A Novel Spatiotemporal Chaotic Model with Provable Security

Abstract

In the application of chaos in cryptography, two questions remain unanswered: Does the chaos-based cipher possess provable security? Can the reproduction of a chaotic model or chaotic sequence be specified as a non-deterministic polynomial complete(NPC) problem or non-deterministic polynomial hard(NPH) problem for cryptanalysts? This paper proposes a spatiotemporal chaotic model called pseudo-random scrambling coupled map lattice (PRSCML) based on the coupled map lattice (CML) and the hybrid elementary cellular automata with a mask (HECA-M). This model can answer the above two questions affirmatively. The experiments reveal the strong chaotic properties of the PRSCML model, including the high Kolmogorov-Sinai entropy, randomness, and ergodicity. Furthermore, the sequences generated by PRSCML are backward and forward secure as the reproduction of a PRSCML model and its sequence are equivalent to the traveling salesman problem (TSP), which is an NPH problem. Meanwhile, the recurrence of a HECA-M belongs to the regular 3-SAT problem, which is an NPC problem. Therefore, the PRSCML model possesses provable security, and its superior performance demonstrates that it has great potential for cryptography. Moreover, this paper can reassure researchers that the security of some chaos-based ciphers can be confirmed for cryptography.