A Strong Hybrid S-Box Scheme Based on Chaos, 2D Cellular Automata and Algebraic Structure

In this paper, we study 2-dimensional nite cellular automata dened by hexagonal local rule with periodic boundary over the eld Z3.We construct the rule matrix corresponding to the hexagonal cellular automata.For some given coecients and the number of columns of hexagonal information matrix, we prove that the hexagonal cellular automata are reversible.

To further enhance the nonlinear and cryptographic properties of chaotic S-boxes, a novel S-box design is proposed based on the discrete chaotic map and improved artificial bee colony algorithm. Firstly, the S-box generated by chaotic sequence is initialized by the opposition-based optimization. Then, the dual transposition artificial bee colony algorithm is used to optimize the population, where the Gaussian swap is engaged to strengthen the optimum efficiency, and make the population acquire a better quality with each other. With the Gaussian mutation operator, the opposition-based optimization performs self-learning to obtain better population. Comparing with some recent S-boxes based on chaos. The S-boxes generated by the proposed scheme can achieve better performance in bijection, nonlinearity, strict avalanche criterion(SAC), bit independence criterion(BIC), I / O XOR distribution and linear approximation probability(LP). It provides a new and effective method for designing S-boxes with good cryptographic properties.

Cellular Automata (CA) is used in pseudo-random number generators (PRNG) to produce high-rate random numbers. The randomness of such numbers directly depends upon the CA rules and the number of neighbor cells. The two-dimensional (2D) CA has several limitations such as, finding the best CA rules, boundary cell problems, etc. To address the problems existing in the 2D CA, we propose a random number generator based on 3D cellular automata. The proposed generator is based on rule numbers 43, 85, 170, and 201, and incremental boundary conditions. The rules are randomly changed after each cycle depending on a clock bit mechanism. The output bits are then passed to the Diehard and ENT test suites to test its randomness [1]. The results reveal that the bit stream generated by the proposed scheme passes all the tests present in the test suites.

In this article coset diagrams of the action of PSL(2, Z) on a PL(F_p) are obtained, through parametrization, which yields one of the eight finite generalized triangle groups which are homomorphic images or quotients of PSL(2, Z). Other than this we analyzed the coset diagrams for the parameter for three finite generalized triangle groups. One of the most dependable methods for achieving data security has been the block cipher. S-Boxes constructed using algebraic structure have gained popularity recently because of their advantageous cryptographic properties and high non-linearity have been found in these structures, which attract researchers. With the help of these parametrized actions, a novel algebraic method to create 2^8 S-Boxe was established. The S-Box provides strong cryptographic qualities of nonlinearity 112, differential uniformity 6, linear approximation probability of 0.0576 and differential attack probability of 0.0039. To assess the practical applicability of our S-box, we integrate it into an image encryption scheme and present experimental results to showcase its efficacy in real-world scenarios. When used with an image encryption framework, the following results were obtained: NPCR = 0.9959, UACI = 0.3348, and approx. Entropy 7.98. Therefore, GTG based parametrisation has been shown to be an effective and secure alternative to traditional algebraic construction method for S-Boxes.

Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers. Since constructing non-linear components through algebraic structures is crucial for the confusion aspects of encryption schemes, relying solely on these structures can result in limited key spaces. To address this issue, a complex non-chain ring with combination of Henon map based algorithm is presented. This proposed work aims to enhance both security and key space by utilizing complex algebraic structures. In this study, we investigate the use of unit elements from non-chain rings, establishing a mapping from the group of units to Galois fields to enhance the algebraic robustness of the scheme. A substitution box is constructed from Galois field and is applied in image processing. For pixel mixing, the Henon map is employed, and the exclusive OR operation is performed using a key generated from image pixels and the substitution box. The algorithm’s performance is evaluated using standard parameters such as histograms, Structural Similarity Index Measure (SSIM), correlation analysis, and National Institute of Standards and Technology (NIST) tests. For S-box analysis, we apply the strict avalanche criterion (SAC), bit independence criterion (BIC), linear approximation probability (LAP), and differential approximation probability (DAP). This algebraic approach utilizes a robust and state-of-the-art image encryption system that is highly effective against potential attackers.

