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

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

Block cipher has been a standout amongst the most reliable option by which data security is accomplished. Block cipher strength against various attacks relies on substitution boxes. In literature, extensively algebraic structures, and chaotic systems-based techniques are available to design the cryptographic substitution boxes. Although, algebraic and chaotic systems-based approaches have favorable characteristics for the design of substitution boxes, but on the other side researchers have also pointed weaknesses in these approaches. First-time multilevel information fusion is introduced to construct the substitution boxes, having four layers; Multi Sources, Multi Features, Nonlinear Multi Features Whitening and Substitution Boxes Construction. Our proposed design does not hold the weakness of algebraic structures and chaotic systems because our novel s-box construction relies on the strength of true random numbers. In our proposed method true random numbers are generated from the inevitable random noise of medical imaging. The proposed design passes all the substitution box security evaluation criteria including Nonlinearity, Bit Independence Criterion (BIC), Strict Avalanche Criterion (SAC), Differential Approximation Probability (DP), Linear Approximation Probability (LP), and statistical tests, including resistance to Differential Attack, Correlation Analysis, 2D, 3D histogram analysis. The outcomes of the evaluation criteria validate that the proposed substitution boxes are effective for block ciphers; furthermore, the proposed substitution boxes attain better cryptographic strength as compared to very recent state-of-the-art techniques.

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

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

Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers. Since constructing non-linear components through algebraic structures is crucial for the confusion aspects of encryption schemes, relying solely on these structures can result in limited key spaces. To address this issue, a complex non-chain ring with combination of Henon map based algorithm is presented. This proposed work aims to enhance both security and key space by utilizing complex algebraic structures. In this study, we investigate the use of unit elements from non-chain rings, establishing a mapping from the group of units to Galois fields to enhance the algebraic robustness of the scheme. A substitution box is constructed from Galois field and is applied in image processing. For pixel mixing, the Henon map is employed, and the exclusive OR operation is performed using a key generated from image pixels and the substitution box. The algorithm’s performance is evaluated using standard parameters such as histograms, Structural Similarity Index Measure (SSIM), correlation analysis, and National Institute of Standards and Technology (NIST) tests. For S-box analysis, we apply the strict avalanche criterion (SAC), bit independence criterion (BIC), linear approximation probability (LAP), and differential approximation probability (DAP). This algebraic approach utilizes a robust and state-of-the-art image encryption system that is highly effective against potential attackers.

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

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.

The strict avalanche criterion (SAC) was introduced by Webster and Tavares [10] in a study of cryptographic design criteria. This is an indicator for local property. In order to improve the global analysis of cryptographically strong functions, Zhang and Zheng [11] introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as σfe∑vΔf2(v), where Δf(v)e∑x (−1)f(x)⊕f(x}⊕ v). In this paper, we give a few methods to construct Boolean functions controlling five good cryptographic properties, namely balancedness, good local and GAC, high nonlinearity and high algebraic degree. We improve upon the results of Stanica [8] and Zhang and Zheng [11].

A new S-box construction method meeting strict avalanche criterion

A substitution box is used to induce nonlinearity in plaintext for encryption systems. Recently, the application of chaotic maps to encryption applications has resulted in some interesting nonlinear transformations. In this paper, we propose an efficient method to design nonlinear components for block ciphers that are based on TD-ERCS chaotic sequence. The new substitution box is analyzed for nonlinearity, bit independence, strict avalanche criterion, generalized majority logic criterion, and differential and linear approximation probabilities. The results show high resistance to differential and linear cryptanalysis in comparison to some recently proposed chaotic substitution boxes.

