Security Evaluation of Two-Dimensional Chaotic Function for Cryptographic Primitives Element

Technologies in Industry 4.0 leverage various cryptographic systems to enhance the security of data and communication networks. Among these systems, primitive cryptographic methods, such as symmetric cryptography, play a crucial role. These include block ciphers, stream ciphers, hash functions, and pseudorandom number generators, all of which rely on core properties like randomness, confusion, and diffusion. In this context, chaos functions emerge as an effective solution for achieving these properties, as they are characterized by outputs that are both random and deterministic while being highly sensitive to input changes. A two-dimensional chaos function, in particular, can be constructed using a one-dimensional chaos function as its foundation, enabling broader and more continuous chaotic properties. This study develops algorithms for two-dimensional chaos functions to serve as building blocks for cryptographic primitives. The chaos functions explored include the Arnold Cat Map, Baker Map, Tinker Bell Map, Henon Map, Duffing Map, Zeraoulia-Sprott Map, Horshoe Map, and Linear Piecewise Map. These algorithms are evaluated based on their confusion and diffusion capabilities, and their randomness is assessed using the NIST SP800-22 Revision 1A test. The results indicate that the algorithm utilizing the Tinker Bell chaotic function demonstrates exceptional randomness, confusion, and diffusion properties, making it an ideal candidate for cryptographic primitives such as block ciphers, stream ciphers, hash functions, and pseudorandom number generators (PRNGs). The proposed Tinker Bell chaotic function, with its optimal parameter set, excels in terms of randomness and cryptographic strength, as demonstrated by the confusion, diffusion, and NIST SP800-22 test results. Furthermore, the proposed algorithm has a time complexity of O(n), where n represents the number of iterations of the chosen chaotic function. This ensures that the algorithm is both efficient and scalable, performing effectively even with larger inputs.