The non-orthogonal multiple access-passive optical network (NOMA-PON) is facing the dual security threats of primary user interference and unauthorized third-party user eavesdropping, so efficient data security enhancement techniques are crucial. To solve these problems, we propose a fixed-point extended (FE)-logistic chaotic mapping to reduce the computational complexity while employing a two-dimensional (2D) cellular automata (CA) and Turing pattern (TP) cascading scramble (CA-TPCS) encryption algorithm to further improve the sensitivity of the NOMA-PON system. The CA-TPCS consists of 2D-CA dynamic bit encryption and Turing symbol substitution (TSS). By using FE chaos to construct 2D-CA and adopting index sort to extract the TSS matrix, dynamic diffusion of bits and scrambling of a 2D symbol matrix are achieved. To ensure the key privacy, we employ a dual key mechanism, and uplink data is introduced as the private key. To verify the feasibility of the proposed method, a simulation validation is built on a 17.6 Gb/s power division multiplexing-orthogonal frequency division multiplexing (PDM-OFDM) NOMA-PON system transmitted over 25 km standard single mode fiber (SSMF). The results show that the proposed scheme has no effect on the optimal power allocation rate (PAR) values and the values are all 3. Meanwhile, the receiver sensitivity gains of 0.2 and 0.3 dB are obtained for high-power and low-power users after encryption. The ciphertext has good diffusion and statistical properties, and the key space is flexibly controlled by the FE precision f, the length l of the transmitted bit, and the size T of the TP, with the value of 22f+l+T×T. The results show that the proposed scheme is not only very compatible with PDM technology but also can realize the dual defense of internal aggression and external aggression. It has a good application prospect in the future NOMA-PON.

Block cipher has been a standout amongst the most reliable option by which data security is accomplished. Block cipher strength against various attacks relies on substitution boxes. In literature, extensively algebraic structures, and chaotic systems-based techniques are available to design the cryptographic substitution boxes. Although, algebraic and chaotic systems-based approaches have favorable characteristics for the design of substitution boxes, but on the other side researchers have also pointed weaknesses in these approaches. First-time multilevel information fusion is introduced to construct the substitution boxes, having four layers; Multi Sources, Multi Features, Nonlinear Multi Features Whitening and Substitution Boxes Construction. Our proposed design does not hold the weakness of algebraic structures and chaotic systems because our novel s-box construction relies on the strength of true random numbers. In our proposed method true random numbers are generated from the inevitable random noise of medical imaging. The proposed design passes all the substitution box security evaluation criteria including Nonlinearity, Bit Independence Criterion (BIC), Strict Avalanche Criterion (SAC), Differential Approximation Probability (DP), Linear Approximation Probability (LP), and statistical tests, including resistance to Differential Attack, Correlation Analysis, 2D, 3D histogram analysis. The outcomes of the evaluation criteria validate that the proposed substitution boxes are effective for block ciphers; furthermore, the proposed substitution boxes attain better cryptographic strength as compared to very recent state-of-the-art techniques.

Efficient high nonlinearity S-box generating algorithm based on third-order nonlinear digital filter

Feature Extraction is a long active topic in image processing, and it attracts lots of attention over the last five decades due to its uses in real-life applications. Edge detection method allows users to discover the features of an image for a notable change in the gray level. This texture indicates an ending of one region and the beginning of another in the image. Likewise, over the last few decades, researchers have been exploring to exploit the simple computing model of Cellular Automata (CA) with local neighborhood structure in image processing techniques. The usage of CA in applications of medical image-processing is identified by Kendall Preston [1] in 1979. It is found that edge detection using CA has a potential advantage over traditional approaches for its lightweight nature and computational efficiency. This paper introduces a new technique for image edge detection using two-dimensional CA. The method can use specific rule sets of CA using the Von Neumann neighborhood for edge detection with null boundary conditions. The performance analysis of the scheme is done and compared with some existing standard edge detection techniques. The results obtained from the proposed technique is very promising for feature extraction.

An approach based on an application of cellular automata (CA) to the problem of two-dimensional (2D) patterns or images reconstruction from ones with only partial information available is presented in the paper. 2D CA are used to process patterns/images, and genetic algorithm (GA) is applied to discover CA rules, which will be able to reconstruct original patterns/images from, e.g. destroyed or modified ones. A number of experiments have been conducted to reconstruct patterns and human face images with use of the proposed approach. Results of experiments show that CA rules discovered by GA in the learning process allow to reconstruct images with large number of damaged pixels.

