S-box Design Research Articles

A novel method of dynamic S-box design based on combined chaotic map and fitness function

This paper introduces a method of generating a strong S-box by using combined chaotic system and fitness function. Our method presents an algorithm which has two stages: static S-box generation and dynamic S-box optimization. Chaotic sequences generation, sequences discretization are involved in the first stage. Moreover, the proposed static S-box is converted into a dynamic S-box with the help of fitness function. The optimal S-box satisfies the following criteria: bijectivity, nonlinearity, strict avalanche criteria, output bits independence criterion, equiprobable inputs/outputs XOR distribution. Extensive experiments demonstrate that the proposed algorithm has excellent performance in cryptography and attacks resistance.

S-box design based on optimize LFT parameter selection: a practical approach in recommendation system domain

The strength of cryptography encryption is strongly depended upon the substitution box (S-box), hence highly non-linear S-box is appreciated in cryptography. In this work, we proposed a scheme to select the optimized values for control parameters (a, b, c, d) of linear fractional transform (LFT) to achieve an S-box with non-linearity of 112. For dynamic parameter values, we used location of chaotic sequences. The proposed s-box tested on different criteria such as non-linearity method (NL), probability methods (linear approximation (LP), differential approximation (DP), strictly avalanche criteria (SAC) and bit independence criteria (BIC). Our result shows that proposed s-box achieves better or equal to cryptographic strength as compared with state-of-the-art techniques. Moreover, we tested the proposed s-box based encryption method in recommendation system scenario with the idea of text-to-image conversion. The statistical analysis of this image encryption shows the bright prospects of the proposed method.

On the effect of chaotic system in performance characteristics of chaos based s-box designs

Many cryptographic protocol have been realized using similarities between chaos and cryptology. One of the most successful examples of these protocols has been s-box structures. S-box structures are a popular topic because they are the only component that provides nonlinearity property in many encryption algorithms. Therefore, in the literature, chaos based s-box designs have been proposed for almost all chaotic system classes. However, the effect of chaotic systems on these designs has not been studied in all aspects. The purpose of this study is to address this problem. It has been shown in the study that strong s-box structures can be designed by using systems that do not display chaotic behavior. This result has revealed the necessity of reexamining many designs in chaos based cryptology literature. A raw literature analysis has shown that the number of studies related to chaos based s-box designs over the last decade is more than 250. Therefore, it is thought that study outputs will bring a different perspective for chaos based cryptology literature.

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.

Construction of Cryptographically Secure AES S-Box using Second-order Reversible Cellular Automata

In cryptography the block ciphers are the mostly used symmetric algorithms. In the existing system the standard S-Box of Advanced Encryption Standard(AES) is performed using the irreducible polynomial equation in table form known as look-up tables(LUTs). For more security purposes, second-order reversible cellular automata based S-box is created. The security aspects of the S-Box used in the AES algorithm are evaluated using cryptographic properties like Strict Avalanche Criteria, Non-Linearity, Entropy, and Common Immunity Bias. The design of S-Box using second-order reversible Cellular Automata is better concerning security and dynamic aspect as compared to the classical S-boxes used Advanced Encryption Standard.

CSL: FPGA Implementation of Lightweight Block Cipher for Power-constrained devices

The exploration of interconnected devices, embedded devices, sensors, and various network-connected devices helps to communicate each other and exchange communications. These devices overcome with security threats related to privacy and data exchange over billions of devices are interconnected. Lightweight block ciphers aim to provide a feasible solution for power-constrained devices which includes Radio-frequency identification (RFID) tags, ubiquitous computing, wireless sensor network, aggregation network and IoT. In this paper, we have implemented a lightweight block cipher compact, secure, and lightweight (CSL). It operates on 64-bit block size, and key size varies from 64-bit to 128-bit key for encryption and decryption. The hardware implementation of CSL algorithm was thrived using field programmable gate array (FPGA) architecture. A pipelined design of compact S-boxes implemented on Digilent Nexys 4 DDR Artix™-7 board. Our experimental results of CSL consumes 1145 LUTs (Lookup Tables) and has fewer memory requirements. CSL shows resistant against various cryptanalytic attacks.

