Construction Of S-boxes Research Articles

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

In recent years, a large number of S-Box design schemes have been proposed. However, after detection we found that most of them contain fixed point or reverse fixed point, which may be an exploitable weakness in cryptography. In order to design a strong S-Box construction algorithm, and eliminate fixed point and reverse fixed point intelligently, we first designed an improved coupling quadratic map (ICQM), which is surjective and has good ergodicity and randomness, verified by bifurcation diagram, Lyapunov exponent and strict randomness testing tool of TestU01. Then we reconstructed a keyed strong S-Box scheme without weakness based on ICQM and backtracking. Experiments results indicated the effectiveness of the proposed S-Box construction scheme.

Spin Me Right Round Rotational Symmetry for FPGA-Specific AES: Extended Version

The effort in reducing the area of AES implementations has largely been focused on application-specific integrated circuits (ASICs) in which a tower field construction leads to a small design of the AES S-box. In contrast, a naive implementation of the AES S-box has been the status-quo on field-programmable gate arrays (FPGAs). A similar discrepancy holds for masking schemes—a well-known side-channel analysis countermeasure—which are commonly optimized to achieve minimal area in ASICs. In this paper, we demonstrate a representation of the AES S-box exploiting rotational symmetry which leads to a 50% reduction in the area footprint on FPGA devices. We present new AES implementations which improve on the state-of-the-art and explore various trade-offs between area and latency. For instance, at the cost of increasing 4.5 times the latency, one of our design variants requires 25% less look-up tables (LUTs) than the smallest known AES on Xilinx FPGAs by Sasdrich and Güneysu at ASAP 2016. We further explore the protection of such implementations against side-channel attacks. We introduce a generic methodology for masking any n-bit Boolean functions of degree t with protection order d. The methodology is exact for first-order and heuristic for higher orders. Its application to our new construction of the AES S-box allows us to improve previous results and introduce the smallest first-order masked AES implementation on Xilinx FPGAs, to date.

A Novel Optimization Method for Constructing Cryptographically Strong Dynamic S-Boxes

The resistance of S-box-based cryptosystems to linear cryptanalysis is often determined by the nonlinearity (NL) and the linear approximation probability (LAP) of the underlying S-box. Constructing dynamic bijective S-boxes with high nonlinearity is a challenging problem. In this paper, we propose a novel S-box construction method based on the concept of constrained optimization. The proposed method uses a random-restart hill-climbing algorithm to construct randomized S-boxes and maximize the nonlinearity of each Boolean function under bijectivity constraints. The proposed algorithm dramatically reduced the S-box construction time. Compared to recent S-box construction methods, the proposed method strikes a better balance among the three design objectives of dynamic S-boxes, namely, cryptographic strength, dynamicity, and speed of construction. On the average, the proposed method constructs a new dynamic $8\times 8$ S-box with NL=112 every 118 ms, whereas a NL=110 S-box can be generated in 5.3 ms, which makes it suitable for real time applications. The proposed method also constructs $8\times 8$ S-boxes with NL=114, which is among the highest reported in literature. Moreover, we demonstrate the extensibility of the proposed constrained optimization formulation to improve other S-box design criteria. Namely, we propose an algorithm to optimize the LAP of an S-box while preserving its NL and bijectivity.

A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field

Cryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encryption Standard (AES) is the most effective encryption algorithm proposed till now. Substitution-box (S-box) is the most crucial and only nonlinear component in AES (or any cryptographic algorithm), which provides data confusion. A highly nonlinear S-box offers high confidentiality and security against cryptanalysis attacks; hence, the design of S-box is very crucial in any encryption algorithm. To address this challenge, we propose the action of matrices (conforming to the basis of P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> [Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ]) on the Galois field GF (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> ). Consequently, a novel algebraic technique for S-box construction to generate highly nonlinear 8 × 8 S-boxes based on by our proposed algorithm, we obtain 1.324×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sup> different S-boxes. Standard S-box tests analyze the cryptographic strength of our proposed S-boxes. The examined results show that the proposed S-boxes possess state-of-the-art cryptographic properties. Moreover, we also demonstrate the effectiveness of the proposed S-boxes in image encryption applications using the majority logic criterion.

