A reversible system based on hybrid toggle radius-4 cellular automata and its application as a block cipher

TL;DR

This paper introduces a reversible hybrid cellular automata system called HCA, which is used to develop a new block cipher, with theoretical and empirical analyses demonstrating its security and scalability advantages.

Contribution

It presents a novel reversible cellular automata-based block cipher and analyzes its security, reversibility, and scalability within modern computational paradigms.

Findings

HCA's reversibility is theoretically validated.

Security analysis links HCA to NP-complete Hamiltonian cycle problem.

Empirical tests show HCA's robustness and randomness qualities.

Abstract

The dynamical system described herein uses a hybrid cellular automata (CA) mechanism to attain reversibility, and this approach is adapted to create a novel block cipher algorithm called HCA. CA are widely used for modeling complex systems and employ an inherently parallel model. Therefore, applications derived from CA have a tendency to fit very well in the current computational paradigm where scalability and multi-threading potential are quite desirable characteristics. HCA model has recently received a patent by the Brazilian agency INPI. Several evaluations and analyses performed on the model are presented here, such as theoretical discussions related to its reversibility and an analysis based on graph theory, which reduces HCA security to the well-known Hamiltonian cycle problem that belongs to the NP-complete class. Finally, the cryptographic robustness of HCA is empirically evaluated through several tests, including avalanche property compliance and the NIST randomness suite.