Properties Of S-boxes Research Articles

On some relations of SCA-related properties of S-box under the Hamming weight leakage mode

Abstract— Physical implementations of cryptographic algorithms are vulnerable to so-called side-channel attacks, in which sensitive information can be recovered through the analysis of the leakages produced by the operating device. In the particular case of block ciphers, substitution boxes are often the target of such attacks, as they are the main nonlinear component of the cipher. Literature survey contains some definitions of theoretical properties to measure the resistance provided by substitution boxes with respect to the imminent threat of side-channel attacks. The fundamental questions we board in this paper are: are all these properties related? And if so, what can we tell of their relation? We pretend to bring some clarification to this subject using some well-known side-channel related properties of S-box.

Method to Improve the Cryptographic Properties of S-Boxes

Method to Improve the Cryptographic Properties of S-Boxes

STUDY OF THE CRYPTOGRAPHIC STRENGTH OF THE S-BOX OBTAINED ON THE BASIS OF EXPONENTIATION MODULO

This article presents one of the main transformations of symmetric block ciphers used to protect confidential information, a new method for obtaining a non-linear S block, and an analysis of the results obtained. The S-box obtained by this method can be used as a non-linear transformation in block cipher algorithms to protect confidential data transmitted over an open channel. In most well-known works in the field of analysis and synthesis of modern block symmetric ciphers, S-box is used as a mathematical apparatus for cryptographic Boolean functions. In this case, each S-box is represented by a set of composite Boolean functions whose properties characterize the efficiency of the nonlinear substitution node. Substitution nodes for modern symmetric primitives, including key unfolding functions, are usually implemented as replacement tables. Considering that in most modern block symmetric ciphers for introducing round keys, the encryption algorithm uses a linear operation (bitwise addition modulo 2), S-blocks are the only elements responsible for the cryptographic stability of block encryption algorithms. The required number of rounds of block symmetric ciphers is selected taking into account the results of the cryptographic analysis performed, provided that the properties of S-boxes are specified. As the main criteria and performance indicators, the balance and nonlinearity of composite Boolean functions are used; strict avalanche criterion (SAC), propagation criterion; algebraic degree; the value of the autocorrelation function. In this article, a study was made of the nonlinearity and strict avalanche criterion (SAC) of the S-box used in the block symmetric encryption algorithm. The results of the study were compared with the S-boxes of modern cryptographic algorithms and showed good results.

A Novel Construction of Substitution Box Based on Polynomial Mapped and Finite Field With Image Encryption Application

In the modern block cipher, the substitution box (S-box) is a nonlinear constituent that plays a substantial role to create the confusion in ciphertext. S-boxes with low value of differential uniformity and high value of nonlinearity are considered more secure against cryptanalysis attacks. For the construction of 8×8 S-boxes, an efficient and novel scheme is presented in this paper. This scheme based on polynomial mapped and finite field which work only for even integers without multiple of 4 in the range (2-254). Firstly, we take a quadratic polynomial mapped for the construction of S-box from the newly designed map. To keep the S-box bijective, swap each missing entries with repeating entries after that we acquire the initial box. Secondly, to increase the randomness of initial S-box special permutations of symmetric group S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">256</sub> used and generated the proposed S-box. Lastly, to examine the validity of the suggested S-box we used various tests such as nonlinearity (NL), bit independence criteria (BIC), strict avalanche criteria (SAC), differential uniformity (DU) and linear approximation probability (LAP) which all certify algebraic properties of S-box. Moreover, the features of newly constructed S-box compared with recent S-boxes from literature which show superior performance against intruders’ attacks. Further, S-box is utilized in image encryption scheme and apply MLC (majority logic criterion) and histogram analysis to examined the encryption quality. Our results shows that proposed S-box based encryption scheme is very good as compared to other encryption methods.

On the impossibility of an invariant attack on Kuznyechik

Currently numerous cryptographic systems are based on SP-networks. These primitives are supposed to be secure but recent investigations show that some attacks are possible. The aim of this work is to study how secure the Russian standardized block cipher Kuznyechik over invariant attacks. We study the already known decompositions of its permutation and show the ways of constructing invariant subsets. A new approach to invariant attacks is presented and it proves that there are no subsets based on S-Box properties that are invariant under round functions of Kuznyechik.

