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

In block ciphers, the substitution boxes (S-boxes) are used with the purpose to induce confusion in cryptosystems. For the last three decades most of algebraic and chaotic S-boxes are based on the associative algebras of Galois fields. However, recently a little but remarkable work on the designing of S-boxes over some local associative algebras have been published, which is in fact a mock of the associative algebras of Galois fields. The main purpose of these establishments is to hide data and improve the security levels of crypto algorithms. In this study we redesign S-boxes over the elements of inverse property loop. The fascinating features of this structure are; it’s non-associativity and the existence of the inverse of zero element. These properties not only increase the availability of the number of structures but also provide easy approach in constructing S-boxes. The newly designed S-boxes are assessed by various analyses, which include nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probabilities, and differential approximation probabilities. Majority logic criterion is also performed to evaluate its application in various encryption systems.

Region of interest-based medical image encryption technique based on chaotic S-boxes

For first-order complex digital filters with two's complement arithmetic, it is proved in this correspondence that overflow does not occur at the steady state if the eigenvalues of the system matrix are inside or on the unit circle. However, if the eigenvalues of the system matrix are outside the unit circle, chaotic behaviors would occur. For both cases, a limit cycle behavior does not occur. For second-order complex digital filters with two's complement arithmetic, if all eigenvalues are on the unit circle, then there are two ellipses centered at the origin of the phase portraits when overflow does not occur. When limit cycle occurs, the number of ellipses exhibited on the phase portraits is no more than two times the periodicity of the symbolic sequences. If the symbolic sequences are aperiodic, some state variables may exhibit fractal behaviors; at the same time, irregular chaotic behaviors may occur in other phase variables

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.

Substitution-boxes are the main deciding components in symmetric-key cryptosystems for resisting many cryptanalytic attacks. It has been a challenging task for the designers to construct strong S-box which satisfies multiple cryptographic properties simultaneously. A number of S-box studies have been investigated in literature; but, the generated S-box found to exhibit one single property with good score. This paper proposes a novel creation of S-boxes which possess excellent scores of multiple cryptographic properties instead of only one property. The suggested hybrid S-box method explores the science of two-dimensional cellular automata theory, discrete chaotic maps, and algebraic group structure. The proposed anticipated 8×8 S-box holds excellent security performance features such as: minimum nonlinearity as high as 110, no fixed points, satisfaction of strict avalanche and bits independence criterions, differential uniformity as low as 6, linear approximation probability as low as 0.0703, and auto-correlation function (absolute indicator) of 40. The performance comparison indicates the proposed S-box has superior features, greater inherent security and robustness strength than many available state of the art S-box methods.

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.

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.

A strong substitution-box is main ingredient in cryptography. Many encryption schemes have been proposed since 1970’s such as DES, AES and IDEA. In this paper we construct S-boxes using a new technique, our proposed algorithm relies on modified Pascal’s triangle and elliptic curve. The substitution-boxes are analyzed by non-linearity, strict avalanche criterion, bit independence criterion, differential approximation probability and linear approximation probability. Comparison is also made with some existing S-boxes such as AES, APA, Gray, $$S_{8}$$ AES, Skipjack, Xyi and residue prime. We use our proposed substitution-boxes for image encryption and noise removal.

Little theoretical work has been done on (n, m)-functions when $$\frac{n}{2}<m<n$$ , even though these functions can be used in Feistel ciphers, and actually play an important role in several block ciphers. Nyberg has shown that the differential uniformity of such functions is bounded below by $$2^{n-m}+2$$ if n is odd or if $$m>\frac{n}{2}$$ . In this paper, we first characterize the differential uniformity of those (n, m)-functions of the form $$F(x,z)=\phi (z)I(x)$$ , where I(x) is the (m, m)-inverse function and $$\phi (z)$$ is an $$(n-m,m)$$ -function. Using this characterization, we construct an infinite family of differentially $$\Delta $$ -uniform $$(2m-1,m)$$ -functions with $$m\ge 3$$ achieving Nyberg’s bound with equality, which also have high nonlinearity and not too low algebraic degree. We then discuss an infinite family of differentially 4-uniform $$(m+1,m)$$ -functions in this form, which leads to many differentially 4-uniform permutations. We also present a method to construct infinite families of $$(m+k,m)$$ -functions with low differential uniformity and construct an infinite family of $$(2m-2,m)$$ -functions with $$\Delta \le 2^{m-1}-2^{m-6}+2$$ for any $$m\ge 8$$ . The constructed functions in this paper may provide more choices for the design of Feistel ciphers.

