**4. Conclusions**

In the present work, the modified version of the logistic map proposed in [9] was presented. The extensive dynamical analysis has shown that the proposed system exhibits phenomena like crisis, antimonotonicity, and coexisting attractors. This technique to increase the complexity of a map can

be tested on other systems in the future. The map was then applied to constuct the chaos-based pseudo-random bit generator, utilizing techniques like multiple map comparison, bit reversal, and *XOR*. In addition, the key space of the proposed algorithm is much higher than the indicated threshold of 2100. Future aspects of this work will consider the application of the proposed PRBG to image encryption, the generation of multiple bits per iteration, as well as fractional versions of the map. It is of interest to develop the adaptive chaotic maps with controllable symmetry of a higher order based on the proposed map. It was previously shown that such systems are prospective for stream encryption algorithms [29,41]. Moreover, the obtained results can be applied to other cryptographic problems, including encoding multimedia data, creating watermarks and QR codes, generating checksums using chaotic hash functions, etc.

**Author Contributions:** C.V., L.M., A.T., D.B., J.M.M.-P. and H.N. contributed equally to this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is co-financed by Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project "Reinforcement of Postdoctoral Researchers—2nd Cycle" (MIS-5033021), implemented by the State Scholarships Foundation (IKY).

**Acknowledgments:** The authors would like to thank the anonymous reviewers for theis comments.

**Conflicts of Interest:** The authors declare no conflict of interest.
