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

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
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.

scholarly journals A New Two-Dimensional Mutual Coupled Logistic Map and Its Application for Pseudorandom Number Generator

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Xuan Huang ◽  
Lingfeng Liu ◽  
Xiangjun Li ◽  
Minrong Yu ◽  
Zijie Wu
Keyword(s):  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Security Analysis ◽  
Three Dimensional ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Two Dimensional ◽  
Practical Applications

Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

scholarly journals Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps

2015 ◽  
Vol 2015 ◽  
pp. 1-23 ◽  
Author(s):  
Wafaa S. Sayed ◽  
Ahmed G. Radwan ◽  
Hossam A. H. Fahmy
Keyword(s):  
Lyapunov Exponent ◽  
Bifurcation Diagram ◽  
Degrees Of Freedom ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Maximum Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Financial Modeling ◽  
Design Flexibility ◽  
Special Case

The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications. This paper investigates a set of four generalized logistic maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications such as quantitative financial modeling. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map. Mathematical analysis for each generalized map includes bifurcation diagrams relative to all parameters, effective range of parameters, first bifurcation point, and the maximum Lyapunov exponent (MLE). Independent, vertical, and horizontal scales of the bifurcation diagram are discussed for each generalized map as well as a new bifurcation diagram related to one of the added parameters. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.

scholarly journals An image encryption scheme employing key related skipping

2018 ◽  
Vol 69 (2) ◽  
pp. 93-105 ◽  
Author(s):  
Jakub Oravec ◽  
Ján Turán ◽  
L’uboš Ovseník ◽  
Tomáš Huszaník
Keyword(s):  
Phase Space ◽  
Image Encryption ◽  
Statistical Tests ◽  
Logistic Map ◽  
Encryption Algorithm ◽  
Encryption Scheme ◽  
Image Pixels ◽  
Encrypted Images ◽  
Image Encryption Algorithm ◽  
Chaotic Logistic Map

Abstract This paper describes an image encryption algorithm which utilizes chaotic logistic map. Values generated by this map are used in two steps of algorithm which shuffles image pixels and then changes their intensities. Design of the encryption scheme considers possibility of various attacks, such as statistical, differential or phase space reconstruction attacks. Robustness against last mentioned type of attacks is introduced by selective skipping of values generated by the map. This skipping depends on key entered by user. The paper also verifies properties of proposed algorithm by common measures and by set of statistical tests that examine randomness of computed encrypted images. Results are compared with other approaches and they are also briefly discussed.

scholarly journals Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

2017 ◽  
Vol 27 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Sylvain Contassot-Vivier ◽  
Jean-François Couchot ◽  
Christophe Guyeux ◽  
Pierre-Cyrille Heam
Keyword(s):  
Uniform Distribution ◽  
Hamiltonian Cycle ◽  
Chaotic Behavior ◽  
Statistical Tests ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Expected Length ◽  
Obvious Consequence ◽  
Pseudorandom Number Generation

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a [Formula: see text]-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distribution is calculated. Finally practical experiments show that the generators successfully pass the classical statistical tests.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

scholarly journals Yet Another Pseudorandom Number Generator

2017 ◽  
Vol 63 (2) ◽  
pp. 195-199 ◽  
Author(s):  
Borislav Stoyanov ◽  
Krzysztof Szczypiorski ◽  
Krasimir Kordov
Keyword(s):  
Boolean Function ◽  
Data Security ◽  
Statistical Tests ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Number Generation ◽  
Pseudorandom Number Generation ◽  
High Level

Abstract We propose a novel pseudorandom number generator based on R¨ossler attractor and bent Boolean function. We estimated the output bits properties by number of statistical tests. The results of the cryptanalysis show that the new pseudorandom number generation scheme provides a high level of data security.

Sign in / Sign up

Export Citation Format

Share Document