A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design

Lambić, Dragan

doi:10.1007/s11071-020-05503-y

Cited by 129 publications

(54 citation statements)

References 44 publications

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“…Y. Naseer [19] construct an S-box using the action of symmetric group S8 on Galois Field GF (2 8 ). Nowadays some authors use a chaos theory and symmetric group [32][33][34][35] for the construction of S-boxes. But all the above-mentioned structures for the construction of S-boxes are based on associative algebraic structures.…”

Section: A Related Workmentioning

confidence: 99%

A Power Associative Loop Structure for the Construction of Non-Linear Components of Block Cipher

et al. 2020

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In the symmetric key cryptography, the purpose of the substitution box is to generate confusion and hence improve the security of the whole cryptosystem. For this reason, many algebraic substitution boxes are constructed depending upon the associative algebras of Galois fields. In this paper, the power associative loop is used for the construction of substitution boxes. This novel structure comprises excellent features which include, the inverse of zero element, non-associativity and fewer constraints as compared to the cyclic group and Galois field. In comparison to existing substitution boxes, the substitution boxes based upon power associative loop are comparatively easy and the above-mentioned properties offer the number of structures to construct highly nonlinear substitution boxes. To obtain the number of substitution boxes, we further applied the symmetric group of order 16 on the proposed substitution box. The evaluation of proposed boxes with different algebraic and statistical analyses like nonlinearity test, strict avalanche criterion, bit independence criterion, linear approximation probability and differential approximation probability indicate the strength of proposed substitution boxes. Majority logic criterion results depict that proposed substitution boxes have better cryptographic strength to apply in different techniques of secure communication.

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Section: A Related Workmentioning

confidence: 99%

A Power Associative Loop Structure for the Construction of Non-Linear Components of Block Cipher

et al. 2020

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“…The proposed S-box was also found to show good SAC behavior, as our SAC value of 0.5007 is quite better than the scores of S-boxes constructed in References [ 23 , 24 , 25 , 26 , 27 , 28 , 30 , 33 , 34 , 41 , 42 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], as evident from Table 7 and Figure 2 b. The proposed S-box satisfies the SAC criterion quite diligently as compared to other contemporary S-boxes.…”

Section: Performance Results and Analysesmentioning

confidence: 81%

Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme

Ahmad

Alsolami

2020

Entropy

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Static substitution-boxes in fixed structured block ciphers may make the system vulnerable to cryptanalysis. However, key-dependent dynamic substitution-boxes (S-boxes) assume to improve the security and robustness of the whole cryptosystem. This paper proposes to present the construction of key-dependent dynamic S-boxes having high nonlinearity. The proposed scheme involves the evolution of initially generated S-box for improved nonlinearity based on the fractional-order time-delayed Hopfield neural network. The cryptographic performance of the evolved S-box is assessed by using standard security parameters, including nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, etc. The proposed scheme is able to evolve an S-box having mean nonlinearity of 111.25, strict avalanche criteria value of 0.5007, and differential uniformity of 10. The performance assessments demonstrate that the proposed scheme and S-box have excellent features, and are thus capable of offering high nonlinearity in the cryptosystem. The comparison analysis further confirms the improved security features of anticipated scheme and S-box, as compared to many existing chaos-based and other S-boxes.

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“…Therefore, the proposed method involves the nonlinearity improvisation plan as the technique for evolving preliminary S-box for over all nonlinearity feature of the S-box. Table 3 makes it evident that the proposed S-box has considerably higher nonlinearity performance over many recently investigated S-boxes in [8,24,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][63][64][65]. The excellent nonlinearity performance over many existing studies demonstrates that the proposed method is fairly effective in making the high nonlinear transformation of plaintext to ciphertext as compared to other methods.…”

Section: Comparative Analysismentioning

confidence: 91%

Efficient Dynamic S-Box Generation Using Linear Trigonometric Transformation for Security Applications

et al. 2021

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Protection of data transmitted over the network from illegal access is one of the major challenges being posed by exponential growth of data in online digital communication. Modern cryptosystems assist in data sanctuary by utilizing substitution-boxes (S-boxes). This paper presents a modest and novel technique to erect dynamic and key dependent S-boxes with the help of a novel linear trigonometric transformation. A new optimization plan is also suggested to improvise the nonlinearity characteristic of the preliminary S-box generated through trigonometric transformation. The proposed technique has the competence to create significant quantity of cryptographic strong S-boxes with the help of projected scheme. A specimen S-box is procreated, and standard performance criteria is applied to appraise the cryptographic strength of the resultant S-box and other known S-boxes available in the literature. Comparative performance analyses validate the noteworthy contribution of the proposed scheme for the generation of dynamic and secure S-boxes. An image privacy preserving scheme based on the proposed Sbox is also suggested to validate the fact that it holds strong candidature for modern cryptosystems to protect multimedia data.

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A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design

Cited by 129 publications

References 44 publications

A Power Associative Loop Structure for the Construction of Non-Linear Components of Block Cipher

A Power Associative Loop Structure for the Construction of Non-Linear Components of Block Cipher

Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme

Efficient Dynamic S-Box Generation Using Linear Trigonometric Transformation for Security Applications

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