A cellular automation method is one of calculation methods, which allows for modeling of complex joint phenomena that take place in material during and after the deformation in the meso‐ and micro‐scale. The phenomena, which can be taken into consideration with high precision, are processes connected with microstructure evolution. For modeling by cellular automata (CA) are mainly used two‐dimensional ones, because of more expensive calculations by three‐dimensional CA. But three‐dimensional phenomena cannot be generally reduced to two‐dimensional solution. In the paper a description of a modified three‐dimensional CA is presented. The model of microstructure contains three parts: deformation of grains, recrystallization and grains growth after recrystallization. Recrystallization is considered as a process without division on the different kinds (dynamic, metadynamic or static). It consists of two stages: nucleation and new grains growth. Nucleation rate and grain growth rate are dependent on parameters of deformation. In the model such parameters as temperature, strain, strain rate, dislocation density, crystallographic orientation and some others are taken into account. Along with calculation of microstructure evolution, model allows for prediction of mechanical properties, for example flow stress. A flow stress calculations reckon processes of hardening and softening using model of the dislocation density development in consideration with an effect of the recrystallization. Some results of simulations based on 3D cellular automaton are presented in the paper.

Cellular automata (CA) are known for their capability in exhibiting interesting emergent behaviour and capacity to generate complex and often aesthetically appealing patterns through the local interaction of rules. Mean information gain has been suggested as a measure of discriminating structurally different two-dimensional (2D) patterns. This paper addresses quantitative evaluation of the complexity of CA generated configurations. In particular, we examine information gain as a spatial complexity measure for discriminating multi-state 2D CA generated configurations. This information-theoretic quantity, also known as conditional entropy, takes into account conditional and joint probabilities of cell states in a 2D plane. The effectiveness of the measure is shown in a series of experiments for multi-state 2D patterns generated by CA. The results of the experiments show that the measure is capable of distinguishing the structural characteristics including symmetries and randomness of 2D CA patterns.

A novel agent based, artificial life model, for the evolution of mimicry is presented. This model is a predator-prey co-evolution scenario where pattern representation phenotype is simulated with Cellular Automata, while behaviors of pattern recognition is configured with Hopfield Network. A visual three dimensional toroidal cube is used to construct a universe in which agents have complete freedom of mobility, genetic representation of behavior and reproduction capability to evolve new behaviors in successive generations. These agents are classified into categories of predator and prey species. Genome of prey species control their mobility and palatability, while 2D Cellular Automata (CA) is used to represent a pattern, where the rule to generate the CA is also genetically represented. Through evolution, successive generations of prey species develop new patterns to represent them both visually and to the predators. Predators are agents with the primary purpose of providing selection pressure for the evolution of mimicry. They are equipped with Hopfield Network memory to recognize new CA pattern and make intelligent decisions to consume the prey based on their level of palatability. Using the above construction of ideas, successful emulation of the natural process of mimicry is achieved. Also complex behavior pattern of Batesian and Mullerian mimicry is simulated and studied.

Construction of 4 × 4 Substitution Box Using Elliptic Curves and Algebraic Group Structures

Cellular Automata (CA) represent an interesting approach to design Substitution Boxes (S-boxes) having good cryptographic properties and low implementation costs. From the cryptographic perspective, up to now there have been only ad-hoc studies about specific kinds of CA, the best known example being the χ nonlinear transformation used in Keccak. In this paper, we undertake a systematic investigation of the cryptographic properties of S-boxes defined by CA, proving some upper bounds on their nonlinearity and differential uniformity. Next, we extend some previous published results about the construction of CAbased S-boxes by means of a heuristic technique, namely Genetic Programming (GP). In particular, we propose a “reverse engineering” method based on De Bruijn graphs to determine whether a specific S-box is expressible through a single CA rule. Then, we use GP to assess if some CA-based S-box with optimal cryptographic properties can be described by a smaller CA. The results show that GP is able to find much smaller CA rules defining the same reference S-boxes up to the size 7 × 7, suggesting that our method could be used to find more efficient representations of CA-based S-boxes for hardware implementations. Finally, we classify up to affine equivalence all 3 × 3 and 4 × 4 CA-based S-boxes.