A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period

In this paper, a very low complexity method is proposed to achieve a guaranteed substantial extension in the period of a popular class of chaos-based digital pseudo-random number generators (PRNGs). To this end, the relation between the chaotic PRNG and multiple recursive generators is investigated and some theorems are provided to show that how a simple recursive structure and an additive piecewise-constant perturbation inhibit unpredictable short period trajectories and ensure an a priori known long period for the chaotic PRNG. The statistical performance of the proposed PRNG is evaluated, and the results show that it is a good candidate for applications in which long-period secure pseudo-random sequence generators at a low complexity level are required.

[1]  Wu Xiaofu,et al.  Design and realization of an FPGA-based generator for chaotic frequency hopping sequences , 2001 .

[2]  Sergej Celikovský,et al.  Hyperchaotic encryption based on multi-scroll piecewise linear systems , 2015, Appl. Math. Comput..

[3]  Tommaso Addabbo,et al.  Digitized Chaos for Pseudo-random Number Generation in Cryptography , 2011, Chaos-Based Cryptography.

[4]  Fatih Özkaynak,et al.  Cryptographically secure random number generator with chaotic additional input , 2014 .

[5]  L. Cardoza-Avendaño,et al.  A novel pseudorandom number generator based on pseudorandomly enhanced logistic map , 2016, Nonlinear Dynamics.

[6]  Karl Entacher,et al.  Bad subsequences of well-known linear congruential pseudorandom number generators , 1998, TOMC.

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

[8]  M. Andrecut,et al.  Logistic Map as a Random Number Generator , 1998 .

[9]  M. J. Werter.  An improved chaotic digital encoder , 1998 .

[10]  Sergio Callegari,et al.  Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications , 2002, Proc. IEEE.

[11]  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.

[12]  Yong Wang,et al.  A pseudorandom number generator based on piecewise logistic map , 2015, Nonlinear Dynamics.

[13]  S. Tezuka.  Uniform Random Numbers: Theory and Practice , 1995 .

[14]  Michael V. Basin,et al.  A family of hyperchaotic multi-scroll attractors in Rn , 2014, Appl. Math. Comput..

[15]  H. T. Engstrom.  On sequences defined by linear recurrence relations , 1931 .

[16]  Harald Niederreiter,et al.  Introduction to finite fields and their applications: List of Symbols , 1986 .

[17]  Naixue Xiong,et al.  Analysis and Design of Digital Chaotic Systems With Desirable Performance via Feedback Control , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[18]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[19]  Jürgen Lehn,et al.  On the period length of pseudorandom vector sequences generated by matrix generators , 1989 .

[20]  Gerard Parr,et al.  Complexity of chaotic binary sequence and precision of its numerical simulation , 2012 .

[21]  Chengqing Li,et al.  Cryptanalyzing image encryption using chaotic logistic map , 2013, Nonlinear Dynamics.

[22]  İsmail Öztürk,et al.  A novel method for producing pseudo random numbers from differential equation-based chaotic systems , 2015 .

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

[24]  Z. Galias,et al.  The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems?and How to Avoid Them , 2013, IEEE Circuits and Systems Magazine.

[25]  Yicong Zhou,et al.  Cascade Chaotic System With Applications , 2015, IEEE Transactions on Cybernetics.

[26]  Daniel Curiac,et al.  Chaos-Based Cryptography: End of the Road? , 2007, The International Conference on Emerging Security Information, Systems, and Technologies (SECUREWARE 2007).

[27]  Massimo Alioto,et al.  A Class of Maximum-Period Nonlinear Congruential Generators Derived From the Rényi Chaotic Map , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Gianluca Mazzini.  DS-CDMA systems using q-level m sequences: coding map theory , 1997, IEEE Trans. Commun..

[29]  M. Mackey,et al.  Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics , 1998 .

[30]  Guangchun Luo,et al.  An image encryption scheme based on chaotic tent map , 2016, Nonlinear Dynamics.

[31]  K. Kelber,et al.  N-dimensional uniform probability distribution in nonlinear autoregressive filter structures , 2000 .

[32]  Philippe Bouysse,et al.  DSP implementation of self-synchronised chaotic encoder-decoder , 2000 .

[33]  W. G. Chambers,et al.  Guaranteeing the period of linear recurring sequences (mod 2e) , 1993 .

[34]  Pierre L'Ecuyer,et al.  Uniform random number generation , 1994, Ann. Oper. Res..

[35]  Brian D. Ripley,et al.  Thoughts on pseudorandom number generators , 1990 .

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

[37]  Mieczyslaw Jessa,et al.  Designing security for number sequences generated by means of the sawtooth chaotic map , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.