zbMATH — the first resource for mathematics

A new two-dimensional mutual coupled logistic map and its application for pseudorandom number generator. (English) Zbl 1435.37054
Summary: Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65C10 Random number generation in numerical analysis
94A60 Cryptography
65P20 Numerical chaos
Full Text: DOI
[1] Kalouptsidis, N., Signal Processing Systems. Signal Processing Systems, Telecommunications and Signal Processing Series (1996), New York, NY, USA: Wiley, New York, NY, USA
[2] Addabbo, T.; Alioto, M.; Fort, A.; Rocchi, S.; Vignoli, V., A feedback strategy to improve the entropy of a chaos-based random bit generator, IEEE Transactions on Circuits and Systems I: Regular Papers, 53, 2, 326-337 (2006) · Zbl 1388.65010
[3] Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G., Keystream cryptanalysis of a chaotic cryprographic method, Computer Physics Communications, 156, 205-207 (2003) · Zbl 1006.94017
[4] Zhang, B.; Feng, D., Improved multi-pass fast correlation attacks with applications, Science China Information Sciences, 54, 8, 1635-1644 (2011) · Zbl 1267.94107
[5] Courtois, N. T.; Meier, W., Algebraic attack on stream ciphers with linear feedback, Proceedings of the EUROCRYPT ’03 · Zbl 1038.94525
[6] Oishi, S.; Inoue, H., Pseudo-random number generators and chaos, Transactions of the Institute of Electronics and Communication Engineers of Japan E, E65, 9, 534-541 (1982)
[7] Szczepański, J.; Kotulski, Z., Pseudorandom number generators based on chaotic dynamical systems, Open Systems and Information Dynamics, 8, 2, 137-146 (2001) · Zbl 0993.65010
[8] Li, P.; Li, Z.; Halang, W. A.; Chen, G., A multiple pesudorandom-bit generator based on a spatiotemporal chaotic map, Physics Letters A, 349, 6, 467-473 (2006)
[9] Francois, M.; Grosges, T.; Barchiesi, D.; Erra, R., Pseudo-random number generator based on mixing of three chaotic maps, Communications in Nonlinear Science and Numerical Simulation, 19, 4, 887-895 (2014)
[10] Hu, H. P.; Liu, L. F.; Ding, N. D., Pseudorandom sequence generator based on Chen chaotic system, Computer Physics Communications, 184, 3, 765-768 (2013)
[11] Liu, L.; Miao, S.; Hu, H.; Deng, Y., Pseudorandom bit generator based on non-stationary logistic maps, IET Information Security, 10, 2, 87-94 (2016)
[12] Wang, L.; Wang, F. P.; Wang, Z. J., Novel chaos-based pseudo-random number generator, Acta Physica Sinica, 55, 8, 3964-3968 (2006) · Zbl 1202.65010
[13] Stojanovski, T.; Kocarev, L., Chaos-based random number generators - Part I: analysis, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48, 3, 281-288 (2001) · Zbl 0997.65002
[14] Stojanovski, T.; Pihl, J.; Kocarev, L., Chaos-based random number generators - Part II: practical realization, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48, 3, 382-385 (2001) · Zbl 0997.65003
[15] Wang, Y.; Liu, Z.; Ma, J.; He, H., A pseudorandom number generator based on piecewise logistic map, Nonlinear Dynamics, 83, 4, 2373-2391 (2016) · Zbl 1354.65012
[16] Kanso, A.; Smaoui, N., Logistic chaotic maps for binary numbers generations, Chaos, Solitons & Fractals, 40, 5, 2557-2568 (2009)
[17] Sahari, M. L.; Boukemara, I., A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption, Nonlinear Dynamics, 94, 1, 723-744 (2018)
[18] Lv, X.; Liao, X.; Yang, B., A novel pseudo-random number generator from coupled map lattice with time-varying delay, Nonlinear Dynamics, 94, 1, 325-341 (2018)
[19] Wang, X.; Luan, D., A novel image encryption algorithm using chaos and reversible cellular automata, Communications in Nonlinear Science and Numerical Simulation, 18, 11, 3075-3085 (2013) · Zbl 1329.94081
[20] Murillo-Escobar, M. A.; Cruz-Hernández, C.; Abundiz-Pérez, F.; López-Gutiérrez, R. M.; Acosta Del Campo, O. R., A RGB image encryption algorithm based on total plain image characteristics and chaos, Signal Processing, 109, 119-131 (2015)
[21] Wang, Y.; Wong, K.-W.; Liao, X.; Xiang, T.; Chen, G., A chaos-based image encryption algorithm with variable control parameters, Chaos, Solitons & Fractals, 41, 4, 1773-1783 (2009) · Zbl 1198.94005
[22] Xiao, F.; Gao, X.-P., An approach for short-term prediction on time series from parameter-varying systems, Journal of Software, 17, 5, 1042-1050 (2006) · Zbl 1101.68795
[23] Machkour, M.; Saaidi, A.; Benmaati, M. L., A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher, 3D Research, 6, article 36 (2015)
[24] Deng, Y.; Hu, H.; Xiong, W.; Xiong, N. N.; Liu, L., Analysis and design of digital chaotic systems with desirable performance via feedback control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45, 8, 1187-1200 (2015)
[25] Wang, X.; Qin, X.; Lin, T., A novel true random number generator based on mouse movement and a one-dimensional chaotic map, Mathematical Problems in Engineering, 2012 (2012) · Zbl 1264.65007
[26] Wang, X.-Y.; Qin, X., A new pseudo-random number generator based on CML and chaotic iteration, Nonlinear Dynamics, 70, 2, 1589-1592 (2012)
[27] Liu, Y.; Tong, X. J., A new pseudorandom number generator based on complex number chaotic equation, Chinese Physics B, 21, 9, article 090506 (2012)
[28] Tong, X.; Cui, M., Feedback image encryption algorithm with compound chaotic stream cipher based on perturbation, Science China Information Sciences, 53, 1, 191-202 (2010)
[29] Pincus, S. M., Approximate entropy as a measure of system complexity, Proceedings of the National Acadamy of Sciences of the United States of America, 88, 6, 2297-2301 (1991) · Zbl 0756.60103
[30] Bandt, C.; Pompe, B., Permutation entropy: a natural complexity measure for time series, Physical Review Letters, 88, 17 (2002)
[31] Toomey, J. P.; Kane, D. M., Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy, Optics Express, 22, 2, 1713-1725 (2014)
[32] Beker, H.; Piper, F. C., Cipher Systems: The Protection of Commnications (1982), New York, NY, USA: Wiley, New York, NY, USA
[33] Rukhin, A.; Sota, J.; Nechvatal, J., A statistical test suite for random and pseudorandom number generators for cryptographic applications, NISTSpecial Publication 800-22 (2010)
[34] L’Ecuyer, P.; Simard, R., TestU01: a C library for empirical testing of random number generators, ACM Transactions on Mathematical Software, 33, 4, 1-22 (2007) · Zbl 1365.65008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.