A novel method for producing pseudo random numbers from differential equation-based chaotic systems

Öztürk, İsmail; Kılıç, Recai

doi:10.1007/s11071-015-1932-5

Cited by 40 publications

(18 citation statements)

References 35 publications

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“…The distinct properties of chaos, such as diffusion and confusion can, in principle, ensure pseudo-random numbers of high-quality, mainly because of the sensitivity to initial conditions, ergodicity, mixing properties, complex numerical patterns, relatively simple equations and their determinism [3,5,39,28]. Therefore, significant progress has been reported, for instance chaos-based PRNGs were proposed using chaotic systems [35,10,7,33,19,34,13,38], cellular automata [47,25,46], quantum chaotic maps [1,2,53] and even mixing the physical chaotic sources, e.g. chaotic semiconductor lasers [48,21].…”

Section: Introductionmentioning

confidence: 99%

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Machicao

Bruno

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincaré diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps such as the logistic map can be considered as good PRNG methods.

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Section: Introductionmentioning

confidence: 99%

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Machicao

Bruno

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…), перемещающихся на двух опорах. В последние годы появились работы, посвященные проблемам стабилизации обратного маятника, связанного с движущимся двухколесным транспортным средством [6][7][8]. Эти исследования имеют потенциальные перспективы применения во многих областях, таких как транспорт и разведка, в связи с компактной конструкцией, удобством эксплуатации, высокой маневренностью и низким расходом топлива таких устройств.…”

Section: Introductionunclassified

“…Г u t h x t Г Г u h x t h x t =(25) и с помощью специальной предельной конструкции на все непрерывные. Так как выход этого оператора не является дифференцируемым, то в дальнейшем используется аппроксимация люфта моделью Боука-Вена[7]. Эта известная полуфизическая модель широко используется для феноменологического описания гистерезисных эффектов.…”

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Stabilization of Inverted Pendulum on a Two-Wheeled Vehicle

Ryazhskih¹,

Семенов²,

Rukavicin³

et al. 2017

MMPh

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Рассматривается механическая система, состоящая из двухколесной тележки, на оси которой располагается обратный маятник. Задача заключается в формировании такого управляющего воздействия, формируемого по принципу обратной связи, которое, с одной стороны, обеспечивало бы заданный закон движения механического средства, а с другой, стабилизировало бы неустойчивое положение маятника. Ключевые слова: механическая система; двухколесное транспортное средство; обратный маятник; люфт; стабилизация; управление.

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“…aperiodicity, deterministic dynamics, ergodicity and sensitivity to initial conditions, they have recently been utilized in cryptosystems [18]- [23]. To encrypt the Δ modulation systems, while the required random bits can be generated from a hardware-based generator (e.g., using thermal noise [24] and radioactive decay [25]) or from softwarebased generators (e.g., linear congruential generators [26]), chaotic systems are very simple to realize and offer a hybrid structure with the features of hardware and software based approaches [27]- [30]. The number of the chaotic systems have been increased over time in the literature, which allows us to benefit from chaotic dynamics for generating efficient chaotic random bits for use in cryptographic applications [31]- [35].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Encryption Based Data Transmission Using Delta and Delta-Sigma Modulators

Ablay¹

2016

International Journal of Applied Mathematics, Electronics and Computers

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Delta and Delta-Sigma modulation methods have been getting a great interest recently due to the great progress in analogdigital very large scale integration technology. Since the outputs of these methods are digital, the data can be securely encrypted using very simple standard hardware. In this work, a chaotic random bit generator based approach for encrypting digital data of the delta and delta-sigma modulators is studied. The chaotic bit generation can easily be implemented in the digital hardware of the modulators due to simplicity of the chaotic dynamics. The randomness of the generated chaotic bits are proved with visual and statistical tests. The security of the proposed approach is evaluated via key space estimation based attacks. The efficiency of the methods is validated with simulations.

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A novel method for producing pseudo random numbers from differential equation-based chaotic systems

Cited by 40 publications

References 35 publications

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Stabilization of Inverted Pendulum on a Two-Wheeled Vehicle

Chaotic Encryption Based Data Transmission Using Delta and Delta-Sigma Modulators

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