Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences

Lee, Po‐Han; Chen, Yi; Pei, Soo‐Chang; Chen, Yih-Yuh

doi:10.1016/j.cpc.2004.04.001

Cited by 16 publications

(5 citation statements)

References 23 publications

(37 reference statements)

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“…Nevertheless, periodic windows can appear in this interval, for example, when b = 3.8339 or b = 3.4704. Lee et al studied [34] that there is a correlation between positive sign Lyapunov's exponents (λ) and good chaotic random number sequences. This exponent provides information about how the chaotic system is sensitive to initial conditions.…”

Section: A Lightweight Stream Ciphersmentioning

confidence: 99%

GS3: A Lightweight Method of Generating Data Blocks With Shuffling, Scrambling, and Substituting Data for Constrained IoT Devices

Alcaraz-Velasco,

Palomares,

Olivares

2024

IEEE Internet Things J.

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The enabling devices and sensors of the Internet of Things (IoT) are characterized by devices with limited resources, where the computation and the energy consumption should be optimized. Application fields such as healthcare or multimedia content bring up security and privacy issues. Therefore, data security is critical. However, to obtain it, high computing resources are required. To avoid it, in this work, we propose a lightweight method to protect data transmissions in sensor devices. We present the GS3 method, it is based on a procedure set by Generating the data block, Shuffling, Scrambling, and applying Substitution boxes on the data. Our experimental results will show that GS3 introduces a minimal overhead, of just two bytes corresponding to the Cyclic Redundant Control 16 (CRC16) integrity control in the length of the messages concerning the original data. According to the execution time with respect of other encryption-based methods, even a 50% less than Chacha20 algorithm, as fewer steps and simpler computation procedures are required. Therefore, GS3 is a good choice to be used in resource-constrained IoT devices in which data integrity and security are required, taking into account the data freshness.

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Section: A Lightweight Stream Ciphersmentioning

confidence: 99%

GS3: A Lightweight Method of Generating Data Blocks With Shuffling, Scrambling, and Substituting Data for Constrained IoT Devices

Alcaraz-Velasco,

Palomares,

Olivares

2024

IEEE Internet Things J.

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“…Moreover, once the system is in chaotic status, the overall motion behavior is stable whereas the partial is unstable, and at least one of which Lyapunov exponents is positive, in addition, in the case that although the discrete chaotic systems and the continuous chaotic systems in the same dimension, the non-linear dynamic behavior of the former is more complex. In 2004, Lee suggested the close relative between the randomness presented by the chaotic sequences and the Lyapunov exponents of the corresponding chaotic system [24]. Nowadays, scholars are devoted to constructing a reasonable theoretical system for building high-dimensional discrete chaotic systems, the majority use methods that control chaos through feedback values of the states, methods that introduce parameters to perturb chaotic systems, and trial and error methods to construct high-dimensional discrete chaotic systems [25][26][27][28][29], be that as it may, these methods make it difficult to construct chaotic systems in more than four dimensions.…”

Section: Introductionmentioning

confidence: 99%

A new method for constructing discrete hyperchaotic systems with a controllable range of Lyapunov exponents and its application in information security

Zeng

Wang

et al. 2023

Phys. Scr.

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Since people use chaos extensively for a wide range of applications in data encryption and secure communications, a new method for designing practical high-dimensional discrete hyperchaotic systems is proposed for the first time in this paper. This method controls the range of the Lyapunov exponents in reverse by adding control variables so that the range of the values of the Lyapunov exponents is controlled within a specified interval, which is more suitable for engineering applications. Then, it is mathematically proved that the method ensures that the orbits of chaotic systems are globally finite and their Lyapunov exponents are bounded. In addition, as a practical demonstration of the selective image encryption scheme based on target template matching introduced in this paper, a 6-D discrete hyperchaotic system was created, and the analysis of the simulation results verifies the applicability of the 6-D hyperchaotic system designed by the method presented in this paper in the field of image encryption.

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“…Such properties have subtle relation with some requirements of secure encryption system, especially sensitivity with respect to change of secret key [2], [3], [4]. So, designing chaos-based encryption schemes emerged as a new research direction to reinforce information security of data sent through the Internet [5], [6], [7], [8], [9]. However, any digital chaotic system implemented in finiteprecision devices definitely degrade of various extents [10], [11], which may cause serious security flaws [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Wang

et al. 2016

IEEE Trans. Circuits Syst. I

211

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Abstract-Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaneys definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.

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Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences

Cited by 16 publications

References 23 publications

GS3: A Lightweight Method of Generating Data Blocks With Shuffling, Scrambling, and Substituting Data for Constrained IoT Devices

GS3: A Lightweight Method of Generating Data Blocks With Shuffling, Scrambling, and Substituting Data for Constrained IoT Devices

A new method for constructing discrete hyperchaotic systems with a controllable range of Lyapunov exponents and its application in information security

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

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