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Highly dispersive S‐boxes are desirable in cryptosystems as nonlinear confusion sub‐layers for resisting modern attacks. For a near optimal cryptosystem resistant to modern cryptanalysis, a highly nonlinear and low differential probability (DP) value is required. We propose a method based on a piecewise linear chaotic map (PWLCM) with optimization conditions. Thus, the linear propagation of information in a cryptosystem appearing as a high DP during differential cryptanalysis of an S‐box is minimized. While mapping from the chaotic trajectory to integer domain, a randomness test is performed that justifies the nonlinear behavior of the highly dispersive and nonlinear chaotic S‐box. The proposed scheme is vetted using well‐established cryptographic performance criteria. The proposed S‐box meets the cryptographic performance criteria and further minimizes the differential propagation justified by the low DP value. The suitability of the proposed S‐box is also tested using an image encryption algorithm. Results show that the proposed S‐box as a confusion component entails a high level of security and improves resistance against all known attacks.

In 2020 E. Sakalauskas with coauthors published a paper defining perfectly secure Shannon cipher based on matrix power function, proposing effective parallelization, and ensuring no need for multiple rounds encrypting one data block [1]. In this paper we present computational results with the avalanche effect and bit independence criterion (BIC). These criteria are important when describing the rate of confusion of bits in the ciphertext. It was observed that increasing matrix order and group size enhance BIC and avalanche effect results converging to the desired values. Based on the outputs it is possible to pick appropriate parameters satisfying security needs and available memory in a device where appropriate keys are going to be stored. [ABSTRACT FROM AUTHOR]

Substitution box is a significant and only nonlinear constituent of block cipher. S-box plays a central role in converting the intelligible message or plain text, into an enciphered format. Construction of strong S-boxes is an important area of interest for security experts. In this work, we develop a new method to evolve S-boxes with the help of coset graph for the action of P S L 2 , Z on projective line over the finite field GF (28), a special type of bijective map g and the symmetric group S256 The capability of the proposed S-boxes to mitigate cryptanalysis is investigated through various performance analyzing parameters. The outcomes of the comparison with the familiar S-boxes indicate that the working abilities of newly designed S-boxes are better than that of many of the well-known S-boxes. [ABSTRACT FROM AUTHOR]

The bit independence criterion was proposed to evaluate the security of the S-boxes used in block ciphers. This paper proposes an algorithm that extends this criterion to evaluate the degree of independence between the bits of inputs and outputs of the stream ciphers. The effectiveness of the algorithm is experimentally confirmed in two scenarios: random outputs independent of the input, in which it does not detect dependence, and in the RC4 ciphers, where it detects significant dependencies related to some known weaknesses. The complexity of the algorithm is estimated based on the number of inputs l, and the dimensions, n and m, of the inputs and outputs, respectively. [ABSTRACT FROM AUTHOR]

Highly dispersive S‐boxes are desirable in cryptosystems as nonlinear confusion sub‐layers for resisting modern attacks. For a near optimal cryptosystem resistant to modern cryptanalysis, a highly nonlinear and low differential probability (DP) value is required. We propose a method based on a piecewise linear chaotic map (PWLCM) with optimization conditions. Thus, the linear propagation of information in a cryptosystem appearing as a high DP during differential cryptanalysis of an S‐box is minimized. While mapping from the chaotic trajectory to integer domain, a randomness test is performed that justifies the nonlinear behavior of the highly dispersive and nonlinear chaotic S‐box. The proposed scheme is vetted using well‐established cryptographic performance criteria. The proposed S‐box meets the cryptographic performance criteria and further minimizes the differential propagation justified by the low DP value. The suitability of the proposed S‐box is also tested using an image encryption algorithm. Results show that the proposed S‐box as a confusion component entails a high level of security and improves resistance against all known attacks. [ABSTRACT FROM AUTHOR]

