DEVELOPMENT OF GENERATORS OF PSEUDORANDOMS SEQUENCES BASED ON HASH FUNCTIONS USING MULTIDIMENSIONAL CHAOTIC SYSTEMS

Abstract

In this paper, we propose hash-function based on multidimensional chaotic systems, specifically an eight-dimensional Lozi system. The hash function leverages the inherent properties of chaotic systems, including pseudo-randomness and extreme sensitivity to initial conditions. Unlike other similar chaotic-based hash generators, the proposed approach uses perturbation of the system parameters, those that define the chaotic behavior, by incorporating each incoming block of information. At every iteration, new parameters are derived from the joint interaction of the current system state and the respective information block. The input data is injected and transformed, while the chaotic dynamics of the system are preserved. Throughout the iterative process, each information block is influenced not only by the system’s state variables but also by the current parameter values. A further layer of security is provided by utilizing a 256-bit key, which serves to initialize the system’s starting state. The proposed algorithm is designed to operate using fixed-point arithmetic with 32-bit number representation: one bit is allocated for the sign, one for the integer part, and the remaining 30 bits for the fractional part. This division ensures efficient use of the 32-bit format, efficient computing and provides platform-independent, consistent performance – unlike floating-point arithmetic, whose results can vary across different hardware and compilers. The algorithm can be adapted to alternate arithmetic or larger word sizes if needed. Additionally, this work investigates the proposed algorithm’s resistance to differential attack and collisions, as well as its viability as a pseudorandom sequence generator. The statistical properties of sequences was assessed using the NIST Statistical Test Suite (NIST STS), which confirmed the capability of algorithm for cryptography applications.