The Shannon entropy: An efficient indicator of dynamical stability

Cincotta, Pablo Miguel; Giordano, C.; Silva, Raphael Alves; Beaugé, C.

doi:10.1016/j.physd.2020.132816

Cited by 45 publications

(30 citation statements)

References 37 publications

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“…The ciphertext with a higher Shannon Entropy value will be more statistically difficult to decompose by an attacker. The value was calculated in reference to previous studies [55]- [58]:…”

Section: B Security Comparisonmentioning

confidence: 99%

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Hermawan¹,

Winarko²,

Ashari³

2021

International Journal on Advanced Science, Engineering and Information Technology

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RSA is the most popular public-key cryptography. The main strength of the algorithm is based on the difficulty of factoring in a large integer number. RSA has also been applied in a system with limited resource environments like single-board computers (SBC). To ensure data security, a recommendation to use a key size longer than 2048 bits generates challenges for implementing RSA in the SBC. This research proposes an EPNR (Eight Prime Numbers of Modified RSA) method, a modified double RSA based on eight prime numbers combined with the CRT method, to speed up the random key generation and decryption mechanism. The method is implemented in a Raspberry Pi 4 Model B+. The running time and security performances of the EPNR were analyzed and compared to the other models. Compared to the others model based on the standard RSA scheme, the proposed model is faster 21.78 times in a random key generation, 9.03 times in encryption and decryption processing. The EPNR has resistance to Wiener, statistical, and factorization attacks (GNFS and Fermat). Using standard RSA in the second encryption mechanism, the GNFS is not yet effective for attacking the proposed model. The modified Fermat Factorization algorithm is more difficult and needed more extra times for factoring a large composite number into eight prime numbers correctly. The method will be useful for implementing certificates authentication and distribution of the secret key. It is very suitable to enhance more secure RSA implementation in an SBC environment.

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“…The ciphertext with a higher Shannon Entropy value will be more statistically difficult to decompose by an attacker. The value was calculated in reference to previous studies [55]- [58]:…”

Section: B Security Comparisonmentioning

confidence: 99%

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Hermawan¹,

Winarko²,

Ashari³

2021

International Journal on Advanced Science, Engineering and Information Technology

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“…The Shannon entropy thus serves as an efficient tool to quantify stability, but its greatest benefit is that the direct estimation of the diffusion coefficient of the chaotic diffusion is also feasible. Following Cincotta et al (2021a) and Cincotta et al (2021b), the local diffusion coefficient for the trajectory in the interval ( , + ) is given by…”

Section: The Shannon Entropy Formalismmentioning

confidence: 99%

“…These early applications of the entropy were limited to discrete dynamical maps of low dimensions, whereas the first application to a more complex, planetary-type problem was presented in Beaugé & Cincotta (2019) where the dynamics of the planar restricted three-body problem (3BP) was investigated in the vicinity of first-order mean-motion resonances. Later, Cincotta et al (2021a) and Cincotta et al (2021b) studied the planar (non-restricted) 3BP, more specifically, they have chosen the HD 20003 and HD 181433 exoplanetary systems, respectively, to test the sensitivity of the Shannon entropy formalism on real systems. In the present paper, we extend the use of the Shannon entropy to the planar (non-restricted) four-body problem (4BP) via performing a dynamical analysis of the Kepler-60 three-planet extrasolar system.…”

Section: Introductionmentioning

confidence: 99%

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system

Kővári,

Érdi,

Sándor

2021

Preprint

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In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the 2-body resonances circulate and that of the 3-body resonance librates; and (ii) the chain of two 2-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration but we state too that, in either case, the relevant resonance plays an important role to stabilize the system. The derived stability times are no shorter than 10 8 yrs in the central parts of the resonances.

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“…The events with low probability are generally had more surprising packages and information than the events with high probability because high-probability events are common in nature. The method used to calculate the amount of information that a random variable may possess is named Shannon information [1] and later on called entropy [2]. Clausius initially introduced entropy in the late nineteenth century by studying the dish gas disorder problem and quantifying the disorder produced by the gas through a measure named entropy [3].…”

Section: Introductionmentioning

confidence: 99%

“…where V is the variable that takes values " v " from the universal set V , and F is the fuzzy set on V that represents vague predicate. If v is any particular value of V , it is said to belong to the fuzzy group with membership grade F(v) , the degree of truth, and T(p) of the proposition is used in (1).…”

Section: Introductionmentioning

confidence: 99%

Neutrosophic entropy measures for the Weibull distribution: theory and applications

Sherwani

Arshad

Albassam

et al. 2021

Complex Intell. Syst.

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Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it.

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The Shannon entropy: An efficient indicator of dynamical stability

Cited by 45 publications

References 37 publications

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system

Neutrosophic entropy measures for the Weibull distribution: theory and applications

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