Statistical tests and chaotic synchronization based pseudorandom number generator for string bit sequences with application to image encryption

Abstract Recently, a stream encryption scheme using d-bit segment sequences has been proposed. This scheme may generate key avalanche effect. The randomness tests of d-bit segment pseudorandom number generator will be important for implementing such a scheme. Firstly this paper extends Beker and Piper’s binary pseudorandom sequence statistical test suite to d-bit segment sequences case. Secondly, a novel 3-dimensional polynomial discrete chaotic map (3DPDCM) is proposed. The calculated Lyapunov exponents of the 3DPCDM are 0.213, 0.125 and − 3.228. Using the 3DPDCM constructs a 6-dimensional generalized synchronization chaotic system. Based on this system, a 8-bit segment chaotic pseudorandom number generator (CPRNG) is introduced. Using the generalized test suite tests 100 key streams generated via the 8-bit PRNG with different initial conditions and perturbed system parameters. The tested results are similar to those of the key streams generated via RC4 PRNG. As an application, using the key streams generated via the CPRNG and the RC4 PRNG encrypts an RGB image Landscape. The results have shown that the encrypted RGB images have significant avalanche effects. This research suggests that the requirements for PRNGs are not as strict as those under the traditional avalanche criteria. Suitable designed chaos-based d-bit string PRNGs may be qualified candidates for the stream encryption scheme with avalanche effect.

[1]  Wayne H. Enright,et al.  Robust and reliable defect control for Runge-Kutta methods , 2007, TOMS.

[2]  Muhammad Rezal Kamel Ariffin,et al.  Synchronization and a secure communication scheme using optical star network , 2013 .

[3]  D. V. Senthilkumar,et al.  Characteristics and synchronization of time-delay systems driven by a common noise , 2010 .

[4]  Paul Woafo,et al.  Chaotic synchronization with experimental application to secure communications , 2009 .

[5]  Samrat L. Sabat,et al.  A fast chaotic block cipher for image encryption , 2014, Commun. Nonlinear Sci. Numer. Simul..

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

[7]  Annabelle Lee,et al.  SP 800-29. A Comparison of the Security Requirements for Cryptographic Modules in FIPS 140-1 and FIPS 140-2 , 2001 .

[8]  Hyoungshick Kim,et al.  An image encryption scheme with a pseudorandom permutation based on chaotic maps , 2010 .

[9]  Rima Assaf,et al.  Efficient neural chaotic generator for image encryption , 2014, Digit. Signal Process..

[10]  J. Sprott.  Chaos and time-series analysis , 2001 .

[11]  P. Shyamala,et al.  Chaos Based Image Encryption Scheme , 2011 .

[12]  Lamberto Rondoni,et al.  Multi-image encryption based on synchronization of chaotic lasers and iris authentication , 2012 .

[13]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[14]  Ioannis M. Kyprianidis,et al.  Image encryption process based on chaotic synchronization phenomena , 2013, Signal Process..

[15]  Lequan Min,et al.  A novel stream encryption scheme with avalanche effect , 2013 .

[16]  Muhammad Rezal Kamel Ariffin,et al.  Noise induced synchronization of time-delayed semiconductor lasers and authentication based asymmetric encryption , 2013 .

[17]  Lequan Min,et al.  A generalized synchronization theorem for discrete-time chaos system with application in data encryption scheme , 2007, 2007 International Conference on Communications, Circuits and Systems.

[18]  Sharon C. Glotzer,et al.  Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices , 2011, J. Comput. Phys..

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

[20]  A. Kanso,et al.  A novel image encryption algorithm based on a 3D chaotic map , 2012 .

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

[22]  Robert A. J. Matthews,et al.  On the Derivation of a "Chaotic" Encryption Algorithm , 1989, Cryptologia.

[23]  Amir Akhavan,et al.  A symmetric image encryption scheme based on combination of nonlinear chaotic maps , 2011, J. Frankl. Inst..

[24]  Lequan Min,et al.  Generalized Synchronization in an Array of nonlinear Dynamic Systems with Applications to Chaotic CNN , 2013, Int. J. Bifurc. Chaos.

[25]  Lequan Min,et al.  Study on the Statistical Test for String Pseudorandom Number Generators , 2013, BICS.

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