An algorithm for the construction of substitution box for block ciphers based on projective general linear group

Altaleb, Anas; Saeed, Muhammad Sarwar; Hussain, Iqtadar; Aslam, Muhammad

doi:10.1063/1.4978264

Cited by 43 publications

(25 citation statements)

References 22 publications

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“…I. Hussain [15] uses Galois Field and symmetric group for the construction of S-boxes. Similarly, A. Altaleb [16] uses the action of a projective general linear group on Galois Field GF (2 8 ) and also uses symmetric group S256 for the construction of varieties of S-boxes. M. Hussain in [17] uses an artificial bee colony and chaotic map to construct an S-box.…”

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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“…Many other researchers have designed S-Boxes using several techniques and concepts like graph isomorphism [45], coset diagrams [46], linear fractional transformation [47][48][49][50], etc. Ciphers based on S-box are highly dependent on the security features of the used S-box.…”

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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“…Many researchers have designed S-Boxes that are cryptographically strong using such mappings. One such mapping is linear fractional transformation (LFT), which was exhaustively explored for the construction of the S-boxes [ 49 , 50 , 51 , 52 ]. However, the process of generating these S-Boxes using LFT is very complicated and time consuming.…”

Section: Proposed Substitution Boxmentioning

confidence: 99%

“…The authors analyzed the strength of their S-Box against cryptographic properties, like SAC, BIC, NL, LP, DP, etc. The authors in [ 50 , 51 , 52 ] proposed efficient algorithms to design good S-Boxes based on LFT and the projective general linear group on Galois field, respectively. The proposed S-Boxes showed good performances when compared with other existing S-Boxes.…”

Section: Introductionmentioning

confidence: 99%

A Novel Construction of Efficient Substitution-Boxes Using Cubic Fractional Transformation

Zahid

Arshad

Ahmad

2019

Entropy

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A symmetric block cipher employing a substitution–permutation duo is an effective technique for the provision of information security. For substitution, modern block ciphers use one or more substitution boxes (S-Boxes). Certain criteria and design principles are fulfilled and followed for the construction of a good S-Box. In this paper, an innovative technique to construct substitution-boxes using our cubic fractional transformation (CFT) is presented. The cryptographic strength of the proposed S-box is critically evaluated against the state of the art performance criteria of strong S-boxes, including bijection, nonlinearity, bit independence criterion, strict avalanche effect, and linear and differential approximation probabilities. The performance results of the proposed S-Box are compared with recently investigated S-Boxes to prove its cryptographic strength. The simulation and comparison analyses validate that the proposed S-Box construction method has adequate efficacy to generate efficient candidate S-Boxes for usage in block ciphers.

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An algorithm for the construction of substitution box for block ciphers based on projective general linear group

Cited by 43 publications

References 22 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

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

A Novel Construction of Efficient Substitution-Boxes Using Cubic Fractional Transformation

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