Enhanced Chaos-based Pseudo Random Numbers Generator

Enhancing chaos-based PRNGs quality is the subject of this paper. The big problem that chaotic systems suffer from is the limited arithmetic computation size, that is; dynamical degradation in digital chaotic systems appears due to the digitization process. Quantization error, limited cycle-length and worse statistical proprieties of the chaotic sequence are in fact the most shortcomings of implementing chaotic systems on digital computers. In this paper, we have proposed a simple method for purifying as maximum as possible digital chaotic systems from aforementioned shortcomings. The method consists of using a mechanism to perturb the chaotic orbits during randomly chosen periods, and in the same time using another circuit to convert the chaotic sequence to another one that provide good statistical proprieties. The proposed scheme has been applied on the Logistic chaotic map using low arithmetic computation size, the results in terms of cycle-length and uniformity showed that the proposed scheme is so better compared to the original system and can extremely enhance the chaotic proprieties of a given digital chaotic system.

[1]  Y. Uyaroglu,et al.  Signal Masking Applications Using Chaotic Circuits , 2022 .

[2]  Lahcene Merah,et al.  A pseudo random number generator based on the chaotic system of Chua's circuit, and its real time FPGA implementation , 2013 .

[3]  Guanrong Chen,et al.  On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps , 2005, Int. J. Bifurc. Chaos.

[4]  W. Tang,et al.  A fast image encryption system based on chaotic maps with finite precision representation , 2007 .

[5]  Slawomir T. Fryska,et al.  Computer dynamics and shadowing of chaotic orbits , 1992 .

[6]  Yaobin Mao,et al.  Design and FPGA Implementation of a Pseudo-Random Bit Sequence Generator Using Spatiotemporal Chaos , 2006, 2006 International Conference on Communications, Circuits and Systems.

[7]  Cheng-Fang Huang,et al.  Design of random digital sequence generators and its application of secure communication , 2011, Proceedings of 2011 International Conference on Fluid Power and Mechatronics.

[8]  Kim-Fung Man,et al.  A Chaos-Based Pseudo-Random Number Generator and its Application in Voice Communications , 2007, Int. J. Bifurc. Chaos.

[9]  Akif Akgul,et al.  A novel chaos-based encryption algorithm over TCP data packet for secure communication , 2016, Secur. Commun. Networks.

[10]  B. Noble,et al.  On certain integrals of Lipschitz-Hankel type involving products of bessel functions , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[11]  Chengyan Jiang,et al.  A Valid Algorithm of Converting Chaos Sequences to Uniformity Pseudo-random Ones , 2009, 2009 International Symposium on Information Engineering and Electronic Commerce.

[12]  N. H. Said,et al.  W Coupling Two Chaotic Systems in Order to Increasing the Security of a Communication System-Study and Real Time FPGA Implementation , 2013 .

[13]  Lakhmi C. Jain,et al.  Advances in Intelligent Information Hiding and Multimedia Signal Processing - Proceedings of the Thirteenth International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2017, August, 12-15, 2017, Matsue, Shimane, Japan, Part II , 2018, IIH-MSP.

[14]  Ziqi Zhu,et al.  A dynamic nonlinear transform arithmetic for improving the properties chaos-based PRNG , 2010, 2010 8th World Congress on Intelligent Control and Automation.

[15]  Lih-Yuan Deng,et al.  Period Extension and Randomness Enhancement Using High-Throughput Reseeding-Mixing PRNG , 2012, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[16]  Rogelio Hasimoto-Beltran,et al.  Cycle detection for secure chaos-based encryption , 2011 .

[17]  X. Mou,et al.  On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision , 2003 .

[18]  Lahcene Merah,et al.  Real-time cryptosystem based on synchronized chaotic systems , 2015 .

[19]  Oksasoglu,et al.  Chaotic masking scheme with a linear inverse system. , 1995, Physical review letters.

[20]  Sang Tao,et al.  Perturbance-based algorithm to expand cycle length of chaotic key stream , 1998 .

[21]  Sheng Liyuan,et al.  Pseudo-random number generator based on TD-ERCS chaos and its statistic characteristics analysis , 2005 .

[22]  J. Cernák.  Digital generators of chaos , 1996 .

[23]  M. Blank.  Pathologies generated by round-off in dynamical systems , 1994 .

[24]  Lingfeng Liu,et al.  Counteracting the dynamical degradation of digital chaos via hybrid control , 2014, Commun. Nonlinear Sci. Numer. Simul..