An image encryption system based on generalized discrete maps

Radwan, Ahmed G.; Abd-El-Hafiz, Salwa K.; AbdElHaleem, Sherif H.

doi:10.1109/icecs.2014.7049977

Cited by 16 publications

(3 citation statements)

References 15 publications

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“…Encryption schemes that offer better performance utilizing such simple maps usually use innovative combinations of them. Such combinations could be even suitable for more complicated image encryption applications, for example, the encryption techniques presented in [36,61].…”

Section: Encryption Systemmentioning

confidence: 99%

“…Thus, the map has not been mathematically analyzed in a generic way. Other generalized logistic, tent, and sine maps have been recently investigated in [34][35][36]. In this paper, generalizations providing extra degrees of freedom are proposed that could be adapted to fit certain specifications, keeping the advantage of simple mathematical relation using 1D maps only.…”

Section: Introductionmentioning

confidence: 99%

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

Sayed

Radwan

Fahmy

2015

Discrete Dynamics in Nature and Society

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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.

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Section: Encryption Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sayed

Radwan

Fahmy

2015

Discrete Dynamics in Nature and Society

Self Cite

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“…Chaos theory has always attracted the interest of scientific research because it has a wide spectrum of applications, such as in secure communication [1,2], cryptography [3][4][5][6][7][8], circuit theory [9][10][11][12], and modeling multidisciplinary phenomena in physics, chemistry, and biology [13][14][15]. This is due to the fact that chaotic systems exhibit aperiodic, bounded, long-time evolution and sensitive dependence on initial conditions for some ranges of parameters.…”

Section: Introductionmentioning

confidence: 99%

Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems

et al. 2017

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This paper proposes a novel generalized switched synchronization scheme amongnfractional-order chaotic systems with various operating modes. Digital dynamic switches and dynamic scaling factors are employed, which offer many new capabilities. Dynamic switches determine the role of each system as a master or a slave. A system can either have a fixed role throughout the simulation time (static switching) or switch its role one or more times (dynamic switching). Dynamic scaling factors are used for each state variable of the master system. Such scaling factors control whether the master is a single system or a combination of several systems. In addition, these factors determine the generalized relation between the original systems from which the master system is built as well as the slave system(s). Moreover, they can be utilized to achieve different kinds of generalized synchronization relations for the purpose of generating new attractor diagrams. The paper presents a mathematical formulation and analysis of the proposed synchronization scheme. Furthermore, many numerical simulations are provided to demonstrate the successful generalized switched synchronization of several fractional-order chaotic systems. The proposed scheme provides various functions suitable for applications such as different master-slave communication models and secure communication systems.

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