Over binary filed F2 there are 16 primitive irreducible polynomials of degree 8, and hence one can construct 16 Galois field extensions of order 256. In this paper, we provide a novel technique to design 16 different robust 8 × 8 substitution boxes (S-boxes) over the elements these 16 Galois fields. For the purpose, on these Galois fields we define 16 linear fractional transformations as: z ⟼ (az + b)/(cz + d), where z is any arbitrary element in any of Galois fields and a, b, c, d are fixed elements from any Galois field GF(28). Accordingly for fixed parameters a, b, c, d, we obtained 16 distinct S-boxes. The algebraic strength of the proposed S-boxes is analyzed by Nonlinearity test, Strict Avalanche Criterion (SAC), Linear Approximation Probability (LP), Bit Independent Criterion (BIC), and Differential Approximation Probability (DP). As an application, by the majority logic criterion (MLC), entropy, correlation, contrast, energy and homogeneity of a plain image and its encrypted image through newly proposed S-box are assessed. Further, to fix the rank of proposed S-boxes, a comparison of these analyses is given with AES S-box, APA S-box, Residue Prime S-box, Gray S-box, Xyi S-box, Skipjack S-box and S8 AES S-box.

Cryptography deals with designing practical mathematical algorithms having the two primitive elements of confusion and diffusion. The security of encrypted data is highly dependent on these two primitive elements and a key. S-box is the nonlinear component present in a symmetric encryption algorithm that provides confusion. A cryptographically strong bijective S-box structure in cryptosystem ensures near-optimal resistance against cryptanalytic attacks. It provides uncertainty and nonlinearity that ensures high confidentiality and security against cryptanalysis attacks. The nonlinearity of an S-box is highly dependent on the dispersal of input data using an S-box. Cryptographic performance criteria of chaos-based S-boxes are worse than algebraic S-box design methods, especially differential probability. This article reports a novel approach to design an 8 × 8 S-box using chaos and randomization using dispersion property to S-box cryptographic properties, especially differential probability. The randomization using dispersion property is introduced within the design loop to achieve low differential uniformity possibly. Two steps are involved in generating the proposed S-box. In the first step, a piecewise linear chaotic map (PWLCM) is utilized to generate initial S-box positions. Generally, the dispersion property is a post-processing technique that measures maximum nonlinearity in a given random sequence. However, in the second step, the concept is carefully reverse engineered, and the dispersion property is used within the design loop for systematic dispersal of input substituting sequence. The proposed controlled randomization changes the probability distribution statistics of S-box’s differentials. The proposed methodology systematically substitutes the S-box positions that cause output differences to recur for a given input difference. The proposed S-box is analyzed using well-established and well-known statistical cryptographic criteria of nonlinearity, strict avalanche criteria (SAC), bit independence criteria (BIC), differential probability, and linear probability. Further, the S-box’s boomerang connectivity table (BCT) is generated to analyze its strength against boomerang attack. Boomerang is a relatively new attacking framework for cryptosystem. The proposed S-box is compared with the state-of-the-art latest related publications. Results show that the proposed S-box achieves an upper bound of cryptographic properties, especially differential probability. This work hypothesizes that highly dispersive hamming distances at output difference, generated a systematic S-box. The mixing property of chaos generated trajectories utilized for decimal mapping. To test the randomness of generated chaotic trajectories, a cryptographically secure pseudo-random sequence was generated using a chaotic map that was tested using the National Institute of Standards and Technology (NIST) NIST-800-22 test suit.

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

Substitution boxes with resilient cryptographic possessions are normally utilized in block ciphers to give the substantial property of nonlinearity. They are important to resist standard attacks such as linear and differential cryptanalysis. A cryptographically robust S-box must be sound with respect to cryptographic properties like nonlinearity, bit independent criteria, strict avalanche criteria, linear and differential approximation probability. In this paper, we have developed an innovative construction scheme of nonlinear component of block cipher based on the action of projective linear groups on the projective line, and the permutation triangle groups. This nonlinear component, namely S-box, is responsible for making the relation between plaintext and ciphertext intractable which is one of the most important requirements of any modern block ciphers. By widening the scope of the proposed S-boxes, we have applied these lightweight nonlinear components in watermarking scheme.

The theory of chaos is applied to the construction of substitution boxes used in encryption applications. The synthesis process of the proposed substitution boxes is presented, which is based on chaotic Baker’s map and TDERC chaotic sequences. The objectives of the new substitution box are to provide enhanced resistance against differential and linear cryptanalysis. The constructed substitution boxes uses Galois field elements and relies on discrete chaotic maps while keeping differential and linear approximation probabilities to desired levels.