On the Design of Chaos-Based S-Boxes

Substitution boxes (S-boxes) are critical nonlinear elements to achieve cryptanalytic resistance of modern block and stream ciphers. Given their importance, a rich variety of S-box construction strategies exists. In this paper, S-boxes generated by using chaotic functions (CF) are analyzed to measure their actual resistance to linear cryptanalysis. The aforementioned papers emphasize on the average nonlinearity of the S-box coordinates only, ignoring the rest of the S-box components in the process. Thus, the majority of those studies should be re-evaluated. Integrating such S-boxes in a given cryptosystem should be done with a considerable caution. Furthermore, we show that in the context of nonlinearity optimization problem the profit of using chaos structures is negligible. By using two heuristic methods and starting from pseudo-random S-boxes, we repeatedly reached S-boxes, which significantly outperform all previously published CF-based S-boxes, in those cryptographic terms, which the aforementioned papers utilize for comparison. Moreover, we have linked the multi-armed bandit problem to the problem of maximizing an S-box average coordinate nonlinearity value, which further allowed us to reach near-optimal average coordinate nonlinearity values significantly greater than those known in literature.

Framework for Efficient Medical Image Encryption Using Dynamic S-Boxes and Chaotic Maps

Protecting patient privacy and medical records is a legal requirement. Traditional encryption methods fall short of handling the large volume of medical image data and their peculiar statistical properties. In this paper, we propose a generic medical image encryption framework based on a novel arrangement of two very efficient constructs, dynamic substitution boxes (S-boxes) and chaotic maps. The arrangement of S-box substitution before and after chaotic substitution is shown to successfully resist chosen plaintext and chosen ciphertext attacks. Special precautions are taken to fend off the reset attack against pseudorandom number generators. We show how to implement the generic framework using any key-dependent dynamic S-box construction method and any chaotic map. Experimental results show that the proposed framework successfully passes all security tests regardless of the chaotic map used for implementation. Based on speed analysis, we recommend the use of the classical Baker map or Henon map to achieve encryption throughput approaching 90 MB/s on a modern PC without hardware acceleration.

Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption

We present a simple yet highly dimensional hybrid diode bridge circuit network that can exhibit complex chaotic behaviours. Further, since our network is characterised by smooth fourth-order exponential nonlinearity, we employ a distinctive approach to assess its different properties: we examine the circuit stability near fixed points. Specifically, we evaluate dynamic complexity using the Lyaponov spectrum analysis, bifurcation analysis and phase space trajectories; additionally, we assess coexisting attractors in the parameter space using numerical and experimental analysis. Furthermore, we report assessments of our network in terms of remerging Feigenbaum trees and metastable chaos. Finally, these properties, and especially the chaotic series of the coexisting attractors, were exploited to implement a chaos-based image encryption protocol using S-box construction and PRNG generation mechanisms. To validate the performance of our protocol, we employed standard security analysis including correlation coefficient, pixel change rate, information entropy, time complexity and key space analysis whose outcome were compared alongside available state-of-the-art methods. Outcomes suggest promising applications for our chaotic circuit network in image encryption.

Construction of New S-Box Using Action of Quotient of the Modular Group for Multimedia Security

Substitution box (S-box) is a vital nonlinear component for the security of cryptographic schemes. In this paper, a new technique which involves coset diagrams for the action of a quotient of the modular group on the projective line over the finite field is proposed for construction of an S-box. It is constructed by selecting vertices of the coset diagram in a special manner. A useful transformation involving Fibonacci sequence is also used in selecting the vertices of the coset diagram. Finally, all the analyses to examine the security strength are performed. The outcomes of the analyses are encouraging and show that the generated S-box is highly secure.

