Enhanced digital chaotic maps based on bit reversal with applications in random bit generators

Alawida, Moatsum; Samsudin, Azman; Teh, Je Sen

doi:10.1016/j.ins.2019.10.055

Cited by 80 publications

(38 citation statements)

References 37 publications

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“…It has been well studied that the conventional discrete onedimensional chaotic maps suffered from many problems that affect their degree of chaoticity and usage in security applications [40][41][42]. Specifically, the chaotic logistic map, govern by the Equation (1), possesses limitations such as: non-uniform coverage of whole bounded space in bifurcation behaviour, limited chaotic range for parameter L which is restricted to 3.57 to 4, low value of largest lyapunov exponent, and low value of approximate entropy [43]. The security and robustness of many chaos-based cryptographic algorithms primarily rely on the dynamics of employed chaotic maps.…”

Section: Improved 1-d Chaotic Mapmentioning

confidence: 99%

“…It is the study of qualitative changes in behaviour of a dynamical system when the changes in system parameters are made. This helps to understand the existence of any fixed points, quasi-fixed points, periodic or chaos phenomenon, etc, in the system [43]. The bifurcation diagrams of the four 1-D chaotic maps are depicted in second column of Figure 1.…”

Section: B Bifurcation Analysismentioning

confidence: 99%

“…Hence, through bijection from I Ωi to A 1 , we get S-box S 1 which is shown in Table 6. The finite group G 6 =<x, y, z: x:= (1,38,17,51) y:= (2,48,18,57,30,61,41,32,44,22,35,43,34,62,11,16,58,37,53,10,46,47,29,45,24,56,20,8,6 on the index set of A 2 generates a distinct S-box. After thorough analysis and research, it has been revealed that the S-box related to the element x 3 y 47 z 5 ϵ G 6 offers the highest average value of non-linearity.…”

Section: B Proposed Group Structures and Actionsmentioning

confidence: 99%

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Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

et al. 2020

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This paper presents a hybrid method for the construction of cryptographically strong bijective substitution-boxes by utilizing the merits of chaotic map and algebraic groups. The hybrid method first generates the key-dependent dynamic S-boxes using chaotic heuristic search strategy and then the S-boxes are evolved with the help of potent proposed algebraic group structures. This paper proposes a new improved combination chaotic map to operate initial search strategy. To augment the strength of generated S-boxes, the algebraic group structures are discovered which have the power to improve their cryptographic strength. The performance assessments using standard criterions are rendered to quantify the strengths of proposed bijective S-boxes. The experimental results and comparisons with recent S-box research findings justify the effectiveness and competence of the proposed bijective S-boxes and anticipated hybrid generation method.

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Section: Improved 1-d Chaotic Mapmentioning

confidence: 99%

Section: B Bifurcation Analysismentioning

confidence: 99%

Section: B Proposed Group Structures and Actionsmentioning

confidence: 99%

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Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

et al. 2020

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“…Lyapunov exponent (LE) is a quantitative measure used to determine the degree of chaotic behaviour of a dynamic system. It is a commonly accepted metric that describes the separation between two trajectories starting from extremely close initial points [47]. Mathematically, Lyapunov exponents for a dynamical map…”

Section: D Discrete Hyperchaos Mappingmentioning

confidence: 99%

Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation

Ahmad

Alsolami

2020

Complexity

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This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. The standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box. The simulation and comparison results demonstrate the effectiveness of proposed method for the construction of cryptographically sound S-boxes.

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“…In addition, various frameworks that can improve the properties of simple chaotic systems have been proposed, including a combination of multiple maps [ 46 , 47 , 48 , 49 ], modifying the chaotic sequences generated by chaotic maps [ 50 , 51 , 52 ], and modifying the existing maps [ 53 , 54 , 55 ]. Most of the frameworks set the existing maps as a whole and incorporate them into the fixed format [ 54 , 56 , 57 , 58 ], thus generating new maps with better performance automatically. The single neuronal dynamical system in self-feedbacked Hopfield network is also applicable to existing frameworks, and it can achieve a positive effect.…”

Section: Introductionmentioning

confidence: 99%

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Chen

2021

Entropy

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Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

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Enhanced digital chaotic maps based on bit reversal with applications in random bit generators

Cited by 80 publications

References 37 publications

Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

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