Year 2020,
Volume: 15 Issue: 1, 13 - 18, 03.03.2020
Erkan Tanyıldızı
,
Fatih Özkaynak
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.
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.
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.