A Pseudo-Random Bit Generator Based on Three Chaotic Logistic Maps and IEEE 754-2008 Floating-Point Arithmetic

A novel pseudo-random bit generator (PRBG), combining three chaotic logistic maps is proposed. The IEEE 754-2008 standard for floating-point arithmetic is adopted and the binary64 double precision format is used. A more efficient processing is applied to better extract the bits, from outputs of the logistic maps. The algorithm enables to generate at each iteration, a block of 32 random bits by starting from three chosen seed values. The performance of the generator is evaluated through various statistical analyzes. The results show that the output sequences possess high randomness statistical properties for a good security level. The proposed generator lets appear significant cryptographic qualities.

[1]  Jürgen Lehn,et al.  A non-linear congruential pseudo random number generator , 1986 .

[2]  Eli Biham,et al.  Differential Cryptanalysis of the Data Encryption Standard , 1993, Springer New York.

[3]  Xiao-jian Tian,et al.  Pseudo-random sequence generator based on the generalized Henon map , 2008 .

[4]  Dominique Barchiesi,et al.  A New Pseudo-Random Number Generator Based on Two Chaotic Maps , 2013, Informatica.

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

[6]  R. Rovatti,et al.  A Fast Chaos-based True Random Number Generator for Cryptographic Applications , 2006, 2006 Proceedings of the 32nd European Solid-State Circuits Conference.

[7]  Fu Lee Wang,et al.  Web Information Systems and Mining , 2010, Lecture Notes in Computer Science.

[8]  Vinod Patidar,et al.  A Pseudo Random Bit Generator Based on Chaotic Logistic Map and its Statistical Testing , 2009, Informatica.

[9]  Gonzalo Álvarez,et al.  Trident, a New Pseudo Random Number Generator Based on Coupled Chaotic Maps , 2010, CISIS.

[10]  Xuan Li,et al.  Chaos-based true random number generator using image , 2011, 2011 International Conference on Computer Science and Service System (CSSS).

[11]  Vinod Patidar,et al.  A Random Bit Generator Using Chaotic Maps , 2010, Int. J. Netw. Secur..

[12]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

[13]  Vinod Patidar,et al.  Image encryption using chaotic logistic map , 2006, Image Vis. Comput..

[14]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

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

[16]  Greg Rose.  A Stream Cipher Based on Linear Feedback over GF(28) , 1998, ACISP.

[17]  Jörg Keller,et al.  Period lengths of chaotic pseudo-random number generators , 2007 .

[18]  Jacques M. Bahi,et al.  A Pseudo Random Numbers Generator Based on Chaotic Iterations: Application to Watermarking , 2010, WISM.

[19]  M. Baptista.  Cryptography with chaos , 1998 .

[20]  Dominique Barchiesi,et al.  Pseudo-random number generator based on mixing of three chaotic maps , 2014, Commun. Nonlinear Sci. Numer. Simul..

[21]  Álvaro Herrero,et al.  Computational Intelligence in Security for Information Systems - CISIS'09, 2nd International Workshop, Burgos, Spain, 23-26 September 2009 Proceedings , 2009, CISIS.

[22]  Fuyan Sun,et al.  Cryptographic pseudo-random sequence from the spatial chaotic map , 2009 .

[23]  Vinod Patidar,et al.  A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption , 2011 .

[24]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[25]  Taraneh Eghlidos,et al.  Heuristic guess-and-determine attacks on stream ciphers , 2009, IET Inf. Secur..

[26]  Marco Tomassini,et al.  Generating high-quality random numbers in parallel by cellular automata , 1999, Future Gener. Comput. Syst..

[27]  David Goldberg,et al.  What every computer scientist should know about floating-point arithmetic , 1991, CSUR.

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

[29]  M. Kendall.  Rank Correlation Methods , 1949 .

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