Cryptanalysis of an image cryptosystem based on logistic map

This research presents a method of image encryption that has been designed based on the algorithm of complete shuffling, transformation of substitution box, and predicated image crypto-system. This proposed algorithm presents extra confusion in the first phase because of including an S-box based on using substitution by AES algorithm in encryption and its inverse in Decryption. In the second phase, shifting and rotation were used based on secrete key in each channel depending on the result from the chaotic map, 2D logistic map and the output was processed and used for the encryption algorithm. It is known from earlier studies that simple encryption of images based on the scheme of shuffling is insecure in the face of chosen cipher text attacks. Later, an extended algorithm has been projected. This algorithm performs well against chosen cipher text attacks. In addition, the proposed approach was analyzed for NPCR, UACI (Unified Average Changing Intensity), and Entropy analysis for determining its strength.

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Chaotic logistic map, parabola, and gravity

10.31219/osf.io/g75we ◽

2019 ◽

Author(s):

Matheus Pereira Lobo

Keyword(s):

Logistic Map ◽

Chaotic Logistic Map

I am trying to connect gravity with chaos via the parabola in the logistic map.

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An improved RSA image encryption algorithm using 1-D logistic map

International Journal of communication and computer Technologies ◽

10.31838/ijccts/06.01.01 ◽

2019 ◽

Vol 6 (1) ◽

Keyword(s):

Image Encryption ◽

Logistic Map ◽

Encryption Algorithm ◽

Image Encryption Algorithm

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AN EMPIRICAL APPROACH TO STUDY THE STABILITY OF GENERALIZED LOGISTIC MAP IN SUPERIOR ORBIT

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.10.67 ◽

2020 ◽

Vol 9 (10) ◽

pp. 8375-8384

Author(s):

V. Kumar ◽

Khamosh ◽

Ashish

Keyword(s):

Logistic Map ◽

Empirical Approach ◽

The Stability ◽

Superior Orbit

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Linear and Nonlinear Dynamic Behaviour

10.1093/oso/9780198782933.003.0002 ◽

2018 ◽

Author(s):

Ray Huffaker ◽

Marco Bittelli ◽

Rodolfo Rosa

Keyword(s):

Dynamic Behavior ◽

Dynamic Systems ◽

Dynamic Behaviour ◽

Nonlinear Dynamical Systems ◽

Logistic Map ◽

Nonlinear Dynamical ◽

Deterministic Dynamic ◽

Random Behavior ◽

Single Solution ◽

Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

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Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽

10.3390/e22040474 ◽

2020 ◽

Vol 22 (4) ◽

pp. 474 ◽

Cited By ~ 5

Author(s):

Lazaros Moysis ◽

Christos Volos ◽

Sajad Jafari ◽

Jesus M. Munoz-Pacheco ◽

Jacques Kengne ◽

...

Keyword(s):

Lyapunov Exponent ◽

Image Encryption ◽

Fuzzy Numbers ◽

Statistical Tests ◽

Logistic Map ◽

Simple Rule ◽

Pseudorandom Number ◽

Bifurcation Diagrams ◽

Triangular Numbers ◽

Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

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EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408022640 ◽

2008 ◽

Vol 18 (12) ◽

pp. 3679-3687 ◽

Cited By ~ 6

Author(s):

AYDIN A. CECEN ◽

CAHIT ERKAL

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Lyapunov Exponents ◽

Correlation Dimension ◽

Time Series Data ◽

Logistic Map ◽

Model Identification ◽

Series Data ◽

Largest Lyapunov Exponent ◽

The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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