S-box Design Research Articles

Low-power AES S-box design using dual-basis tower field extension method for cyber security applications

In cryptography, one among several investigated areas is the implementation of AES S-boxes. In this paper, a substitution-box is designed which follows combined data path using dual-basis tower field extension with Golod–Shafarevich theorem fed in immune genetic algorithm for optimization purpose for each and every block. The role of enhanced immune genetic algorithm is as follows: at first, chaotic system generates S-boxes population, these S-boxes which perform excellently are then optimized by a sequence of operators such as extraction of anti-agent and immune selection. Few criteria of S-boxes such as differential uniformity, nonlinear degree, and strict avalanche effect are analyzed. The obtained results are analyzed with CMOS 35 nm and 15 nm technologies to measure the performance of the proposed designs and was observed that the proposed one outperforms in power and area. The optimized S-box can be effectively applied for securing information. The proposed Golod–Shafarevich feeder Immune Genetic Algorithm S-box (GSIGA-Sbox) is compared with two baseline methods such as Reversed Genetic Algorithm S-box (RGA-Sbox) and Discrete Space Chaotic S-box (DSC-Sbox). As a result the proposed GSIGA-Sbox achieves encryption speed of 61 MHZ, decryption speed of 55 MHZ with 24% of power consumption for 35 nm CMOS technology and 57 MHZ encryption speed, 51 MHZ decryption speed with 28% of power consumption for 15 nm CMOS technology.

S-Box Design Based on 2D Multiple Collapse Chaotic Map and Their Application in Image Encryption.

As an essential part of an encryption system, the performance of a chaotic map is critical for system security. However, there are many defects for the existing chaotic maps. The low-dimension (LD) ones are easily predicted and are vulnerable to be attacked, while high-dimension (HD) ones have a low iteration speed. In this paper, a 2D multiple collapse chaotic map (2D-MCCM) was designed, which had a wide chaos interval, a high complexity, and a high iteration speed. Then, a new chaotic S-box was constructed based on 2D-MCCM, and a diffusion method was designed based on the S-box, which improved security and efficiency. Based on these, a new image encryption algorithm was proposed. Performance analysis showed that the encryption algorithm had high security to resist all kinds of attacks easily.

S-box Construction Method Based on the Combination of Quantum Chaos and PWLCM Chaotic Map

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

A method for generation of substitution box based on random selection

Two basic requirements must be met to encrypt data. These requirements are confusion and diffusion properties. In particular, block cipher algorithms are based on a cryptographic component known as substitution-box to provide the need for confusion. Therefore, attack scenarios generally focus on this cryptographic component. There are alternative design approaches for substitution-box design. It is known that each design approach has several advantages and disadvantages. In this study, an alternative method is proposed to address the problems of the substitution-box design approach based on random selection. The success of the proposed method has been tested in three different scenarios. Analysis results for these three scenarios showed that generated substitution-box provides performance increase for nonlinearity criterion from s-box design criteria. Successful results achieved; It points out that improvement cryptographic components can be used in a variety of practical applications such as block ciphers, masks to prevent side-channel attacks, random number generators, and image encryption algorithms.

S-Box Construction Method Based on the Combination of Quantum Chaos and PWLCM Chaotic Map

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

RETRACTED: HPAC-sbox- a novel implementation of predictive learning classifier and adaptive chaotic s-box for counterfeiting sidechannel attacks in an IOT networks

ABSTRACT Today, embedded systems are augmented with the Internet of things and more with the artificial intelligence to make world even connected with aliens. With an IoT networks are getting its insight since it deals with large number of data information, security has considered to be more important and needs to be a diagnosis for every minute. To enhance the security in the network, a mathematically secure algorithms were formulated and runs on the cryptographic embedded chips to counterfeit the risks which are caused by the different attacks such as side channel attacks (SCA) on the networks. Even though many cryptographic encryption algorithms such as AES, DES, RC4 algorithms were gaining its importance, fixed encryption keys, non-intelligent detection of attacks, cognitive countermeasures are some of the real-time challenges in an existing system of encryption. Following the limitations of existing systems, this research article focuses on design of new AES with HPAC-SBOX (Hybrid Prediction and Adaptive Chaos) which integrates powerful predictive learning algorithms and adaptive chaotic logistic S-Box. The following contributions of this research articles are: a) Preparation of Data Sets from the Power consumption traces captured from Multi Core Embedded boards while running the Advanced Encryption Systems(AES) on it b) Implementation of High Speed and High Accurate Prediction learning machines for the prediction of side-channel attacks c) Design of Adaptive Chaotic S-Box using 3-Dlogistic Hyperbolic maps for attacked bits. To evaluate the proposed architecture, experimentation in carried out in an IoT networks and various performance parameters were calculated and analyzed. The results show that the proposed architecture outperforms the other existing algorithms in terms of prediction and performance.

