A novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Murillo-Escobar, Miguel Ángel; Cruz-Hernández, C.; Cardoza-Avendaño, L.; Méndez-Ramírez, Rodrigo

doi:10.1007/s11071-016-3051-3

Cited by 169 publications

(77 citation statements)

References 42 publications

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“…Furthermore, when comparing to other studies, our method is still superior. Under the same accuracy, the key spaces of the PRBG proposed in [19,[34][35][36] are 2 384 , 2 400 , 2 199 , and 2 128 , respectively, which are all smaller than ours.…”

Section: Key Spacementioning

confidence: 61%

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A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics

Huang

Liu

et al. 2019

Complexity

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In this paper, a new chaotic system is proposed based on mixing three-dimensional Chen chaotic system with a chaotic tactics. This new system is proved to be chaotic under Wiggins' chaos definition and can generate chaotic sequences with high complexity. Furthermore, we propose a new pseudorandom bit generator (PRBG) based on this new system. A coding algorithm is used to make the sequences uniform. Both statistical and security tests are provided to show the generated sequences are with good randomness and high complexity to withstand attacks.

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Section: Key Spacementioning

confidence: 61%

“…In this paper, the algorithms are simulated by Matlab R2014a on the 64-bit computer with [35] 20.5383 Ref. [36] 1.7 Ref. [37] 0.4844 Ref.…”

Section: Linear Complexitymentioning

confidence: 99%

A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics

Huang

Liu

et al. 2019

Complexity

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“…By probabilistic methods, the randomness is determined by the test p-value. If the p-value is greater than the significance level 0.01, then it indicates that the sequence is random [26][27][28]. For the sequences S = Dec2bin Mod S θ , 2 32 , the test results of NIST are given in Table 3.…”

Section: Discussionmentioning

confidence: 99%

Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application

Cai

2019

Mathematics

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The Van der Pol oscillator is investigated by the parameter control method. This method only needs to control one parameter of the Van der Pol oscillator by a simple periodic function; then, the Van der Pol oscillator can behave chaotically from the stable limit cycle. Based on the new Van der Pol oscillator with variable parameter (VdPVP), some dynamical characteristics are discussed by numerical simulations, such as the Lyapunov exponents and bifurcation diagrams. The numerical results show that there exists a positive Lyapunov exponent in the VdPVP. Therefore, an encryption algorithm is designed by the pseudo-random sequences generated from the VdPVP. This simple algorithm consists of chaos scrambling and chaos XOR (exclusive-or) operation, and the statistical analyses show that it has good security and encryption effectiveness. Finally, the feasibility and validity are verified by simulation experiments of image encryption.

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“…Given these considerations, we will obtain a higher Q T . is means that the state variables of the 3D Lorenz, Rössler, Chen, Liu and Chen, and MACM CSs in their DVs by using the NAs (6)-(13) have a better representation of f Td , which is very attractive for applications based in chaos such as: master key definition, encryption, and secure communications [9,37,43,56].…”

Section: Complexitymentioning

confidence: 99%

Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

et al. 2019

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Digital implementation of chaotic systems (CSs) has attracted increasing attention from researchers due to several applications in engineering, e.g., in areas as cryptography and autonomous mobile robots, where the properties of chaotic systems are strongly related. The CSs in the continuous version (CV) need to be discretized where chaotic degradation must be analyzed to guarantee preservation of chaos. In this paper, we present a degradation analysis of five three-dimensional CSs and the necessary conditions to implement the discretized versions (DVs) of Lorenz, Rössler, Chen, Liu and Chen, and Méndez-Arellano-Cruz-Martínez (MACM) CSs. Analytical and numerical analyses of chaos degradation are conducted by using the time series method; the maximum discrete step size and the Lyapunov Exponents (LEs) are computed by using the Euler, Heun, and fourth-order Runge–Kutta (RK4) numerical algorithms (NAs). We conducted comparative studies of performance based on time complexity of the five proposed CSs in their DVs by using four embedded systems (ESs) based on three families of Microchip microcontrollers 8-bit PIC16F, 16-bit dsPIC33FJ, and 32-bit PIC32MZ (of low-cost electronic implementation) and a Field Programmable Gate Array (FPGA). Based on the results, the intervals at control parameters to guarantee chaos are proposed, which improves the performance characteristics of the five proposed CSs in their DVs based on digital applications.

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A novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Cited by 169 publications

References 42 publications

A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics

A New Pseudorandom Bit Generator Based on Mixing Three‐Dimensional Chen Chaotic System with a Chaotic Tactics

Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application

Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

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