A New 1D Chaotic Map and &lt;inline-formula&gt; 
                     &lt;tex-math notation="LaTeX"&gt;$\beta$ &lt;/tex-math&gt;
                  &lt;/inline-formula&gt;-Hill Climbing for Generating Substitution-Boxes

Alzaidi, Amer; Ahmad, Musheer; Doja, M. N.; Solami, Eesa Al; Beg, M. M. Sufyan

doi:10.1109/access.2018.2871557

Cited by 91 publications

(12 citation statements)

References 50 publications

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“…These chaos topographies make chaotic systems as a choice for the development of modern ciphers and many researchers have used chaos in the design of S-boxes. Authors [29][30][31][32][33][34][35][36][37][38][39] suggested S-boxes based on chaotic map and analyzed these along with the other existing S-box design methods. Analyses disclosed that the proposed S-boxes are strong against different attacks and hence suggest their usage in modern block ciphers.…”

Section: Related Workmentioning

confidence: 99%

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

Zahid

Arshad

2019

Symmetry

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In this paper, we propose to present a novel technique for designing cryptographically strong substitution-boxes using cubic polynomial mapping. The proposed cubic polynomial mapping is proficient to map the input sequence to a strong 8 × 8 S-box meeting the requirements of a bijective function. The use of cubic polynomial maintains the simplicity of S-box construction method and found consistent when compared with other existing S-box techniques used to construct S-boxes. An example proposed S-box is obtained which is analytically evaluated using standard performance criteria including nonlinearity, bijection, bit independence, strict avalanche effect, linear approximation probability, and differential uniformity. The performance results are equated with some recently scrutinized S-boxes to ascertain its cryptographic forte. The critical analyses endorse that the proposed S-box construction technique is considerably innovative and effective to generate cryptographic strong substitution-boxes.

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Section: Related Workmentioning

confidence: 99%

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

Zahid

Arshad

2019

Symmetry

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“…Various S-box structures were presented based on time delay [18], fractional [19][20][21] and hyperchaotic systems [22,23]. In order to obtain S-box structures with best performance criterion, researchers have combined chaotic systems with optimization algorithm [24][25][26][27][28]. Many approaches combined chaotic systems with mathematical structures which play a more important role than chaos were proposed [29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

Zhou

Kai

et al. 2021

Nonlinear Dyn

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In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudorandom mixed coupling method we present a spatiotemporal chaos which used PS map as local map f(x). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov-Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.

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“…However, the above-mentioned continuous time chaotic system needs to be discretized in a simulation experiment because the computer does not support the continuous nature of a chaotic system. Thus, an increasing number of the S-box construction methods based on discrete-time have been proposed [11][12][13][14][15][16]. Iqtadar [17] proposed an S-box construction method based on a Logistic system, and dynamic S-box construction methods based on chaotic systems were proposed [18,19].…”

Section: Introductionmentioning

confidence: 99%

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Yan

Ding

2021

Electronics

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In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.

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A New 1D Chaotic Map and <inline-formula> <tex-math notation="LaTeX">$\beta$ </tex-math> </inline-formula>-Hill Climbing for Generating Substitution-Boxes

Cited by 91 publications

References 50 publications

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

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