A Statistical Randomness Generation Algorithm Based on Nonlinear Behavior of Discrete Time Chaotic Systems

Year 2020, Volume: 15 Issue: 1, 13 - 18, 03.03.2020

Erkan Tanyıldızı , Fatih Özkaynak

Abstract

Statistical randomness is a critical requirement for many applications. Generally, it is common to use a generator algorithm for statistical randomness. In this study, a generator algorithm proposed benefiting from chaotic systems. This proposed approach is based on chaotic maps with a simpler mathematical model compared to other chaotic system classes. So the generator has high practical applicability. In addition, optimization algorithms to guarantee statistical properties of generator.

Keywords

Randomness , chaos , optimization

References

• [1] Sprott J. Elegant Chaos Algebraically Simple Chaotic Flows. World Scientific, 2010. [2] Özkaynak F. Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dynam 2018; 92(2): 305-313. https://doi.org/10.1007/s11071-018-4056-x [3] Stipčević M, Koç ÇK. True Random Number Generators. In: Koç ÇK (eds) Open Problems in Mathematics and Computational Science. Cham: Springer, 2014. [4] Schindler W. Random Number Generators for Cryptographic Applications. Koç ÇK (ed.): Cryptographic Engineering. Signals and Communication Theory, Berlin: Springer, 2009. [5] Knuth D. The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. 2nd ed. Reading, Massachusetts: Addison-Wesley,1981. [6] Ripley B. Computer Generation of Random Variables: A Tutorial. Int Stat Rev 1983; 51: 301-319. [7] L'Ecuyer P. Random Numbers for Simulation. Commun ACM 1990; 33(1): 85-97. [8] James F. A review of pseudorandom number generators. Compu Phys Commun 1990. 60: 329-344. [9] Lagarias JC. Pseudorandom Number Generators in Cryptography and Number Theory. Proc Symp Appl Math 1990; 42: 115–143. [10] Ritter T. The Efficient Generation of Cryptographic Confusion Sequences. Cryptologia 1991; 15(2): 81-139. [11] Aydın Y, Özkaynak F. A Provable Secure Image Encryption Schema Based on Fractional Order Chaotic Systems. The 23rd International Conference ELECTRONICS 2019; 17-19 June 2019; Palanga, Lithuania. [12] Tapiero CS, Vallois P. Randomness and fractional stable distributions. Physica A: Statistical Mechanics and its Applications 2018; 511: 54-60 [13] Bürhan Y, Artuğer F, Özkaynak F. A Novel Hybrid Image Encryption Algorithm Based on Data Compression and Chaotic Key Planning Algorithms. IEEE 7th International Symposium on Digital Forensic and Security; June 10-12 2019; Barcelos, Portugal. [14] Dastgheib MA & Farhang M. A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period. Nonlinear Dynam 2017; 89: 2957-2966 https://doi.org/10.1007/s11071-017-3638-3 [15] Murillo-Escobar MA, Cruz-Hernández C, Cardoza-Avendaño L, et al. A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dynam 2017 87: 407-425. https://doi.org/10.1007/s11071-016-3051-3 [16] Lv X, Liao X & Yang B. A novel pseudo-random number generator from coupled map lattice with time-varying delay. Nonlinear Dynam 2018; 94: 325-341. https://doi.org/10.1007/s11071-018-4361-4 [17] Özkaynak F. Cryptographically secure random number generator with chaotic additional input. Nonlinear Dynam 2014; 78: 2015-2020. https://doi.org/10.1007/s11071-014-1591-y [18] Sahari ML & Boukemara I. A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption. Nonlinear Dynam 2018; 94: 723-744. https://doi.org/10.1007/s11071-018-4390-z [19] Özkaynak F. The Effects on Performance of Using Chaotic Systems in Entropy Source of Deterministic Random Number Generators. 11th CHAOS 2018 International Conference; 5 - 8 June 2018; Sapienza University of Rome, Italy. pp.415-420 [20] Özer AB. CIDE: Chaotically Initialized Differential Evolution. Expert Syst Appl 2010; 37(6): 4632-4641 [21] Tanyıldızı E, Demir G. Golden Sine Algorithm: A Novel Math-Inspired Algorithm. Advances in Electrical and Comput Eng 2017; 17(2): 71-78. [22] Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M, Vangel M, Banks D, Heckert A, Dray J, Vo S. A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800–22rev1a, 2010. [23] Masoom MA, Umbach D and Saleh AKMDE. Estimating Life Functions of Chi Distribution Using Selected Order Statistics. IIE Transactions 1992; 24(5): 88-98. [24] Özkaynak F. A novel method to improve the performance of chaos based evolutionary algorithms. Optik 2015; 126(24): 5434-5438. https://doi.org/10.1016/j.ijleo.2015.09.098 [25] Persohn KJ, Povinelli RJ. Analyzing logistic map pseudorandom number gen- erators for periodicity induced by finite precision floating-point representation. Chaos Solit Fract 2012; 45: 238–245.