FPGA acceleration of a pseudorandom number generator based on chaotic iterations

As any well-designed information security application uses a very large quantity of good pseudorandom numbers, inefficient generation of these numbers can be a significant bottleneck in various situations. In previous research works, a technique that applies well-defined discrete iterations, satisfying the reputed Devaney's definition of chaos, has been developed. It has been proven that the generators embedding these chaotic iterations (CIs) produce truly chaotic random numbers. In this new article, these generators based on chaotic iterations are redesigned specifically for Field Programmable Gate Array (FPGA) hardware, leading to an obvious improvement of the generation rate. Analyses illustrate that statistically perfect and chaotic random sequences are produced. Additionally, such generators can also be cryptographically secure. To show the effectiveness of the method, an application in the information hiding domain is finally proposed.

[1]  Jacques M. Bahi,et al.  A Novel Pseudo-random Number Generator Based on Discrete Chaotic Iterations , 2009, 2009 First International Conference on Evolving Internet.

[2]  M. Bernhard Introduction to Chaotic Dynamical Systems , 1992 .

[3]  Jacques M. Bahi,et al.  Suitability of chaotic iterations schemes using XORshift for security applications , 2014, J. Netw. Comput. Appl..

[4]  Pierre L'Ecuyer,et al.  TestU01: A C library for empirical testing of random number generators , 2006, TOMS.

[5]  Soo-Chang Pei,et al.  Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences , 2004, Comput. Phys. Commun..

[6]  Angelo Vulpiani,et al.  Properties making a chaotic system a good pseudo random number generator. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Zhi-Hong Guan,et al.  A novel digital watermark algorithm based on chaotic maps , 2007 .

[8]  Jason Wittenberg,et al.  Clarify: Software for Interpreting and Presenting Statistical Results , 2003 .

[9]  Coskun Bayrak,et al.  A new hybrid nonlinear congruential number generator based on higher functional power of logistic maps , 2009 .

[10]  Christophe Guyeux,et al.  An improved watermarking algorithm for Internet applications , 2010 .

[11]  Jacques M. Bahi,et al.  FPGA Design for Pseudorandom Number Generator Based on Chaotic Iteration used in Information Hiding Application , 2013, ArXiv.

[12]  Christophe Guyeux,et al.  A new chaos-based watermarking algorithm , 2010, 2010 International Conference on Security and Cryptography (SECRYPT).

[13]  Octavio Nieto-Taladriz,et al.  FPGA for pseudorandom generator cryptanalysis , 2006, Microprocess. Microsystems.

[14]  J. Terno Robert, F., Discrete Iterations. A Metric Study. Berlin‐Heidelberg‐New York‐Tokyo, Springer‐Verlag 1986. XVI, 195 S., 126 Abb., DM138,–. ISBN 3‐540‐13623‐1 (Springer Series in Computational Mathematics 6) – Translation from the French , 1987 .

[15]  Richard J. Simard,et al.  A Software Library in ANSI C for Empirical Testing of Random Number Generators , 2013 .

[16]  Philip Heng Wai Leong,et al.  Compact FPGA-based true and pseudo random number generators , 2003, 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 2003. FCCM 2003..

[17]  F. Montoya Vitini,et al.  Bound for linear complexity of BBS sequences , 1998 .

[18]  Jacques M. Bahi,et al.  Evaluating Quality of Chaotic Pseudo-Random Generators: Application to Information Hiding , 2011, ArXiv.

[19]  Laurent Larger,et al.  Nonlinear dynamics: Optoelectronic chaos , 2010, Nature.

[20]  Jacques M. Bahi,et al.  Chaotic Iterations versus Spread-Spectrum: Chaos and Stego Security , 2010, 2010 Sixth International Conference on Intelligent Information Hiding and Multimedia Signal Processing.

[21]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[22]  Jacques M. Bahi,et al.  Steganography: A Class of Secure and Robust Algorithms , 2012, Comput. J..

[23]  J.-L. Danger,et al.  High speed true random number generator based on open loop structures in FPGAs , 2009, Microelectron. J..

[24]  Manuel Blum,et al.  A Simple Unpredictable Pseudo-Random Number Generator , 1986, SIAM J. Comput..

[25]  Jacques M. Bahi,et al.  An Improved Watermarking Scheme for Internet Applications , 2010, 2010 2nd International Conference on Evolving Internet.

[26]  Jacques M. Bahi,et al.  Topological chaos and chaotic iterations application to hash functions , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).