О криптографических свойствах S-блоков

The article is devoted to the study of cryptographic properties of S-boxes. S-box is a function that accepts n bits at the input, converts them according to a certain algorithm and returns m bits at the output. n and m are not necessarily equal. S-boxes are one of the main components of modern cryptographic algorithms that determine their nonlinearity. To protect cryptographic algorithms from various types of attacks, S-boxes must meet a number of criteria. The purpose of this work is to study the existing cryptographic properties of S-boxes, which will allow us to further analyze the existing criteria that S-boxes must meet and make a reasonable choice of a set of criteria for optimal S-boxes. This article provides an overview of the main properties of S-boxes that are important in the formation of optimality criteria. Differential uniformity, difference distribution table, nonlinearity, linear distribution table, algebraic degree, algebraic immunity, algebraic complexity, avalanche effect, strict avalanche effect, distance to strictly avalanche effect, completeness, linear structures, balancedness, correlation immunity, bit independence criterion, propagation criterion, period, number of fixed points and opposite fixed points, cycles, inversions, increases, boomerang connection table, boomerang difference table are considered. The existing methods of generating S-boxes with the necessary optimal characteristics are also considered.

Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps

Chaotic maps play a vital role in the development of cryptographic techniques being used in today’s world. Efficient and highly secure algorithms can be constructed based on chaotic maps. Chaotic maps have the intrinsic property of being highly sensitive to initial conditions. In this paper, we have presented a novel scheme for construction and optimization of substitution boxes (S-boxes) based on mixed two dimensional (2D) chaotic maps in which cryptographic properties of S-boxes are optimized based on initial conditions of their parent 2D chaotic map. The proposed scheme and the resulting substitution boxes are analyzed with existing cryptanalysis techniques and their results have been compared with some other algorithms available in literature. The proposed scheme has been found to be more efficacious than other algorithms. The outcomes of security analysis indicate that our proposed technique and resulting optimized non-linear component in the current era of information technology.

Cryptographic Strength Evaluation of AES S-box Variants

In recent years, researchers have constructed AES s-box variants by customising the values of the parameters in the equation of AES s-box. Strength of these s-box variants is evaluated against the cryptographic properties like avalanche effect, nonlinearity and bit independence criteria, however, there are other important cryptographic properties of s-box, which need to be evaluated before adopting the s-box. In this paper, all types of AES s-box variants are reproduced and evaluated against ten cryptographic properties. The results of five properties, differential and linear probability, nonlinearity, balance and algebraic degree remains the same for any s-box variant due to isomorphic equivalence nature of the variants; whereas, strict avalanche effect, bit independence criteria, correlation immunity, cyclic and fix-point properties showed different results for different s-box variant. Finally, the results are compared with the standard AES s-box and conclusion of overall security of s-box variants with respect to selected properties is conferred.

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.

Cellular automata based S-boxes

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.

Impact of 16-Primitive Irreducible Polynomials Over Erection of High Performance S-Boxes Emanate from Linear Fractional Transformation

As a consequence of fast and most recent enhancements in the sphere of IT, information can be transferred on an enormous distance in a very diminutive time. On the other hand safekeeping of sensitive unclassified information becomes more significant in certain circumstances and for these persistence different Cryptographic strategies exists to protect efficiently the concealment of statistics. In this article, we envisioned an effective methodology developed from linear fractional transformation for the composition of nonlinear constituent recognized as S-box and additionally upshot of application of 16 diverse Primitive Irreducible Polynomials (PIPs) are inspected to increase its performance. Moreover, to inspect the performance of S-box against linear and differential attacks we operated illustrious properties of S-box like linear and differential approximation probabilities. To examine the encryption abilities of S-boxes well-known tests of strict avalanche criterion, nonlinearity and bits independence criterion are also applied.

Analysis of Development of Dynamic S-Box Generation

Advanced Encryption Standard is a symmetric block cipher which is widely used in encrypting data by different organizations to make secure their data from being hacked. The only nonlinear part of Advanced Encryption Standard (AES) is S-Box (Substitution Box), which provides confusion in the algorithm. But the main limitation of the S-Box in AES is that it is a static one throughout the algorithm, which is the main center of attraction for the cryptanalyst to analysis the weakness for certain attacks. Since 2000 onwards a number of algebraic attacks on AES have been carried out, which challenged the security of AES. But at the same time till date a number of researches have being carried out for making AES more secure by using dynamic S-Boxes to provide more confusion to the cryptanalyst. In present paper we tried to address dynamic S-Box techniques and provide their analysis on the basis of S-Box properties, which are essential for secure S-Box construction like Non-linearity, XOR profile, Strict Avalanche criterion (SAC) and Bit independence criteria (BIC). Also these techniques are compared with the original AES results.

