Microcontroller-based Random Number Generator Implementation by Using Discrete Chaotic Maps

Year 2020, Volume: 24 Issue: 5, 832 - 844, 01.10.2020

Serdar Çiçek

https://doi.org/10.16984/saufenbilder.727449

Cited By: 2

Abstract

In recent decades, chaos theory has been used in different engineering applications of different disciplines. Discrete chaotic maps can be used in encryption applications for digital applications. In this study, firstly, Lozi, Tinkerbell and Barnsley Fern discrete chaotic maps are implemented based on microcontroller. Then, microcontroller based random number generator is implemented by using the three different two-dimensional discrete chaotic maps. The designed random number generator outputs are applied to NIST (National Institute of Standards and Technology) 800-22 and FIPS (Federal Information Processing Standard) tests for randomness validity. The random numbers are successful in all tests.

Keywords

chaotic map, random number generators, NIST 800-22, FIPS, microcontroller

References

• Y. Liu and X. Tong, “Hyperchaotic system-based pseudorandom number generator”, IET Information Security, vol. 10, no. 6, pp. 433-441, 2016.
• İ. Koyuncu and A.T. Özcerit, “The design and realization of a new high speed FPGA-based chaotic true random number generator”, Computers and Electrical Engineering, Vol. 58, pp. 203-214, 2017.
• F. Yu, L. Li, Q. Tang, S. Cai, Y. Song and Q. Xu, “A survey on true random number generators based on chaos”, Discrete Dynamics in Nature and Society, Vol. 2019, Article ID: 2545123, 2019.
• X.Y. Wang and Y.X. Xie, “A design of pseudo-random bit generator based on single chaotic system”, International Journal of Modern Physics C, Vol. 23, no. 3, pp.1250024-1 – 1250024-11, 2012.
• S. Ergün and S. Özoğuz, “Truly random number generators based on non-autonomous continuous-time chaos”, International Journal of Circuit Theory and Applications, Vol. 38, pp. 1-24, 2010.
• M.E. Yalçın, J.A.K. Suykens and J. Vandewalle, “True random bit generation from a double-scroll attractor”, IEEE Transactions on Circuit and Systems-I: Regular Papers, Vol. 51, no. 7, pp. 1395-1404, 2004.
• S. Vaidyanathan, A. Akgul, S. Kaçar and U. Çavuşoğlu, “A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography”, The European Physical Journal Plus, Vol. 133, Article number: 46, 2018.
• A. Akgul, C. Arslan and B. Arıcıoglu, “Design of an interface for random number generators based on integer and fractional order chaotic systems”, Chaos Theory and Applications, Vol. 01, no. 1, pp. 1-18, 2019.
• B.C. Bao, H.Z. Li, X. Zhang and M. Chen, “Initial-switched boosting bifurcations in 2D hyperchaotic map”, Chaos, Vol. 30, no. 3, 033107, 2020.
• D. Lambic, “A novel method of S-box design based on discrete chaotic map”, Nonlinear Dynamics, Vol. 87, pp. 2407-2413, 2017.
• A.A. Alzaidi, M. Ahmad, M.N. Doja, E.A. Solami and M.M.S. Beg, “A new 1D chaotic map and β-hill climbing for generating substitution-boxes”, IEEE Access, Vol. 6, pp. 55405-55418, 2018.
• O. Alpar, “Analysis of a new simple one dimensional chaotic map”, Nonlinear Dynamics, vol. 78, no. 2, pp. 771-778, 2014.
• Z. Hua and Y. Zhou, “One-dimensional nonlinear model for producing chaos”, IEEE Transactions on Circuit and Systems-I: Regular Papers, Vol. 65, no. 1, pp. 235-246, 2018.
• L. Liu and S. Miao, “A new simple one-dimensional chaotic map and its application for image encryption”, Multimedia Tools and Applications, Vol. 77, pp. 21445-21462, 2018.
• M. Hènon, “A two-dimensional mapping with a strange attractor”, Communications in Mathematical Physics, Vol. 50, pp. 69-77, 1976.
• L.Q. Chen, “An open-plus-closed-loop control for discrete chaos and hyperchaos”, Physics Letters A, Vol. 281, pp. 327-333, 2001.
• M.F. Barnsley, “Fractals Everywhere”, Academic Press, USA, pp. 85-91, 1993.
• A. Ouannas, A.A. Khennaoui, S. Bendoukha, T.P. Vo, V.T. Pham and V.V. Huynh, “The fractional form of the Tinkerbell map is chaotic”, Applied Sciences, Vol. 8, Article ID: 2640, 2018.
• R. Lozi, “Un attracteur ètrange (?) du type attracteur de hènon”, Journal De Physique, Vol. 39, no. 8, pp. C5-9, 1978.
• Y. Xiao, K. Sun and S. He, “Constructing chaotic map with multi-cavity”, The European Physical Journal Plus, Vol. 135, Article number: 21, 2020.
• Z. Hua, Y. Zhou, C.M. Pun and C.L.P. Chen, “2D sine logistic modulation map for image encryption”, Information Sciences, Vol. 297, pp. 80-94, 2015.
• Z. Liu, T. Xia and J. Wang, “Fractional two-dimensional discrete chaotic map its applications to the information security with elliptic-curve public key cryptography”, Journal of Vibration and Control, Vol. 24, no. 20, pp. 4797-4824, 2018.