Encryption of accounting data using DES algorithm in computing environment

The more and more developed network has caused more and more impact on people’s life and work, providing convenient channels for people’s information exchange, and then improving people’s living and working conditions. However, when data is transmitted through the network, there are hidden security risks, especially important accounting data. Once intercepted and used by criminals, it may cause serious harm to the owner of the data. Based on the above background, the purpose of this article is to study the use of the DES algorithm to encrypt accounting data in a computing environment. This paper proposes an improved quantum genetic algorithm and applies it to the S-box design of the DES algorithm, which improves the non-linearity of the S-box, reduces the differential uniformity, and enhances the security of the DES algorithm. This improved DES algorithm reduces the number of iterations by increasing the key length and iterative processing using a two-round function, which further increases the security of the algorithm and improves the operation speed of the encryption process. It is found that the 64 ciphertexts of the DES algorithm and the number of changed bits compared to the original ciphertext fluctuates around 32 bits, which explains the problems that should be paid attention to when using the DES algorithm to encrypt accounting data. The validity of key characters should be guaranteed to prevent key loss or leakage. Shorter data encryption regular solution.

Generation of Highly Nonlinear and Dynamic AES Substitution-Boxes (S-Boxes) Using Chaos-Based Rotational Matrices

This work reports a novel chaos-based affine transformation generation method, which is based on rotational matrices to design strong key-based S-boxes. Chaotic logistic map’s nonlinear trajectories are used to generate rotational matrices under given design conditions. Thus, the inherent logic is to generate key-based S-boxes, as strong as AES S-box, in terms of cryptographic properties using chaos in affine transformation. The randomness of chaotic sequences is tested using the National Institute of Standard and Technology (NIST) Statistical Test Suit (STS) 800–22 that validates the generated sequences for S-box design. The results show that methodology adapted to design proposed key-based dynamic S-boxes entails near-optimal cryptographic properties so that proposed S-boxes are as stronger as AES S-box.

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 S-Box Design Algorithm Based on a New Compound Chaotic System

Substitution-boxes (S-Boxes) are important non-linear components in block cryptosystem, which play an important role in the security of cryptosystems. Constructing S-Boxes with a strong cryptographic feature is an important step in designing block cipher systems. In this paper, a novel algorithm for constructing S-Boxes based on a new compound chaotic system is presented. Firstly, the new chaotic system, tent–logistic system, is proposed, which has better chaotic performance and wider chaotic range than the tent and logistic system, and can not only increase the randomness of the chaotic sequences but also expand the key space of cryptosystems. Secondly, a novel linear mapping is employed to construct the initial S-Box. Then, the permutation operation on the initial S-Box is performed by using chaotic sequence generated with the tent–logistic system, which improves the cryptographic features of the S-Box. The idea behind the proposed work is to make supplementary safe S-box. Detail tests for cryptographic strength of the proposed S-Box are performed by using different standard benchmarks. The test results and performance analysis show that our proposed S-Box has very smaller values of linear probability (LP) and differential probability (DP) and a satisfactory average value of nonlinearity compared with other S-Boxes, showing its excellent application potential in block cipher system.

An Analysis and Generation Toolbox for Chaotic Substitution Boxes: A Case Study Based on Chaotic Labyrinth Rene Thomas System

One of the successful examples of chaos-based cryptology design proposals is s-box structures based on random selection. There are many s-box design proposals in the literature since chaotic systems are a powerful entropy source. This feature is one of the most important factors affecting successful designs. Another important factor affecting this success is that measurable test criteria for s-box analysis are clearly presented in the literature. This study has developed a toolbox that can analyze these measurable test criteria. This toolbox has shown that the performance measures of the seven previous proposals in the literature are incorrectly calculated. This analysis toolbox has been made free to use for researchers and aims to prevent inaccurate analyses in future studies. Another contribution of the study is the random selection-based s-box generator toolbox. This toolbox can use both classical random function and chaotic system classes as entropy source. Another important output of generator toolbox is the chaotic labyrinth Rene Thomas system, which can be selected as a continuous-time chaotic system. This system has been first used in the s-box generator. This study has been one of the first steps in addressing the analysis problems of the chaos-based cryptology literature. It is thought that along with such studies to be developed in the future will positively affect the success of the chaos-based cryptographic system proposals.