A Random PRESENT Encryption Algorithm Based on Dynamic S-box

S-box mainly plays the role of confusion in the encryption process as an important component. For the new encryption algorithm PRESENT proposed in 2007, S-box impacts on the security of the encryption algorithm directly. This paper briefly describes the process of PRESENT algorithm and proposes an improved S-box to solve the problem that the original PRESENT S-box has anti-fixed point. Then a random PRESENT encryption algorithm based on dynamic S-box is proposed. The dynamic multiple S-boxes technology is used to implement random PRESENT algorithm, to enhance the security of the cryptographic algorithm. Finally, the security analysis is done, and it suggests that dynamic S-box has a superior ability to resist differential attack and linear attack. By comparison to the diffusion rate of original PRESENT S-box, our dynamic S-box has better avalanche effect. With the rapid development of the Internet of Things, the radio frequency identification (RFID), wireless sensor network (WSN), and other new technologies go deep into all aspects of people's work and life. However, RFID and WSN are based on wireless network to transfer information. The transmission of information is not difficult to be obtained, interfered, and even destroyed by the attackers. So information security technology is widely used in protecting networks to enhance the safety of secret information. And the traditional symmetric encryption algorithm is often restricted by hardware, which cannot achieve good effects under the condition of limited hardware and power consumption. Therefore, lightweight cipher algorithm such as PRESENT(1) and LED(2) has gradually become the realistic choice to ensure the information security of Internet of Things. The lightweight block encryption algorithm PRESENT (1), put forward by Bogdanov in 2007, is carefully designed with area and power constraints uppermost in limited conditions. So the PRESENT algorithm still has high security in the application of limited space and power consumption, such as sensor network node. However, the permutation transformation of PRESENT algorithm is different with the column confusion of AES. It uses bit as the permutation function input unit while AES uses byte for permutation. The permutation layer of PRESENT encryption algorithm is a perfectly symmetrical structure and easy implemented. Because the structure of this kind of design has poor diffusibility, the PRESENT algorithm diffusively quality mainly depends on the diffusion properties of S-box. So S-box, as a nonlinear component in lightweight block encryption algorithm, affects the strength of the whole structure of the cipher. To strengthen DES by using existing hardware, an improved method of DES which uses the S-box related to a key is put forward in paper (4), and the researcher has demonstrated the safety of the improved method. Meanwhile, a new key related

AES S-Box Construction using One Dimensional Cellular Automata Rules

S-Box is the only non-linear component in Advanced Encryption Standard(AES) which determine its strength. The Look-Up Table based S-Box of conventional AES occupies large storage space, reduced throughput and consumes more power. This article presents the design of an S-Box based on Reversible Cellular Automata function that reduces the implementation cost. Further, Cellular Automata functions are derived from various rules that are non-linear and S-Box properties are discussed briefly in this paper. With this approach, the time consumption for the AES S-Box is considerably decreased without compromising the nonlinearity of conventional S-Box.

On algebraic properties of S-boxes designed by means of disjoint linear codes

In a recent paper [W. Zhang and E. Pasalic, Constructions of resilient S-Boxes with strictly almost optimal nonlinearity through disjoint linear codes, IEEE Trans Inf Theory 60, no. 3 (2014), pp. 1638–1651], by using disjoint linear codes, Zhang and Pasalic presented a method for constructing t-resilient S-boxes ( even, with strictly almost optimal (currently best) nonlinearity exceeding the value . It was also shown that the algebraic degree and algebraic immunity of these resilient S-boxes are very good, but the resistance of these resilient S-boxes against fast algebraic attacks has not been treated in [W. Zhang and E. Pasalic,Constructions of resilient S-Boxes with strictly almost optimal nonlinearity through disjoint linear codes, IEEE Trans. Inf. Theory 60, no. 3 (2014), pp. 1638–1651]. In this work, we extend the method originally proposed in [E. Pasalic,Maiorana-McFarland class: Degree optimization and algebraic properties, IEEE Trans. Inf. Theory 52, no. 10 (2006), pp. 4581–4595] and used in deriving the upper bound on algebraic immunity of the Maiorana–McFarland class, for establishing the existence of low degree multiplier for the class of S-boxes that uses disjoint linear codes in the design. It is demonstrated that this class of functions has a substantial weakness against fast algebraic cryptanalysis. An alternative approach, based on the use of the associated dual codes is also developed.