A novel efficient image encryption algorithm based on affine transformation combine with linear fractional transformation

Algebraic structures and their hardware–software implementation gain considerable attention in the field of information security and coding theory. Research progress in the applications of arithmetic properties of algebraic structures is being frequently made. These structures are mostly useful in improvement of the cryptographic algorithms. A novel technique is given to design a cryptosystem responsible for lossless for image encryption. The proposed scheme is for the RGB image whose pixels are considered as 24 binary bits, accordingly a unique arrangement for the construction of S-boxes over a Galois field $$ GF\left( {2^{9} } \right) $$ is employed. Consequently, it generates multiple different S-boxes with excellent cryptographic characteristic and hence confusing process of the cryptosystem has been working. Whereas the diffusion process in this cryptosystem is based on Affine transformation over a unit elements of an integers modulo ring $$ {\mathbb{Z}}_{n} $$ . The scrambling of the image data through the Affine transformation escalate the security asset, avoid computational effort and abbreviated the time complexity. In addition, the simulation test and comparative scrutinize illustrate that the proposed scheme is highly sensitive, large keyspace, excellent statistical properties and secure against differential attacks. Therefore, the proposed algorithm is valuable for confidential communication. Furthermore, due to the arithmetic properties of algebraic structures, the proposed scheme would be easily implemented, secure and fast enough to be utilized in real-world applications.

Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field

Elliptic curve cryptography has been used in many security systems due to its small key size and high security compared with other cryptosystems. In many well-known security systems, a substitution box (S-box) is the only non-linear component. Recently, it has been shown that the security of a cryptosystem can be improved using dynamic S-boxes instead of a static S-box. This necessitates the construction of new secure S-boxes. We propose an efficient method to generate S-boxes that are based on a class of Mordell elliptic curves over prime fields and achieved by defining different total orders. The proposed scheme is developed in such a way that for each input it outputs an S-box in linear time and constant space. Due to this property, our method takes less time and space than the existing S-box construction methods over elliptic curves. Computational results show that the proposed method is capable of generating cryptographically strong S-boxes with security comparable to some of the existing S-boxes constructed via different mathematical structures.

Revisiting AES SBox Composite Field Implementations for FPGAs

Composite fields are used for implementing the advanced encryption standard (AES) SBox when compact and side-channel resistant constructions are required. The prior art has investigated efficient implementations of such SBoxes for application specific integrated circuit (ASIC) platforms. On field programmable gate arrays (FPGAs); however, due to the considerably different structure compared with ASICs, these implementations perform poorly. In this letter, we revisit composite field AES SBox implementations for FPGAs. We show how design choices and optimizations can be made to better suit the granular look-up tables that are present in modern FPGAs. We investigate 2880 SBox constructions and show that about half of them are better than the state-of-the-art composite field implementation. Our best SBox implementation is 18% smaller compared with the state-of-the-art implementation on an FPGA.

Generation Of Numerous S-Box for Advanced Encryption Standard

Substitution box is the non-linear part in Symmetric Encryption Algorithm. It gives the various alternate methods for the construction of S-Box by taking AES Substitution Box as base or modified version of AES S-Box. Hence it is proving that either AES S-box or modified version such as Gray S-Box, S8 S-Box is also satisfying the important parameters of S-Box such as nonlinearity, SAC, Bit Independence Criterion, Diffusion Strength, Differential Approximation probability while we are encrypting both the text and image

A new construction of confusion component of block ciphers

Confusion is one of the most important component of modern block ciphers. The security of modern encryption scheme is based on substitution and permutation network (SP-network). The idea of SP-network was proposed by Claude Shannon in 1949. Construction of optimal confusion component (substitution box) has been a prominent topic of interest. In this article, we have proposed a new technique for the construction of S-boxes which fulfill the required cryptographic properties. Our proposed scheme utilized double affine transformation which gives nonlinearity of 112 for each primitive irreducible polynomials of degree 8. The simulation results of our proposed nonlinear component are compared with some recently suggested substitution boxes (S-boxes) which demonstrate that the proposed scheme is more capable to construct strong nonlinear component of block encryption systems.