S-Box Design Based on Discrete Chaotic Map and Improved Artificial Bee Colony Algorithm

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.

Comments on “On the Design of Chaos-Based S-Boxes”

In the above article [1], chaos-based S-box design methods are analyzed in order to reassess the nonlinearity of some previous S-box examples. As a result of the analysis, it is concluded that the majority of cited articles in [1] focus only on the average nonlinearity of S-box coordinates, while remaining S-box components are ignored. On the basis of such analysis, it is concluded that the majority of studies analyzed in [1] should be re-evaluated and used with a considerable caution. However, the analysis in the above article [1] is made based on a major oversight in reviewing previous literature regarding the nonlinearity of S-boxes, which caused a wrong conclusion regarding most of the articles cited in [1].

Dynamic S-Box Design Using a Novel Square Polynomial Transformation and Permutation

New era ciphers employ substitution boxes (S-boxes) which assist in the provision of security for the plaintext in the encryption phase and transforming the ciphertext on the receiver side into original plaintext in the decryption phase. The overall security of a given cipher engaging an S-box greatly depends on the cryptographic forte of the respective S-box. Consequently, many researchers have used different innovative approaches to construct robust S-Boxes. In this article, an innovative and modest square polynomial transformation, the very first time, along with a novel affine transformation and a pioneering permutation approach to construct dynamic S-boxes is proposed. The proposed method has the capability to erect a huge number of robust S-boxes by applying minute changes in the parameters of transformation and permutation processes. An example S-Box is generated, and its recital analysis has been done using typical criteria including bijectivity, strict avalanche criterion, nonlinearity, bit independence criterion, linear probability, differential probability, and fixed-point analysis to check its cryptographic forte. This performance of the proposed S-box is placed side by side against state-of-the-art S-boxes to prove its strength. The performance and comparative analyses authenticate that the projected S-box possesses the true competence for its application in modern-day ciphers.

Human Behaviour Based Optimization Supported With Self-Organizing Maps for Solving the S-Box Design Problem

The cryptanalytic resistance of modern block and stream encryption systems mainly depends on the substitution box (S-box). In this context, the problem is thus to create an S-box with higher value of nonlinearity because this property can provide some degree of protection against linear and differential cryptanalysis attacks. In this paper, we design a scheme built on a human behavior-based optimization algorithm, supported with Self-Organizing Maps to prevent premature convergence and improve the nonlinearity property in order to obtain strong 8 ×8 substitution boxes. The experiments are compared with S-boxes obtained using other metaheuristic algorithms such as Ant Colony Optimization, Genetic Algorithm and an approach based on chaotic functions and show that the obtained S-boxes have good cryptographic properties. The obtained S-box is investigated against standard tests such as bijectivity, nonlinearity, strict avalanche criterion, bit independence criterion, linear probability and differential probability, proving that the proposed scheme is proficient to discover a strong nonlinear component of encryption systems.

2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudo-random mixed coupling method we present a spatiotemporal chaos which used PS map as local map f(x). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov–Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.

Block Cipher Nonlinear Confusion Components Based on New 5-D Hyperchaotic System

The security strengths of block ciphers greatly rely on the confusion components which have the tendency to transform the data nonlinearly into the perplexed form. This paper proposes to put forward a novel scheme of generating cryptographically strong nonlinear confusion components of block ciphers, usually termed as substitution-boxes (S-boxes). The anticipated S-box design scheme is based on a novel five-dimensional (5-D) chaotic system analyzed in this paper. The proposed 5-D dynamical system consists of hyperchaotic phenomenon, KY dimension, conservativity, unstable equilibrium point, and complex phase attractors which are suited for cryptographic applications. The S-box based on hyperchaotic system is made to evolve in order to generate an optimized S-box for high nonlinearity score to make it robust against many linear attacks. The performance analysis of proposed S-box demonstrates that it has bijectivity, high nonlinearity; satisfied strict avalanche criterion and bits independent criterion; low differential and linear probabilities. Moreover, performance appraisal of proposed S-box justifies its better strength and features over many recently investigated S-boxes.

A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field.

Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.

