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

Yıl 2020, Cilt: 15 Sayı: 1, 13 - 18, 03.03.2020

Erkan Tanyıldızı Fatih Özkaynak

Öz

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.

Anahtar Kelimeler

Randomness, chaos, optimization

Kaynakça

• [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.