• Y. Peng, K. Sun, D. Peng and W. Ai, “Dynamics of a higher dimensional fractional-order chaotic map”, Physica A, Vol. 525, pp. 96-107, 2019.
• [A. Alghafis, N. Munir, M. Khan and I. Hussain, “An encryption scheme based on discrete quantum map and continuous chaotic system”, International Journal of Theoretical Physics, Vol. 59, pp. 1227-1240, 2020.
• J. Fridrich, “Symmetric ciphers based on two-dimensional chaotic maps”, International Journal of Bifurcation and Chaos, Vol. 8, no. 6, pp. 1259-1284, 1998.
• X. Liao, X. Li, J. Pen and G. Chen, “A digital secure image communication scheme based on the chaotic Chebyshev map”, International Journal of Communication Systems, Vol. 17, pp. 437-445, 2004.
• S. Papadimitriou, A. Bezerianos, T. Bountis and G. Pavlides, “Secure communication protocols with discrete nonlinear chaotic maps”, Journal of Systems Architecture, Vol. 47, pp. 61-72, 2001.
• M. Zhang and X. Tong, “A new chaotic map based image encryption schemes for several image formats”, The Journal of Systems and Software, Vol. 98, pp. 140-154, 2014.
• R. Li, Q. Liu and L. Liu, “Novel image encryption algorithm based on improved logistic map”, IET Image Processing, Vol. 13, no. 1, pp. 125-134, 2019.
• C. Pak, J. Kim, K. An, C. Kim, K. Kim and C. Pak, “A novel color image LSB steganography using improved 1D chaotic map”, Multimedia Tools and Applications, Vol. 79, pp. 1409-1425, 2020.
• Y. Naseer, D. Shah and T. Shah, “A novel approach to improve multimedia security utilizing 3D mixed chaotic map”, Microprocessors and Microsystems, Vol. 65, pp. 1-6, 2019.
• D. Herbadji, A. Belmeguenai, N. Derouiche and H. Liu, “Colour image encryption scheme based on enhanced quadratic map”, IET Image Processing, Vol. 14, no. 1, pp. 40-52, 2019.
• M.A. Dastgheib and M. Farhang, “A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period”, Nonlinear Dynamics, Vol. 89, pp. 2957-2966, 2017.
• E. Avaroğlu, “Pseudorandom number generator based on Arnold cat map and statistical analysis”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 25, pp. 633-643, 2017.
• D. Lambìc, M. Nikolic, “Pseudo-random number generator based on discrete-space chaotic map”, Nonlinear Dynamics, Vol. 90, pp. 223-232, 2017.
• A.V. Tutueva, E.G. Nepomuceno, A.I. Karimov, V.S. Andreev and D.N. Butusov, “Adaptive chaotic maps and their application to pseudo-random numbers generation”, Chaos, Solitons and Fractals, Vol. 133, 109615, 2020.
• O. Garasym, I. Taralova and R. Lozi, “New Nonlinear CPRNG Based on Tent and Logistic Maps”. In: J. Lü, X. Yu, G. Chen, W. Yu (eds) Complex Systems and Networks. Understanding Complex Systems, Springer, Berlin, Heidelberg, pp.131-161, 2016.
• Magfirawaty, M.T. Suryadi, K. Ramli, “On the design of henon and logistic map-based random number generator”, IOP Conference Series: Journal of Physics: Conference Series, Vol. 893, 012060, 2017.
• S. Ergün, S. Tanrıseven, “Random number generators based on discrete-time chaotic maps”, IEEE EUROCON 18th International Conference on Smart Technologies, pp. 1-4, 2019.
• L. Moysis and A.T. Azar, “New discrete time 2D chaotic maps”, International Journal of System Dynamics Applications, Vol. 6, no. 1, pp.77-104, 2017.
• A.M. Garipcan, E. Erdem, “Implementation and performance analysis of true random number generator on FPGA environment by using non-periodic chaotic signals obtained from chaotic maps”, Arabian Journal for Science and Engineering, Vol. 44, pp. 9427-9441, 2019.
• P. L’ecuyer, R. Simard, “TestU01: A C library for empirical testing of random number generators”, ACM Transactions on Mathematical Software, Vol. 33, no. 4, 22, 2007.
• R. Santoro, O. Sentieys and S. Roy, “On-line monitoring of random number generators for embedded security”, IEEE International Symposium on Circuit and Systems, pp. 3050-3053, 2009.
• D. Lihua, Z. Yong, J. Ligang and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite”, IEEE Tenth International Conference on Computational Intelligence and Security”, pp. 402-404, 2014.
• A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray and S. Vo, “A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications”, National Institute of Standards and Technology (NIST), 2010.
• L. Min, T. Chen and H. Zang, “Analysis of FIPS 140-2 test and chaos-based pseudorandom number generators”, Chaotic Modeling and Simulation, Vol. 2, pp. 273-280, 2013.
• İ. Koyuncu, “Kriptolojik uygulamalar için FPGA tabanlı yeni kaotik osilatörlerin ve gerçek rastgele sayı üreteçlerinin tasarımı ve gerçeklenmesi”, PhD Thesis, Sakarya University, Institute of Science, Sakarya, 2014.