Cryptosystem techniques based on the improved Chebyshev map: an application in image encryption

The use of nonlinear (chaotic) transformations in cryptography to create confusion during encryption process has become a common practice. In this paper, a pair of proficient cryptosystem techniques are proposed in the form of substitution and permutation constructed on the one-dimensional chaotic map (Improved Chebyshev map). Initially, an efficient and simple method for the construction of S-box using one-dimensional chaotic system is presented. The main advantage of the suggested scheme is to generate strong S-boxes depending upon keys used by chaotic map. Then, an efficient encryption scheme based on substitution box and the chaotic map (substitution and permutation system) is presented. Experimental consequences validate the efficiency of anticipated algorithms. A great potential and higher performance for noticeable dominance regarding cryptographic applications can be seen for the presented cryptosystems in comparison with the algorithms already developed in literature.

S-Box on Subgroup of Galois Field

In substitution–permutation network as a cryptosystem, substitution boxes play the role of the only nonlinear part. It would be easy for adversaries to compromise the security of the system without them. 8-bit S-boxes are the most used cryptographic components. So far, cryptographers were constructing 8-bit S-boxes used in cryptographic primitives by exhaustive search of permutations of order 256. However, now for cryptographic techniques with 8-bit S-boxes as confusion layers, researchers are trying to reduce the size of S-box by working with a small unit of data. The aim is to make the techniques compact, fast and elegant. The novelty of this research is the construction of S-box on the elements of the multiplicative subgroup of the Galois field instead of the entire Galois field. The sturdiness of the proposed S-box against algebraic attacks was hashed out by employing the renowned analyses, including balance, nonlinearity, strict avalanche criterion, and approximation probabilities. Furthermore, the statistical strength of the S-box was tested by the majority logic criterion. The fallouts show that the S-box is appropriate for applications for secure data communications. The S-box was also used for watermarking of grayscale images with good outcomes.

An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

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.

Construction of S-Box Based on Chaotic Map and Algebraic Structures

The Advanced Encryption Standard (AES) is widely used in different kinds of security applications. The substitution box (S-box) is the main component of many modern symmetric encryption ciphers that provides confusion between the secret key and ciphertext. The S-box component that is used in AES is fixed. If we construct this component dynamically, the encryption strength of AES would be greater than before. In this manuscript, we used chaotic logistic map, Mobius transformation and symmetric group S 256 to construct S-box for AES. The idea behind the proposed work is to make supplementary safe S-box. The presented S-box is analyzed for the following analyses: linear approximation probability (LP), nonlinearity (NL), differential approximation probability (DP), strict avalanche criterion (SAC), and bit independence criterion (BIC). The analyses show that the proposed technique is useful in generating high resistance S-box to known attacks.

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

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.

Constructions of S-boxes with uniform sharing

In this paper we focus on S-box constructions. We consider the uniformity property of an S-box which plays an important role in Threshold Implementations (TI). Most papers so far have studied TI sharings for given S-boxes. We proceed in the opposite way: starting from n-bit S-boxes with known sharings we construct new (n + 1)-bit S-boxes from them with the desired sharings. In addition, we investigate the self-equivalency of S-boxes and show some interesting properties.

Construction of Cryptographic S-Boxes Based on Mobius Transformation and Chaotic Tent-Sine System

Over the last few decades, different mediums of secure communication use chaos which is demonstrated by some nonlinear dynamical systems. Chaos shows unpredictable behavior and this characteristic is quite helpful in different encryption techniques and for multimedia security. In this work, the chaotic behavior of the improved Tent-Sine map is conferred and ultimately a new method to construct substitution-boxes is proposed. This new method explores the features of chaos through TSS map and algebraic Mobius transformation to generate strong S-boxes. The S-boxes are assessed using standard tests suit which includes nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probability and differential uniformity. Moreover, the proposed S-boxes show excellent statistical properties under majority logic criterions such as correlation, homogeneity, energy, entropy, contrast. The statistical encryption results are demonstrate the better performance of the proposed S-boxes when compared with some of state of the art S-boxes including AES, Gray, APA S8 AES, Skipjack and validate the suitability of anticipated method.