A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm

Substitution-boxes (S-boxes) are unique nonlinear elements, which are used to achieve the property of confusion in modern symmetric ciphers and offer resistance to cryptanalysis. The construction of strong S-boxes has gained considerable attention in the area of cryptography. In fact, the security of transmitted data is highly dependent on the strength of the S-boxes for the prevention of unauthorised access. Therefore, the creation of strong S-box with high nonlinearity score has been considered a significant challenge. This study presented a novel method for the designing of 8 × 8 S-boxes with selected cryptographic characteristics based on a cuckoo search (CS) algorithm and discrete-space chaotic map. Notably, the advantage of the proposed approach is indicated through the efficient randomisation and lower adjustable parameters in CS compared to GA and PSO. Also, this approach utilised a 1D discrete-space chaotic map with virtually unlimited key space to design initial S-boxes, which is another advantage over the methods based on continuous-space chaotic maps, which consist of the limited key space. Moreover, chaotic maps have a potential to overcome the trapping problem of a standard CS in the local optima, and they were used to generate initial S-boxes to achieve the desired quality and facilitate the metaheuristic search. Accordingly, the metaheuristic CS was used to find a notable S-box configuration which fulfilled the established criteria. This objective was achieved by searching for the optimal or near-optimal features which maximised the given fitness function. The performance of the proposed method was evaluated based on the established performance evaluation criteria, including bijectivity, nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and linear probability. Based on the results of proposed method performance was benchmarked against the results of the recently developed S-boxes, it was indicated that the S-boxes exhibited good cryptographic features and could resist various cryptanalysis attacks.

Design of fault-resilient S-boxes for AES-like block ciphers

Substitution functions (S-boxes) play an important role in the security of AES-like cryptosystems, but the cryptosystems are highly vulnerable against fault injection attacks. Some research has been carried out previously to prevent fault injection attacks on AES, but most of the countermeasures are restricted to the detection of faults only, and they only work at the cost of large hardware needed for duplicating the S-boxes. In this paper, we present a design construction of fault-resilient S-boxes for AES-like block ciphers by fault detection and correction. The random evolution of cellular automata with linear and nonlinear neighborhood functions is exploited to design these S-boxes. The proposed design guarantees 100% coverage of single-byte fault correction and double-byte fault detection in the S-boxes. The FPGA implementation shows that our design makes the substitution boxes fault-resilient with 21.34% extra hardware compared to the AES substitution layer.

12×12 S-box Design and its Application to RGB Image Encryption

Customarily, 8×8 S-box is a 16×16 look up table over Galois field GF28, algebra over the binary field F2. A 12×12 S-box over GF212 is not workable as the computer memory does not manage it. The finite chain ring F2[x]<x12> is fundamentally an algebra over the binary field F2. In this paper we considered the advantage and devise a novel method of 12×12 S-box design over the unit elements of finite chain ring F2[x]<x12>. The newly obtained S-box has greatly higher confusion ability than any of 8×8 S-box. To observe this effect, an RGB image encryption application is given. In the proposed encryption scheme, we doubled the bits of 12×12 S-box from 12 to 24 for creating confusion in the data. Consequently, a new method of color image encryption is designed by which 24 binary bits are utilized at the place of byte. Whereas for diffusion we apply the linear permutation P=i×32 mod 257 and finally bitwise Exclusive-or operation is operationalized. Analysis reveals that the proposed image encryption approach might switch many 8×8 S-box based color image encryption schemes.

Low AND Depth and Efficient Inverses: a Guide on S-boxes for Low-latency Masking

In this work, we perform an extensive investigation and construct a portfolio of S-boxes suitable for secure lightweight implementations, which aligns well with the ongoing NIST Lightweight Cryptography competition. In particular, we target good functional properties on the one hand and efficient implementations in terms of AND depth and AND gate complexity on the other. Moreover, we also consider the implementation of the inverse S-box and the possibility for it to share resources with the forward S-box. We take our exploration beyond the conventional small (and even) S-box sizes. Our investigation is twofold: (1) we note that implementations of existing S-boxes are not optimized for the criteria which define masking complexity (AND depth and AND gate complexity) and improve a tool published at FSE 2016 by Stoffelen in order to fill this gap. (2) We search for new S-box designs which take these implementation properties into account from the start. We perform a systematic search based on the properties of not only the S-box but also its inverse as well as an exploration of larger S-box sizes using length-doubling structures. The result of our investigation is not only a wide selection of very good S-boxes, but we also provide complete descriptions of their circuits, enabling their integration into future work.

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.

A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design

In this paper, a new one-dimensional discrete-space chaotic map based on the multiplication of integer numbers and circular shift is presented. Dynamical properties of the proposed map are analyzed, and it exhibits chaotic behavior. The proposed map has fixed points for certain settings, but it is easy to completely avoid them. This map preserves all desirable properties of previous discrete-space chaotic maps and has improved characteristics related to orbit length, computational complexity and memory requirements. These improvements can be particularly useful when implementation in digital devices, which have limited memory and computational resources, is needed. S-box design method based on this chaotic map is presented as an example of its application in cryptography. The results of performance tests show that S-boxes with good cryptographic properties can be generated on the basis of this discrete-space chaotic map.

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.