A Strong Key Expansion Algorithm Based on Nondegenerate 2D Chaotic Map Over GF(2n)

Abstract

The strength of a cryptosystem relies on the security of its key expansion algorithm, which is an important component of a block cipher. However, numerous block ciphers exhibit the vulnerability of reversibility and serialization. Therefore, it is necessary to design an irreversible parallel key expansion algorithm to generate independent round keys. First, a 2D nondegenerate exponential chaotic map (2D-NECM) is constructed, and the results of the dynamic analysis show that the 2D-NECM possesses ergodicity and superior randomness within a large range of parameters. Then, an irreversible parallel key expansion algorithm is designed based on 2D-NECM and primitive polynomial over GF([Formula: see text]). By injecting random perturbation into the initial key, the algorithm can generate different round keys even if the same initial key is used. Simulation results indicate that the algorithm has high security performance. It effectively satisfies the requirements of irreversibility and parallelism, while ensuring the mutual independence of round keys.