From Collatz Conjecture to chaos and hash function

Abstract

The non-linear property of Chaos is a promising approach to information security, and many accomplishments have been made by combining Chaos with several sub-security domains, including chaos-based stream ciphers, block ciphers, image encryption, and hash functions. Most Chaos-based hash functions are insecure or inefficient due to their dependence on complex, attacked multi-dimensional maps or uncertain, weak one-dimensional maps like logistic and tent. The Collatz Conjecture is a mystery that has stumped mathematicians for decades and still has not been solved. This paper aims to introduce a novel approach to addressing current security challenges by utilizing our generalized Collatz process to create a chaos-based hash function. By leveraging the unpredictable behaviour of the Collatz sequence, the proposed hash function aims to enhance ergodicity and entropy properties, thereby making it well-suited for cryptographic applications. In the proposed method, the chaotic variables are governed by cryptographic keys, crucial in generating data sequences. These sequences are then utilized within the diffusion and confusion structures of the hashing function. The design of the chaos-hash model is carefully optimized to exhibit desirable characteristics such as randomness, collision resistance, uniformity, sensitivity to initial conditions, speed, and resistance against cryptanalysis.The primary goal of this research is to develop a robust and efficient chaos-based hash function that addresses the requirements of cryptographic systems. By incorporating the Collatz process and carefully considering key-controlled variables, the proposed model aims to offer enhanced security properties while meeting the necessary criteria for a reliable and effective hashing mechanism. The effectiveness and dependability of the proposed hash function are evaluated by comparing it with two well-known hash algorithms, namely SHA-3 and SHA-2, as well as several other Chaos-based hash algorithms. Through comprehensive evaluations conducted under various circumstances and with different datasets, the suggested hash function consistently outperforms the state-of-the-art alternatives. Experiments involving diverse input scenarios consistently demonstrate that the proposed hash function surpasses the performance of the current leading alternatives. Its superior performance is observed across various evaluation metrics, confirming its effectiveness in generating reliable and secure hash values. The results obtained from the comparative analysis highlight the superiority of the proposed hash function over existing alternatives, validating its potential as a robust solution for various cryptographic applications.