The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access. To improve data security, modern cryptosystems use substitution-boxes. Nowadays, data privacy has become a key concern for consumers who transfer sensitive data from one place to another. To address these problems, many companies rely on cryptographic techniques to secure data from illegal activities and assaults. Among these cryptographic approaches, AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box (S-box). The S-box disguises the relationship between cipher text and the key to guard against cipher attacks. The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box. Therefore, various researchers have employed different techniques to construct high order non-linear S-box. This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group over the finite field and the symmetric group . The motivation for this work is to study the symmetric group and coset graphs. The authors have performed various analyses against conventional security criteria such as nonlinearity, differential uniformity, linear probability, the bit independence criterion, and the strict avalanche criterion to determine its high cryptographic strength. To evaluate its image application performance, the proposed S-box is also used to encrypt digital images. The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.

We study the symbolic sequences associated with a two-dimensional nonlinear map describing a digital filter with 2's complement arithmetic, and the role of the filter parameter a = 2cos θ in determining admissibility of these sequences. We solve an appropriately specialized form of Chua and Lin's inequalities governing admissibility, and obtain a complete identification of the infinite class of periodic symbolic sequences admissible in an open interval having parameter value θ = 0 as left end-point. A key step in the argument, easily established by parity for sequences having odd period, requires a more penetrating analysis in the even case. Computer searches for sequences with periods up to 200 have revealed that this class accounts for the greater number of admissible periodic sequences associated with the map. Our solution provides an efficient construction for the periodic symbolic sequences admissible adjacent to zero, parametrized by the period and the number of +− digit pairs present. We also show that the precise interval of admissibility is (0, π/N), where N is the least period, which permits us to relate the sequences to the points of state space that give rise to them. We thereby obtain a bound on the measure of the subset of state space consisting of the points associated with periodic symbolic sequences, improving previously published bounds. A similar identification of the periodic sequences admissible at the far end of the parameter range, adjacent to θ = π, is deduced.

Steady-state self-oscillations and chaotic behavior of a controlled electromechanical device by using the first Lyapunov value and the Melnikov theory

On the chaotic behavior of the hybrid inverted pendulum and its relation to the lateral dynamics of the walking robots

SummaryCognitive radio (CR) is an emerging technology for optimum spectrum utilization. Spectrum sensing (SS) is the first step of CR. Important challenge in the next generations is wideband SS. Compressive sensing (CS) can be used as an SS in CR to solve this challenge. Sensing matrix (SM) plays an important role in CS. For better performance, SM must have low mutual coherence. The existing matrices in the literature are random and chaotic. All random matrices have a good performance, but they have problems of large memory storage, complexity, sharing bandwidth, and low security. Chaotic matrices (CMs) are the best but still have some problems including the use of sample distance in chaotic sequence that consumes high storage resources, low performance and compression under low signal‐to‐noise ratio (SNR), and low security. In this paper, we propose a new 1‐D chaotic map for constructing a novel SM. The proposed map has simple structure, wide range chaotic behavior, and high security. Its chaotic behavior is confirmed using Lyapunov exponent, bifurcation, and trajectory. The CS performance based on novel CM is measured using absolute error ( , mutual coherence, memory cost, computational complexity, and MSE (mean square error), while evaluated through comparisons with matrices in the literature. The simulation and mathematical results show that the proposed map is a hyperchaotic with efficient chaotic behavior in wide range of parameters and low memory storage and complexity. The results also show that it has low , MSE, and mutual coherence at low SNR with high compression.

The effects of foot injuries regarding bilateral asymmetry and gait dynamics are still poorly understood. Previous work discussed rehabilitation, postural control, and asymmetry, with the models being mainly validated for upper body translations and no or minimal assessment on rotation. The aim of this study was to assess the effect of foot injury on gait dynamics. For this, a wearable sensors system for data collection of the key variables of the of human movement was considered. The dynamics of motion – recorded in the plane of motion using a laser sensor – was assessed using a new projective method which considers the axial rotations, translation, and in-plane rotation patterns for normal human gait vs. simulated gait pathologies. A nonlinear timeseries analysis, along with a Poincare map, phase space, time delay, Lyapunov exponents, and false nearest neighbors (FNN) method have been considered in order to convey the periodicity of the data collected for a healthy individual with and without a simulated injury. The Lyapunov exponents which quantity the degree of separation of nearby trajectories are used to differentiate between the chaotic and non-chaotic behavior. The positive sign of the largest Lyapunov exponents for all data indicated “the exponential separation of nearby trajectories as time evolves”, that is, the chaotic behavior of the system.