Analytical Modeling of Chaotic Sampling of Regular Waveform for Random Number Generation

In this paper, an analytic approach is taken towards the analysis of a class of true random generators where an irregular square wave generated by a continuous-time chaotic oscillator and a comparator structure is used to sample a regular continuous-time waveform. Numerical and analytic equations for probability distribution have been derived for D flip-flop topology. Kernel density estimation method is utilized to describe bit distribution in the output. Then random bits are generated using analytical formulas and results from numerical simulations. Using the concepts of auto correlation and approximate entropy, the relationship between the regular and the chaotic waveform frequencies needed to generate uncorrelated bit stream have been investigated.

[1]  Kunihiro Asada,et al.  IC truly random number generators based on regular & chaotic sampling of chaotic waveforms , 2011 .

[2]  R. Rovatti,et al.  Embeddable ADC-based true random number generator for cryptographic applications exploiting nonlinear signal processing and chaos , 2005 .

[3]  Salih Ergün,et al.  True Random Number Generation Via Sampling From Flat Band-Limited Gaussian Processes , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[5]  J. Alvin Connelly,et al.  A noise-based IC random number generator for applications in cryptography , 2000 .

[6]  Ahmed S. Elwakil,et al.  An integrated circuit chaotic oscillator and its application for high speed random bit generation , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[7]  Alessandro Trifiletti,et al.  A High-Speed Oscillator-Based Truly Random Number Source for Cryptographic Applications on a Smart Card IC , 2003, IEEE Trans. Computers.

[8]  L. Kocarev,et al.  Chaos-based random number generators-part I: analysis [cryptography] , 2001 .

[9]  Alessandro Trifiletti,et al.  A high-speed IC random-number source for SmartCard microcontrollers , 2003 .

[10]  Kunihiro Asada,et al.  A High Speed IC Truly Random Number Generator Based on Chaotic Sampling of Regular Waveform , 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[11]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[12]  Paul C. Kocher,et al.  The intel random number generator , 1999 .

[13]  S. Ergun,et al.  Numerical verification of chaos-based random number generators by using bootstrap method , 2011 .

[14]  Marco Bucci,et al.  A Design of Reliable True Random Number Generator for Cryptographic Applications , 1999, CHES.