On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences

Liu, Lingfeng; Miao, Suoxia; Liu, Bocheng

doi:10.3390/e17041936

Cited by 8 publications

(6 citation statements)

References 29 publications

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“…Then, we used the second set of 128 sensors to evaluate the probabilities of the previously determined bins as in figure 4(e). Eventually, we estimated the entropy per sensor using the classical formula: S = −Σ i p i logp i , where the p i is the bin probability [40,41]. Consider X(F,S,B) denoting the fingerprint built upon features F and S sensors sliced in B bins, where F = 1 (only N feature), S = 256 and B = 4.…”

Section: S[11]@db-a Vs S[11]@db-r (Upper) S[78]@db-a Vs S[78]@db-r (M...mentioning

confidence: 99%

Exploring electrospun nanofibers for physically unclonable functions: a scalable and robust method toward unique identifiers

Bai¹,

Tian²,

Wang³

et al. 2022

J. Phys. D: Appl. Phys.

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Optical physical unclonable functions (PUFs) have great potentials in the security identification of Internet of Things. In this work, electrospun nanofibers are proposed as a candidate for a nanoscale, robust, stable and scalable PUF. The dark-field reflectance images of the polymer fibers are quantitatively analyzed by Hough transform. We find that the fiber length and orientation distribution reach an optimal point as the fiber density grows up over 850 in 400 x 400 pixels for a polyvinylpyrrolidone nanofiber based PUF device. Subsequently, we test the robustness and randomness of the PUF pattern by using the fiber amount as an encoding feature, generating a reconstruction success rate over 80% and simultaneously an entropy of 260 bits within a mean size of 4 cm2. A scale-invariant algorithm is adopted to identify the uniqueness of each pattern on a 256-sensor device. Furthermore, thermo-, moisture as well as photostability of the authentication process are systematically investigated by comparing polyacrylonitrile to polyvinylpyrrolidone system.

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Section: S[11]@db-a Vs S[11]@db-r (Upper) S[78]@db-a Vs S[78]@db-r (M...mentioning

confidence: 99%

Exploring electrospun nanofibers for physically unclonable functions: a scalable and robust method toward unique identifiers

Bai¹,

Tian²,

Wang³

et al. 2022

J. Phys. D: Appl. Phys.

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show abstract

“…As expected, an irregular series should be more complex than a regular one, i.e., a pure stochastic series should have larger complexity value than a regular one in single scale case [ 8 ], and, possessing the partial past history and related structure information, a time series with long-range correlations has larger complexity than a pure stochastic series in multiscale case [ 9 ]. Recently, abundant complexity methods and corresponding improved measures have been proposed, for example, entropy measures, Lyapunov exponents and fractal dimension [ 10 , 11 , 12 , 13 , 14 , 15 , 16 ], where entropy measures are the most favorite for their simplicity in understanding and convenience for program with computing software. Enormous revised nonlinear measures based on permutation entropy (PermEn), approximate entroy (AppEn), sample entropy (SampEn) and fuzzy entropy (FuzzyEn) are proposed to detect the complexity dynamics of physiological, traffic and financial time series which are typically short, and commonly contaminated by noise [ 8 , 11 , 12 , 13 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

Fractional Refined Composite Multiscale Fuzzy Entropy of International Stock Indices

Zhang

2019

Entropy

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Fractional refined composite multiscale fuzzy entropy (FRCMFE), which aims to relieve the large fluctuation of fuzzy entropy (FuzzyEn) measure and significantly discriminate different short-term financial time series with noise, is proposed to quantify the complexity dynamics of the international stock indices in the paper. To comprehend the FRCMFE, the complexity analyses of Gaussian white noise with different signal lengths, the random logarithmic returns and volatility series of the international stock indices are comparatively performed with multiscale fuzzy entropy (MFE), composite multiscale fuzzy entropy (CMFE) and refined composite multiscale fuzzy entropy (RCMFE). The empirical results show that the FRCMFE measure outperforms the traditional methods to some extent.

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“…[ 9 ] studied the relationship between the eigenvalue and Shannon’s entropy of finite symbol sequences. The authors of [ 10 ] studied the relationship between the nonlinear complexity and Shannon’s entropy of random binary sequences. Moreover, the authors of [ 11 ] investigated a method to construct finite length sequences with the large nonlinear complexity on the finite field.…”

Section: Introductionmentioning

confidence: 99%

The Eigenvalue Complexity of Sequences in the Real Domain

Liu

Xiang

et al. 2019

Entropy

Self Cite

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The eigenvalue is one of the important cryptographic complexity measures for sequences. However, the eigenvalue can only evaluate sequences with finite symbols—it is not applicable for real number sequences. Recently, chaos-based cryptography has received widespread attention for its perfect dynamical characteristics. However, dynamical complexity does not completely equate to cryptographic complexity. The security of the chaos-based cryptographic algorithm is not fully guaranteed unless it can be proven or measured by cryptographic standards. Therefore, in this paper, we extended the eigenvalue complexity measure from the finite field to the real number field to make it applicable for the complexity measurement of real number sequences. The probability distribution, expectation, and variance of the eigenvalue of real number sequences are discussed both theoretically and experimentally. With the extension of eigenvalue, we can evaluate the cryptographic complexity of real number sequences, which have a great advantage for cryptographic usage, especially for chaos-based cryptography.

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On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences

Cited by 8 publications

References 29 publications

Exploring electrospun nanofibers for physically unclonable functions: a scalable and robust method toward unique identifiers

Exploring electrospun nanofibers for physically unclonable functions: a scalable and robust method toward unique identifiers

Fractional Refined Composite Multiscale Fuzzy Entropy of International Stock Indices

The Eigenvalue Complexity of Sequences in the Real Domain

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