A Novel Method for Generation of Strong Substitution-Boxes Based on Coset Graphs and Symmetric Groups

Abstract

The success of AES encryption standard created challenges for the cryptographers to construct strong substitution-boxes using different underlying approaches. It is because they are solely responsible to decide the robustness of cryptosystem against linear and differential cryptanalyses. With an aim to fulfill the mentioned requirement of robustness, a novel group theoretic and graphical method is proposed to construct S-box with optimal features. Firstly, a strong S-box is generated with the help of orbits of coset graphs and the action of proposed powerful permutation of symmetric group S 256 . In addition, a specific group is designed the action of whose pairs of permutations has the ability to generate as many as 462422016 strong S-boxes. Few of such proposed S-boxes are reported and assessed against standard performance parameters to validate the effectiveness of proposed findings. The features of proposed S-boxes are compared with most of the recent S-boxes to validate the superior performance. Moreover, they are also applied for image encryption to demonstrate their suitability for multimedia security applications.

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

“…If an S-box is uniform in input/output distribution, then it is said to be resistant. It is preferred that the largest value of differential uniformity (DU) in EX-OR table should be as small as possible [ 48 ]. The differential uniformity is measured as follows: where set X holds all probable input values, and the cardinality of its elements is 256 for 8x8 S-box.…”

“…To quantify the encryption performance exhibited by our S-box, we evaluated the statistical tests, such contrast, correlation, energy, and homogeneity, which are members of the Majority Logic Criteria (MLC) suite. The description and details of these tests are available in author’s previous studies [ 7 , 40 , 48 ]. The statistical scores of encryption performance under MLC analysis are listed in Table 8 and compared with encryption performances of S-boxes investigated in References [ 48 , 61 ].…”

“…The description and details of these tests are available in author’s previous studies [ 7 , 40 , 48 ]. The statistical scores of encryption performance under MLC analysis are listed in Table 8 and compared with encryption performances of S-boxes investigated in References [ 48 , 61 ]. The obtained results for MLC analysis validate the appropriateness of proposed S-box for image encryption applications.…”

Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

“…The group G 5 =<x: x 32 =1> of order 32 with only one generator, that is, x:= (27,24,28,21,3,11,5,25,17,9,23,26,8,12,18,20,7,30,22,14,19,29,15,6,1,10,4,2,32,31,13,16); acts naturally on the index set I Ωi of A 1 that is, 5×5 S-box from chaos-based search. This action can be defined as:…”

“…The successes of AES block cipher and its S-box is mainly responsible for the progress and development of proposals devoted to the creation of S-boxes [22]. All of them are balanced and whose designs are primarily based on concepts such as algebraic techniques, optimization, chaotic maps and systems, etc, [23][24][25][26][27][28][29][30]. Lambić proposed a simple search methodology for yielding S-boxes which is based on chaotic system and composition methods in [31].…”