the GA procedure. The study evaluates the efficiency and effectiveness of the proposed ECC-GA approach through an empirical analysis of execution time, key size, and the size of the search space. The outcomes of this research highlight the potential of genetic algorithms in ECC-key generation, offering a promising alternative for enhancing the security and efficiency of cryptographic systems, especially in resource-limited environments. The exploration of key size and search space may assist in understanding the security implications and computational complexity associated with the proposed method. Overall, the ECC-GA approach opens avenues for further research in innovative key-generation techniques for modern cryptographic applications.