In this paper, we present a novel method to construct cryptographically strong bijective substitution-boxes based on the complicated dynamics of a new hyperchaotic system. The new hyperchaotic system was found to have good characteristics when compared with other systems utilized for S-box construction. The performance assessment of the proposed S-box method was carried out based on criteria, such as high nonlinearity, a good avalanche effect, bit-independent criteria, and low differential uniformity. The proposed method was also analyzed for the batch-generation of 8 × 8 S-boxes. The analyses found that through a proposed purely chaos-based method, an 8 × 8 S-box with a maximum average high nonlinearity of 108.5, or S-boxes with differential uniformity as low as 8, can be retrieved. Moreover, small-sized S-boxes with high nonlinearity and low differential uniformity are also obtainable. A performance comparison of the anticipated method with recent S-box proposals proved its dominance and effectiveness for a strong bijective S-box construction.

A New Hyperchaotic System-Based Design for Efficient Bijective Substitution-Boxes.

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.

https://www.mdpi.com/1099-4300/21/3/245/pdf

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

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.

https://www.mdpi.com/2073-8994/11/3/437/pdf

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

This paper proposes a novel method of constructing strong substitution-boxes (S-boxes) of order n (4 ≤ n ≤ 8) based on a recent optimization algorithm known as sine-cosine algorithm (SCA). The paper also proposes a new 1D chaotic map, which owns enhanced dynamics compared to conventional chaotic map, for generating initial population of S-boxes and facilitating the optimization mechanism of SCA. The proposed method applies the SCA with enhanced chaotic map to explore and exploit the search space for obtaining optimized S-boxes on the basis of maximization of nonlinearity as fitness function. The S-box construction involves three phases such as initialization of population, optimization, and adjustment. The simulation and performance analyses are done using standard measures of nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, and autocorrelation function. The obtained experimental results are compared with some immediate optimization-based and other S-boxes to show the strength of proposed method for constructing bijective S-boxes of salient cryptographic features.

/pdf/sine-cosine-optimization-based-bijective-substitution-boxes-1xsvktw9ee.pdf

Sine-Cosine Optimization-Based Bijective Substitution-Boxes Construction Using Enhanced Dynamics of Chaotic Map

Cryptanalysis and constructing S-Box based on chaotic map and backtracking

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.

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

The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of on projective line over the finite field to construct proposed S-box. The vertices of the cost diagram are elements of which can be represented by powers of , where is the root of irreducible polynomial over . Let denote the elements of which are of the form of even powers of . In the first step, we construct a matrix with the elements of in a specific order, determined by the coset diagram. Next, we consider defined by to destroy the structure of . In the last step, we apply a bijective map on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.

/pdf/a-novel-construction-of-substitution-box-involving-coset-36y50fti9y.pdf

A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of - complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of - cut sets of - complex fuzzy sets and justify the representation of an - complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of - complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an - complex fuzzy set is - complex fuzzy subgroup. Furthermore, we extend the idea of - complex fuzzy normal subgroup to define the quotient group of a group by this particular - complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of by a specific normal subgroup .

/pdf/on-structural-properties-of-x-complex-fuzzy-sets-and-their-4eh6ev760k.pdf

On Structural Properties of ξ -Complex Fuzzy Sets and Their Applications

In this study, we propose the concept of t-intuitionistic fuzzy order of an element of a t-intuitionistic fuzzy subgroup (t-IFSG) of a finite group and examine different important algebraic properties of this phenomena. We also prove many useful algebraic aspects of this notion for a cyclic group. Moreover, we extend this ideology to define t-intuitionistic fuzzy order and index of a t-IFSG of group. In addition, we establish t-intuitionistic fuzzification of Langrange’s theorem.

/pdf/t-intuitionistic-fuzzification-of-lagrange-s-theorem-of-t-21lr4kk0zs.pdf

t-Intuitionistic Fuzzification of Lagrange’s Theorem of t-Intuitionistic Fuzzy Subgroup

Substitution box is the most significant component of block cipher. The property of nonlinearity is of great importance for the design of secure substitution boxes. Therefore, it is necessary to develop new methods for the production of substitution boxes with a high non-linearity score. In this paper, we have introduced a novel group theoretic method to construct a robust S-box with non-linearity score 113.75 greater than that of AES S-box. The performance of generated S-box is found to be excellent, when examined through various other well-known algebraic criteria such as strict avalanche criterion, bit independence criterion, differential uniformity and linear approximation probability. The suitability of proposed S-box is tested for image encryption applications through different statistical analyses. We got very encouraging outcomes from all these examinations which certify that the generated S-box meets all the criteria needed to be reliable for secure communication and image encryption.

Umer Shuaib

Papers

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

A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map

On Structural Properties of ξ -Complex Fuzzy Sets and Their Applications

t-Intuitionistic Fuzzification of Lagrange’s Theorem of t-Intuitionistic Fuzzy Subgroup

A group theoretic construction of highly nonlinear substitution box and its applications in image encryption