Security analysis of the pseudo-random bit generator based on multi-modal maps

In this paper, a security analysis of the pseudo-random bit generator based on multi-modal maps is made, which reveals existence of serious security problems. Depending on parameter k, there are certain number of weak keys causing improper functioning of this generator. Also, based on certain number of consecutive output bits, the initial values of this pseudo-random number generator (PRNG) can be obtained with attack which complexity is significantly less than estimated key space. Although the assumed safety of the example of cipher based on this PRNG (when $$k=3$$k=3) is estimated at $$2^{159}$$2159, it is possible to carry out successful known-plaintext attack with the complexity less than $$2^{128}$$2128. For above-mentioned reasons, analyzed PRNG cannot be considered safe for the use in cryptographic systems.

[1]  Safya Belghith,et al.  Cryptanalysis of a new substitution–diffusion based image cipher , 2010 .

[2]  Ángel Rodríguez-Vázquez,et al.  A switched‐capacitor skew‐tent map implementation for random number generation , 2017, Int. J. Circuit Theory Appl..

[3]  Dragan Lambić,et al.  Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map , 2017 .

[4]  Dragan Lambić,et al.  Security analysis and improvement of a block cipher with dynamic S-boxes based on tent map , 2015 .

[5]  Xingyuan Wang,et al.  Cryptanalysis of an image encryption algorithm using Chebyshev generator , 2014, Digit. Signal Process..

[6]  Gonzalo Álvarez,et al.  Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers , 2011, Chaos-Based Cryptography.

[7]  Willi-Hans Steeb,et al.  The Nonlinear Workbook , 2005 .

[8]  Oscar E. Lanford,et al.  Informal Remarks on the Orbit Structure of Discrete Approximations to Chaotic Maps , 1998, Exp. Math..

[9]  Xiaoling Huang,et al.  Image encryption algorithm using chaotic Chebyshev generator , 2011, Nonlinear Dynamics.

[10]  Esteban Tlelo-Cuautle,et al.  Simulation of Piecewise-Linear One-Dimensional Chaotic Maps by Verilog-A , 2015 .

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

[12]  Fenlin Liu,et al.  Cryptanalyzing an image encryption algorithm with compound chaotic stream cipher based on perturbation , 2017, Nonlinear Dynamics.

[13]  Cuauhtemoc Mancillas-López,et al.  Hardware implementation of pseudo-random number generators based on chaotic maps , 2017 .

[14]  Gonzalo Alvarez,et al.  Cryptanalysis of a family of self-synchronizing chaotic stream ciphers , 2009, 0903.2928.

[15]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[16]  Willi-Hans Steeb.  The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SYMBOLICC++ Programs (6TH Edition) , 2015 .

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

[18]  Vinod Patidar,et al.  A new substitution–diffusion based image cipher using chaotic standard and logistic maps , 2009 .

[19]  S. Li,et al.  Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption , 2009 .

[20]  Xiaohong Zhao,et al.  Differential cryptanalysis of a novel image encryption algorithm based on chaos and Line map , 2016, Nonlinear Dynamics.