Substitution box is a basic nonlinear component in data encryption. It converts the plain text into an enciphered format. The formation of cryptographically secure S-boxes is the most important task for cryptographers to ensure the security of the system. In this paper, we have introduced a novel method to increase the working capability of an S-box without demolishing its basic mathematical structure, that is, Eigen values, characteristic polynomial and determinant of the S-box/ 16 × 16 matrix. We considered Skipjack, Xyi, Prime, Jakimoski, Tang and Iqtadar S-boxes and reshuffled their rows/columns in such a way that they become cryptographically stronger. Algebraically, this can be accomplished by using appropriate permutations of the symmetric group S 16 over rows/columns of the S-boxes. The proposed technique is very constructive in enhancing the performance of S-boxes based on fundamental idea; bijection over the same set. The outcomes of different analyses demonstrated that the improved versions of S-boxes are more reliable than the original ones. [ABSTRACT FROM AUTHOR]

The bit independence criterion was proposed to evaluate the security of the S-boxes used in block ciphers. This paper proposes an algorithm that extends this criterion to evaluate the degree of independence between the bits of inputs and outputs of the stream ciphers. The effectiveness of the algorithm is experimentally confirmed in two scenarios: random outputs independent of the input, in which it does not detect dependence, and in the RC4 ciphers, where it detects significant dependencies related to some known weaknesses. The complexity of the algorithm is estimated based on the number of inputs l, and the dimensions, n and m, of the inputs and outputs, respectively.

In the modern era of secure communication, it is important to create uncertainty in the original data in order to avoid unauthorized entities to extract or manipulate information. From simple methods such as permutations of original data to different mapping algorithms, the security of the ciphers rely on the substitution process. There are many types of components proposed in literature that are evolved by different methodologies and ideas. The prevailing ciphers use substitution boxes (S-boxes) to do this transformation process. In this work, we present a literature review of the design, construction, and analysis of the S-boxes used in block ciphers. The performance of S-boxes depends on the design and algebraic structure used for the construction and is contingent upon its ability to resist against cryptanalysis. We present the details of the S-box synthesis process and issues pertaining to creating resistance against various types of attacks, and highlight the consequences of a particular design methodology. In the infancy of the development of modern block ciphers, Shannon (Bell Syst. Tech. J. 28(4):656–715, 1949 ) presented the idea of encryption with the implementation of substitution-permutation network (SPN). In this process, the data is initially transformed by the substation process and then permuted that ends the first round supported by the secret key for this step. This substitution-permutation process is repeated several times to ensure reliability of encrypted data. The objective of using the substitution-permutation network is to create confusion between cipher text and secret key, and add diffusion in the plaintext. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a method for the construction of 8×8 substitution boxes used in the area of cryptography. A symmetric group permutation S8 is applied on Galois field elements that originally belong to GF(28), and as a consequence, 40320 new substitution boxes are synthesized. The Liu J substitution box is used as a seed in the creation process of the new algebraically complex nonlinear components. The core design of this new algorithm relies on the symmetric group permutation operation which is embedded in the algebraic structure of the new substitution box. We study the characteristics of the newly created substitution boxes and highlight the improved performance parameters and their usefulness in practical applications. In particular, we focus on the nonlinear properties and the behavior of input/output bits and determine the suitability of a particular substitution box for a specific type of encryption application. A comparison with some of the prevailing and popular substitution boxes is presented. [Copyright &y& Elsevier]

The encryption process relies on the use of nonlinear mapping subsystems to create confusion in the ciphertext. The design of these nonlinear components is a challenging task and requires complex algebraic expression for their descriptions. In an effort to increase the complexity of nonlinear mappings, several implementations exhibiting interesting properties are proposed in the literature. In particular, affine-power-affine structure is designed for advanced encryption standard, which improves the complexity of its algebraic expression by increasing the number of terms. Based on the characteristics of affine-power-affine structure, we propose a new nonlinear component that uses the symmetric group permutation S on the Galois field GF(2) elements and provides the possibility to incorporate 40320 unique instances. A rigorous analysis is presented to evaluate the properties of these new nonlinear components by applying nonlinearity analysis, linear approximation analysis, differential approximation analysis, bit independence criterion and strict avalanche criterion. In order to determine the suitability to various encryption applications, the S-boxes are tested with generalized majority logic criterion. [ABSTRACT FROM AUTHOR]