A new S-box construction method based on the fractional-order chaotic Chen system

Özkaynak, Fatih; Çelik, Vedat; Özer, Ahmet Bedri

doi:10.1007/s11760-016-1007-1

Cited by 123 publications

(80 citation statements)

References 37 publications

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“…In recent years, chaotic maps such as logistic map, exponential map, 2D Baker map, Chebyshev map, Tent map, Lorenz system, 3D fourwing autonomous chaotic system, chaotic scaled Zhongtang system, logistic-sine map, fractional-order chaotic Chen system etc. are widely used for random S-box design (Belazi, Khan, Abd El-Latif, & Belghith, 2016;Cavusoglu, Zengin, Pehlivan, & Kacar, 2016;Chen, 2008;Jakimoski & Kocarev, 2001;Lambić, 2014;Liu, Yang, Liu, & Dai, 2015;Ozkaynak, Celik, & Ozer, 2016;Ozkaynak & Ozer, 2010;Wang, Wong, Liao, & Xiang, 2009). Besides these, there are many other methods for the generation of random S-boxes based on various chaotic maps, which to our knowledge all have continuous space domain, except for the method presented in Lambić (2017).…”

Section: Introductionmentioning

confidence: 99%

S-box design method based on improved one-dimensional discrete chaotic map

Lambić

2018

Journal of Information and Telecommunication

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To cite this article: Dragan Lambić (2018) S-box design method based on improved onedimensional discrete chaotic map, Journal of Information and Telecommunication, 2:2, 181-191, DOI: 10.1080/24751839.2018 A new method for obtaining random bijective S-boxes based on improved one-dimensional discrete chaotic map is presented. The proposed method uses a new special case of discrete chaotic map based on the composition of permutations, in order to overcome the problem with potentially short length of the orbits. The proposed special case is based on the composition of permutations and sine function and has a larger minimum length of the orbits compared to the previous special case of the discrete-space chaotic map. The results of performance test show that the example of S-box generated by the proposed method has good cryptographic properties. The proposed method can achieve large key space, which makes it suitable for generation of larger S-boxes, and the process of generation of S-boxes is not affected by approximations of any kind. Also, proposed method has potential to operate at greater speed and with smaller memory requirements than previous S-box generation method based on discrete space chaotic map, which can be particularly useful for lightweight devices such as wireless sensor networks. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

S-box design method based on improved one-dimensional discrete chaotic map

Lambić

2018

Journal of Information and Telecommunication

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“…Besides, Figure 5 depicts the statistical results of the LP of comparison algorithms. These results show that the LP of the proposed S-box is not worse than that of algorithms in [25,26,28,30,32,34,37,38,41]. Furthermore, Table 6 summarizes the above-mentioned evaluating criteria results of the experimental algorithms.…”

Section: Linear Approximation Probability Analysismentioning

confidence: 77%

“…To verify the generated S-box, we analyze its cryptographic criteria and compare it with many other S-boxes designed in [6][7][8][9][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Moreover, our experimental environment is i3 CPU 540 3.07 GHz, memory 2.00 GHz Inter Core, Matlab2012b.…”

Section: Cryptographic Criteria Analyses Of Proposed S-boxmentioning

confidence: 99%

Chaotic S‐Box: Intertwining Logistic Map and Bacterial Foraging Optimization

Tian

2017

Mathematical Problems in Engineering

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As the unique nonlinear component of block ciphers, Substitution box (S-box) directly affects the safety of a cryptographic system. It is important and difficult to design strong S-box that simultaneously meets multiple cryptographic criteria such as bijection, nonlinearity, strict avalanche criterion (SAC), bit independence criterion (BIC), differential probability (DP), and linear probability (LP). Though many chaotic S-boxes have been proposed, the cryptographic performance of most of them needs to be further improved. A new chaotic S-box based on the intertwining logistic map and bacterial foraging optimization is designed in this paper. It firstly iterates the intertwining logistic map to construct many S-boxes and then applies a bacterial foraging optimization algorithm to find the optimal S-box. Moreover, bacterial foraging optimization algorithm considers the nonlinearity and differential uniformity as the fitness functions in the optimization process. We experiment that the proposed S-box can effectively resist multiple types of cryptanalysis attacks.

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“…The sign of Lyapunov exponent (LE) is a useful method that enables to acquire the knowledge about the dynamics of a system. The most important point is the sign of LE, when the dynamics of the system have been investigated . Since at least one LE is positive in chaotic systems, if any system having highest LE is higher than or equal to 0 λ 1 ≥ 0, then it is accepted as a chaotic system; if λ 1 < 0, then it is accepted as a fixed point; and if λ 1 = 0, then it is accepted as a stable limit cycle .…”

Section: Chaos Analyses Of Pucsmentioning

confidence: 99%

A novel high speed Artificial Neural Network–based chaotic True Random Number Generator on Field Programmable Gate Array

Alçın

Koyuncu

Tuna

et al. 2018

Circuit Theory & Apps

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Summary It is well observed that cryptographic applications have great challenges in guaranteeing high security as well as high throughput. Artificial neural network (ANN)–based chaotic true random number generator (TRNG) structure has not been unprecedented in current literature. This paper provides a novel type of high‐speed TRNG based on chaos and ANN implemented in a Xilinx field‐programmable gate array (FPGA) chip. The paper consists of two main parts. In the first part, chaos analyses of Pehlivan‐Uyaroglu_2010 chaotic system (PUCS) have been accomplished to prove that PUCS operates in chaotic regime. So PUCS can be an efficient alternative to the entropy source for classical TRNGs. In the second part, the hardware design of the proposed TRNG has been created using VHDL in Xilinx platform. As a result, the implemented TRNG offers throughput up to 115.794 Mbps. Besides, the generated random numbers have been tested with the FIPS 140‐1 and NIST 800.22 test suites. The high quality of generated true random numbers have been confirmed by passing all randomness tests. The results have shown that the proposed system can provide not only high throughput but also high quality random bit sequences for a wide variety of embedded cryptographic applications.

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A new S-box construction method based on the fractional-order chaotic Chen system

Cited by 123 publications

References 37 publications

S-box design method based on improved one-dimensional discrete chaotic map

S-box design method based on improved one-dimensional discrete chaotic map

Chaotic S‐Box: Intertwining Logistic Map and Bacterial Foraging Optimization

A novel high speed Artificial Neural Network–based chaotic True Random Number Generator on Field Programmable Gate Array

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