Construction of one-way hash functions with increased key space using adaptive chaotic maps

Chaotic hash functions are a prospective branch of modern cryptography. Being compared with traditional hashing algorithms, an approach based on deterministic chaos allows achieving diffusion and confusion with less computational costs. Most of the recently proposed chaotic hash functions use piecewise maps. Cryptosystems based on such maps are not vulnerable to attack by the reconstruction of phase space but their key spaces depend on maps parameters and therefore can be insufficient. In this paper, we propose an approach for the construction of piecewise hash functions from adaptive chaotic maps. The idea is to match different values of the adaptive coefficient to several sub-domains of the chaotic map. Thus, the adaptive coefficient values are part of the hash function key. Therefore, an increase in the sub-functions number potentially enhances the cryptographic strength of the algorithm. Thus, hash functions based on novel adaptive maps have larger key space compared to conventional piecewise maps. We explicitly show that the proposed hash generation technique allows obtaining digests with the required statistical properties. Moreover, we run a collision test to prove that the collision probability is small. The obtained results can be useful in chaos-based cryptography as well for the various simulations of real processes and phenomena with chaotic behavior, in computer graphics and multimedia.