Secure Hash Function Utilizing Asymptotically Coupled Cross-Coupled Map Lattices in Spatial Dimensions

The exploration of spatiotemporal chaos and its integration into cryptographic hash functions has attracted considerable attention, driven by the intrinsic complexity and unpredictability of chaotic systems. In this paper, we introduce a novel cross-coupled map lattice with spatially varying coupling coefficients, diverging from the traditional Cross-Coupled Map Lattice that utilizes fixed coupling coefficients. Our innovative approach incorporates a gradient in the coupling strength along the spatial dimension, which, as evidenced by our experiments, leads to enhanced chaotic indices. Capitalizing on the superior characteristics of the modified cross-coupled map lattice, we have devised a new hash function capable of transforming data of arbitrary length into hash values of 128, 256, or 512 bits. Through extensive experimentation, we have rigorously assessed the security performance of the proposed hash function. Our results indicate that the spatially varying coupling coefficients in the cross-coupled map lattice significantly bolster the hash function's robustness and reliability, rendering it an appealing choice for cryptographic applications and secure data transmission.