A novel multi-dimensional encryption technique to secure the grayscale images and color images in public cloud storage

Image encryption is one of the techniques which is used to maintain the image confidentiality. Trust is needed to be created and retained in the cloud between the service provider and the end user. The existing image encryption methods are using a map structure, Rubik cube method, DCT-based approach and s-box designs. The existing algorithms are mostly designed with the concept of offline image encryption. While coming to the online encryption, the image encryption algorithms needed to be redefined with a lightweight approach with an improved security level or same security level of existing algorithms. These things are taken into consideration in the proposed multi-dimensional encryption technique design. The proposed technique is using two phases to perform the encryption. The proposed technique’s two phases are image pixel shuffling phase and image pixel rearrange phase. The proposed technique is already tested successfully on the standard grayscale images, and the results were obtained and it satisfied the objectives. In this paper, the proposed technique was tested on the standard color images and the gained results. Those results have been used to analyze the performance and efficiency of proposed technique with the existing technique, by using different parameters which include PSNR, MSE, information entropy, coefficient correlation, NPCR and UPCI.

S-Boxes Construction Based on the Cayley Graph of the Symmetric Group for UASNs

Modern block ciphers can be used for designing security schemes to meet the security requirements in underwater acoustic sensor networks. The substitution boxes (S-boxes) used in block ciphers must have good cryptographic properties to resist various attacks. The difficulty in the design of S-boxes is that the cryptographic properties of S-boxes have no obvious distribution. In this paper, we investigate the certain subgraph of the Cayley graph of the symmetric group to get some information about the distribution of the cryptographic properties of S-boxes. Based on the information obtained, an algorithm for designing S-boxes with good cryptographic properties is proposed. The security analysis shows that the preferred S-box constructed by the proposed algorithm has good cryptographic properties.

Side-Channel Analysis of Chaos-Based Substitution Box Structures

There is a theoretically strong relationship between chaos and cryptology. In practice, one of the most successful applications of this relationship is chaos-based s-box structures. However, the performance metrics of chaos-based s-box designs are worse compared to those for s-box structure based on algebraic techniques used in modern encryption algorithms, such as the AES algorithm. What is the reason for using chaos-based s-box structures, even though they have worse cryptographic characteristics? Researchers claim that they may be an alternative defense against implementation attacks, especially side-channel analyses. However, no studies have supported or refuted this claim so far. In this paper, side-channel analyses have been performed for two different chaos-based s-box structures. These two s-box structures have been selected for having with the best and worst performance measurements for s-box structures previously proposed in the literature. The results were compared with the AES s-box structure. Analysis of the results showed that chaos-based s-box structures are more resistant against side-channel attacks. Therefore, chaos-based designs may be an alternative defense against implementation attacks, as alleged. However, both algebraic and chaos-based s-box designs have been observed to be insecure if the attacker has more than 30 plaintexts in the side channel analyses. These results show that implementation analysis studies are required in the chaos-based cryptology literature.

An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization

Elliptic curves (ECs) are considered as one of the highly secure structures against modern computational attacks. In this paper, we present an efficient method based on an ordered isomorphic EC for the generation of a large number of distinct, mutually uncorrelated, and cryptographically strong injective S-boxes. The proposed scheme is characterized in terms of time complexity and the number of the distinct S-boxes. Furthermore, rigorous analysis and comparison of the newly developed method with some of the existing methods are conducted. Experimental results reveal that the newly developed scheme can efficiently generate a large number of distinct, uncorrelated, and secure S-boxes when compared with some of the well-known existing schemes.

Spin Me Right Round Rotational Symmetry for FPGA-Specific AES

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 naïve 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 wellknown 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 of 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 first-order side-channel analysis attacks. Targeting the small area footprint on FPGAs, we introduce a heuristic-based algorithm to find a masking of a given function with d + 1 shares. Its application to our new construction of the AES S-box allows us to introduce the smallest masked AES implementation on Xilinx FPGAs, to-date.

