Pseudo-Chaotic Lossy Compressors for True Random Number Generation

This paper presents a compression method that exploits pseudo-chaotic systems, to be applied to True Random Bit Generators (TRBGs). The theoretical explanation of the proposed compression scheme required the projection of some results achieved within the Ergodic Theory for chaotic systems on the world of digital pseudo-chaos. To this aim, a weaker and more general interpretation of the Shadowing Theory has been proposed, focusing on probability measures, rather than on single chaotic trajectories. The design of the compression scheme has been theoretically discussed in order to assure the final entropy of the compressed TRBG to be arbitrarily close to the maximum limit of 1 bit/time-step. The proposed solution requires extremely low-complex hardware circuits for being implemented, assures a constant throughput and is based on theoretical results of general validity.

[1]  Massimo Alioto,et al.  A feedback strategy to improve the entropy of a chaos-based random bit generator , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Werner Schindler,et al.  Evaluation Criteria for True (Physical) Random Number Generators Used in Cryptographic Applications , 2002, CHES.

[3]  M. Mirzakhani,et al.  Introduction to Ergodic theory , 2010 .

[4]  Fritz Colonius,et al.  Six Lectures on Dynamical Systems , 1996 .

[5]  Ronen Shaltiel,et al.  True Random Number Generators Secure in a Changing Environment , 2003, CHES.

[6]  Tommaso Addabbo,et al.  An Efficient and Accurate Method for the Estimation of Entropy and Other Dynamical Invariants for Piecewise Affine Chaotic Maps , 2009, Int. J. Bifurc. Chaos.

[7]  Tommaso Addabbo,et al.  Exploiting Chaotic Dynamics for a-d converter Testing , 2010, Int. J. Bifurc. Chaos.

[8]  Massimo Alioto,et al.  A Variability-Tolerant Feedback Technique for Throughput Maximization of Trbgs with Predefined Entropy , 2010, J. Circuits Syst. Comput..

[9]  Nagarajan Ranganathan,et al.  High-speed VLSI designs for Lempel-Ziv-based data compression , 1993 .

[10]  Fabrizio Lombardi,et al.  Compression of VLSI test data by arithmetic coding , 2004 .

[11]  P. Walters.  Introduction to Ergodic Theory , 1977 .

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

[13]  Fabrizio Lombardi,et al.  Compression of VLSI test data by arithmetic coding , 2004, 19th IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems, 2004. DFT 2004. Proceedings..

[14]  Tommaso Addabbo,et al.  Efficient implementation of pseudochaotic piecewise linear maps with high digitization accuracies , 2012, Int. J. Circuit Theory Appl..

[15]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[16]  Tommaso Addabbo,et al.  Invariant Measures of Tunable Chaotic Sources: Robustness Analysis and Efficient Estimation , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  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.

[18]  M. Kieffer,et al.  Vehicle tracking based on robust bounded-error nonlinear state estimation using interval analysis , 2004, Proceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004..

[19]  David Salomon,et al.  Data Compression: The Complete Reference , 2006 .

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

[21]  Hüseyin Koçak,et al.  SHADOWING IN DISCRETE DYNAMICAL SYSTEMS , 1996 .

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

[23]  Cheng-Wen Wu,et al.  Unified VLSI systolic array design for LZ data compression , 2001, IEEE Trans. Very Large Scale Integr. Syst..

[24]  Abraham Boyarsky,et al.  Laws of chaos , 1997 .

[25]  Berk Sunar,et al.  A Provably Secure True Random Number Generator with Built-In Tolerance to Active Attacks , 2007, IEEE Transactions on Computers.

[26]  Markus Jakobsson,et al.  How to turn loaded dice into fair coins , 2000, IEEE Trans. Inf. Theory.

[27]  P. Elias.  The Efficient Construction of an Unbiased Random Sequence , 1972 .

[28]  P. L'Ecuyer,et al.  About polynomial-time “unpredictable” generators , 1989, WSC '89.

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

[30]  Jacob Ziv,et al.  The Universal LZ77 Compression Algorithm Is Essentially Optimal for Individual Finite-Length $N$-Blocks , 2009, IEEE Transactions on Information Theory.