An S-box Construction Algorithm Based on Spatiotemporal Chaos

Yuan, Hao; Luo, Longyan; Wang, Yong

doi:10.1109/cmc.2010.48

Cited by 6 publications

(4 citation statements)

References 10 publications

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“…The coupled map lattice (CML) is a classical spatiotemporal chaos has been deeply studied and widely applied [42][43][44][45] in cryptography. Its adjacent couplings can describe by the following equation:…”

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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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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“…Then, an S-box construction method, based on the combined 2D Baker system and Chebyshev system, was proposed in [20]. A low-dimensional chaotic system is easier to be used in the actual secure communication due to its simple form, fast encryption speed, and easier implementation in hardware and software compared with a hyperchaotic system [21,22]. However, the low dimensional discrete-time chaotic map shares some common potential dangers: weak parameter space, short periodic behavior, blank window, and uneven output distribution, which limit its application in the construction methods of the S-box.…”

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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“…Yuan et al . in their paper used spatiotemporal chaos to generate S‐Box. The most used spatiotemporal chaotic system is the coupled map lattice:

x_{n + 1} (i) = (1 - ε) f (x_{n} (i)) + \frac{ε}{2} [f (x_{n} (i + 1)) + f (x_{n} (i - 1))]

where f is the logistic map used as a local map despite its drawbacks and n and i are respectively the time index and the lattice index.…”

Section: Related Workmentioning

confidence: 99%

“…The second one does not depend on synchronization, which is an important asset. In many digital chaotic crypto‐systems, constructing good dynamic substitution boxes (S‐Boxes) instead of static ones is the main issue . The S‐Box is the only nonlinear component in block ciphers and the principal source of confusion property needed to conceive strong crypto‐systems.…”

Section: Introductionmentioning

confidence: 99%

Efficient and secure chaotic S‐Box for wireless sensor network

Zaibi

Peyrard

Kachouri

et al. 2013

Security Comm Networks

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Information security using chaotic dynamics is a novel topic in the wireless sensor network (WSN) research field. After surveying analog and digital chaotic security systems, we give a state of the art of chaotic S-Box design. The substitution tables are nonlinear maps that strengthen and enhance block crypto-systems. This paper deals with the design of new dynamic chaotic S-Boxes suitable for implementation on wireless sensor nodes. Our proposed schemes are classified into two categories: S-Box based on discrete chaotic map with floating point arithmetic (cascading piecewise linear chaotic map and a three-dimensional map) and S-Box based on discrete chaotic map with fixed-point arithmetic (using discretized Lorenz map and logistic-tent map). The security analysis and implementation process on WSN are discussed. The proposed methods satisfy Good S-Box design criteria and exceed the performance of Advanced Encryption Standard static S-Box in some cases. The energy consumption of different proposals and existing chaotic S-Box designs are investigated via a platform simulator and a real WSN testbed equipped with TI MSP430f1611 micro-controller. The simulations and the experimental results show that our proposed S-Box design with fixed-point arithmetic Lorenz map has the lowest energy-consuming profile compared with the other studied and proposed S-Box design.

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An S-box Construction Algorithm Based on Spatiotemporal Chaos

Cited by 6 publications

References 10 publications

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

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

Efficient and secure chaotic S‐Box for wireless sensor network

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