Cycle detection for secure chaos-based encryption

Digital generators of chaos present several limitations that affect the vulnerability of chaotic encryption systems, among the most important are degraded probability distribution and short cycle lengths. Periodic perturbations of the chaotic parameter and/or state variable have been employed to deal with these limitations, although blindfold; the periodicity of the perturbation is set up during the initialization process without reference to the cycle length of the chaotic map under consideration. For best results, the periodicity of the perturbation must be close to the actual cycle length. So far, it is analytically impossible and numerically impractical (for real-time applications) to have a priori information of the cycle length. In this work we propose an on-the-fly detection and quantification of the chaotic cycle length to eliminate short cycles (which make cryptosystems vulnerable to attacks) and maximize the strength of long cycles by perturbing the system at the right time. Our proposal consists of two algorithms: (1) Unrestricted Search Algorithm (USA), which tracks down the cycle without any assumption or restriction on the digital chaotic trajectory, and (2) Ergodic Search Algorithm (ESA), which assumes ergodic trajectories to reduce the cycle search space, without this being a necessary requirement for the analyzed trajectory. USA and ESA are intended to increase the security of chaotic encryption systems without compromising their performance. Furthermore, they can be employed for the development of new chaotic-map independent encryption systems, where a full knowledge of the map is not required.

Research highlights
► We propose on-the-fly chaotic cycle detection algorithms for robust encryption.
► Cycle detection avoids reusing chaotic trajectories during the encryption process.
► Cycle detection with trajectory perturbation increases the strength of long cycles.
► The algorithms are intended for the creation of map independent encryption systems.
► The algorithms can be embedded in chaotic cryptosystems at no computational cost.