Design of a strong S-box based on a matrix approach

In this paper, we present a matrix approach based on the rule 90 cellular automata, and a fractional linear transformation over Galois field $$GF(2^8)$$ , to implement a strong substitution box (S-box). To make the assessment of this proposal, some standard tests are performed, and the obtained numerical results show that this proposed S-box is comparable or superior to some S-boxes used as benchmarks in this work. Also, to measure the strength of the S-box in image encryption, some statistical tests are carried out, which prove that our proposal exhibits appealing security properties.

Smashing the Implementation Records of AES S-box

Canright S-box has been known as the most compact S-box design since its introduction back in CHES’05. Boyar-Peralta proposed logic-minimization heuristics that could reduce the gate count of Canright S-box from 120 gates to 113 gates, however synthesis results did not reflect much improvement. In CHES’15, Ueno et al. proposed an S-box that has a slightly higher area, but significantly faster than the previous designs, hence it was the most efficient (measured by area×delay) S-box implementation to date. In this paper, we propose two new designs for the AES S-box. One design has a smaller implementation area than both Canright and the 113-gate S-boxes. Hence, our first design is the smallest AES S-box to date, breaking the 13 years implementation record of Canright. The second design is faster and smaller than the Ueno S-box. Hence, our second design is both the fastest and the most efficient S-box design to date. While doing so, we also propose new logicminimization heuristics that outperform the previous algorithms of Boyar-Peralta. Finally, we conduct an exhaustive evaluation of each and every block in the S-box circuit, using both structural and behavioral HDL modeling, to reach the optimum synergy between theoretical algorithms and technology-supported optimization tools. We show that involving the technology-supported CAD tools in the analysis results in several counter-intuitive results.

Generic Low-Latency Masking in Hardware

In this work, we introduce a generalized concept for low-latency masking that is applicable to any implementation and protection order, and (in its most extreme form) does not require on-the-fly randomness. The main idea of our approach is to avoid collisions of shared variables in nonlinear circuit parts and to skip the share compression. We show the feasibility of our approach on a full implementation of a one-round unrolled Ascon variant and on an AES S-box case study. Additionally, we discuss possible trade-offs to make our approach interesting for practical implementations. As a result, we obtain a first-order masked AES S-box that is calculated in a single clock cycle with rather high implementation costs (60.7 kGE), and a two-cycle variant with much less implementation costs (6.7 kGE). The side-channel resistance of our Ascon S-box designs up to order three are then verified using the formal analysis tool of [BGI+18]. Furthermore, we introduce a taint checking based verification approach that works specifically for our low-latency approach and allows us to verify large circuits like our low-latency AES S-box design in reasonable time.

Construction of chaotic quantum magnets and matrix Lorenz systems S-boxes and their applications

When we listen regarding quantum cryptography, the first thinking that comes up to mind is, how can there be any connection between physics and cryptographic ciphers. In fact, it comes into view that is one of the hottest research in the field of cryptology to exploit physics and has been confirmed as the important objective in the protection of digital data. The topic of quantum magnets and matrix Lorenz Systems has begun to draw increasing attention in recent years. In last decade, chaotic systems have been utilized in many encryption algorithms. In this regard, Lorenz chaotic system based on differential equations achieved more recognition because of its fundamental sensitivity to initial conditions and easiness in use. This manuscript has two parts. First, we have constructed substitution boxes (S-Boxes) based on quantum magnets and matrix Lorenz chaotic system and permutation of the symmetric group S256 and then designated an image encryption algorithm based on proposed S-boxes and Lorenz chaotic system. In cryptography, it is essential to construct secure S-Boxes to propose cryptographically strong systems. Recently, some image encryption techniques that are weak against robustness have been proposed based on chaotic S-boxes. In the first part of the manuscript, an S-Box design is proposed. Continuous-time Lorenz system is chosen as the chaotic system. The presented image encryption algorithm is based on two rounds of a novel chaotic substitution-permutation network uses proposed S-boxes for substitution purpose by iterations of the Lorenz chaotic system and special kind of permutation process to get the full cipher image. The proposed algorithms for S-box construction and image encryption give very good and coherent performance results when we analyze them with renowned analyses.