On cross-correlation properties of S-boxes and their design using semi-bent functions

In this paper, several methods for constructing substitution boxes S-boxes with good cross-correlation properties are proposed. We firstly analyze the cross-correlation properties of bent functions and derive a sufficient condition that the absolute indicator Δf,g of two bent functions f and g achieve its lowest possible value 2ni¾?2. More precisely, it is sufficient that f+g is also a bent function, which then implies that the absolute indicator of vectorial bent functions equals to 2ni¾?2. This indicates an erroneous conclusion in by Zhou et al., claiming that if f is bent, then Δf,g=2ni¾?2 if and only if g is an affine function, which is not true. Furthermore, because of a strong relationship between the cross-correlation properties and disjoint spectra semi-bent functions, two classes of highly nonlinear vectorial semi-bent functions with very good cross-correlation properties are proposed. In particular, the first class of vectorial semi-bent functions introduced here compares favorably to other methods in terms of the cross-correlation properties of its component functions. In addition, A sufficient condition that the absolute indicator of two bent functions achieves its lowest value is derived.A construction of S-boxes with good auto-correlation properties from vectorial bent functions is given.Two classes of nonlinear vectorial semi-bent functions with good auto-correlation properties are proposed.Copyright © 2014 John Wiley & Sons, Ltd.

The Algebra Properties of the S-Boxes of Several Block Ciphers

S-boxes bring nonlinearity to block ciphers and strengthen their cryptographic security. A detailed analysis of the cryptographic properties of S-boxes of several block ciphers, such as SMS4, AES, Camellia and SEED, are made in this paper. Some algebraic properties of boolean function of S-boxes such as balanceness, non-linearity, algebraic degree and walsh spectrums are well investigated. We reveal the advantages and disadvantages of those S-boxes used in SMS4, AES, Camellia and SEED as compared with each other.

New Analysis Methods on Strict Avalanche Criterion of S-Boxes

S-boxes (Substitution boxes) are keystones of modern symmetric cryptosystems (block ciphers, as well as stream ciphers). S-boxes bring nonlinearity to cryptosystems and strengthen their cryptographic security. They are used for confusion in data security An S-box satisfies the strict avalanche criterion (SAC), if and only if for any single input bit of the S-box, the inversion of it changes each output bit with probability one half. If a function (cryptographic transformation) is complete, then each output bit depends on all of the input bits. Thus, if it were possible to find the simplest Boolean expression for each output bit in terms of the input bits, each of these expressions would have to contain all of the input bits if the function is complete. From some important properties of S-box, the most interesting property SAC (Strict Avalanche Criterion) is presented and to analyze this property three analysis methods are proposed. Keywords— S-boxes, cryptosystems, strict avalanche criterion, function, analysis methods.

Relating Differential Distribution Tables to Other Propertiesof of Substitution Boxes

Due to the success of differential and linear attacks on a large number of encryption algorithms, it is important to investigate relationships among various cryptographic, including differential and linear, characteristics of an S-box (substitution box). After discussing a precise relationship among three tables, namely the difference, auto-correlation and correlation immunity distribution tables, of an S-box, we develop a number of results on various properties of S-boxes. More specifically, we show (1) close connections among three indicators of S-boxes, (2) a tight lower bound on the sum of elements in the leftmost column of its differential distribution table, (3) a non-trivial and tight lower bound on the differential uniformity of an S-box, and (4) two upper bounds on the nonlinearity of S-boxes (one for a general, not necessarily regular, S-box and the other for a regular S-box).

CRYPTANALYSIS OF SUBSTITUTION-PERMUTATION NETWORKS USING KEY-DEPENDENT DEGENERACY

This paper presents a novel cryptanalysis of Substitution-Permutation Networks using a chosen plaintext approach. The attack is based on the highly probable occurrence of key-dependent degeneracies within the network and is applicable regardless of the method of S-box keying. It is shown that a large number of rounds is required before a network is resistant to the attack. Experimental results have found 64-bit networks to be cryptanalyzable for as many as 8 to 12 rounds depending on the S-box properties.