Design of substitution nodes (S-Boxes) of a block cipher intended for preliminary encryption of confidential information

Khompysh, Ardabek; Kapalova, Nursulu; Algazy, Kunbolat; Dyusenbayev, Dilmukhanbet; Sakan, Kairat

doi:10.1080/23311916.2022.2080623

Cited by 8 publications

(9 citation statements)

References 12 publications

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“…Let's consider a way to obtain an S-box consisting of three steps. At the first, an irreducible polynomial is chosen that step generates a multiplicative group in the Galois field GF(2 8 ) and an irreducible polynomial is called a base [14]. The selected polynomial is exponentiated modulo P(x):…”

Section: Methods For Obtaining the S-boxmentioning

confidence: 99%

“…According to [14], the degree of nonlinearity of Boolean functions NL(f) is defined as the minimum Hamming distance between the i-th Boolean function and linear functions. Degree of non-linearity NL(f) is determined using the W.Hadamard transform.…”

Section: Nonlinearitymentioning

confidence: 99%

“…In this regard, a comprehensive study of the S-box, which is one of the transformations of this algorithm, is considered one of the most important tasks. The method for obtaining the S-box used in the AL03 encryption algorithm is described in [14].…”

Section: Introductionmentioning

confidence: 99%

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Study of the Cryptographic Strength of the S-Box Obtained on the Basis of Exponentiation Modulo

Khompysh

Kapalova

Algazy

et al. 2022

sjaitu

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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.

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Section: Methods For Obtaining the S-boxmentioning

confidence: 99%

Section: Nonlinearitymentioning

confidence: 99%

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Study of the Cryptographic Strength of the S-Box Obtained on the Basis of Exponentiation Modulo

Khompysh

Kapalova

Algazy

et al. 2022

sjaitu

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“…The robustness of the cipher is directly related to the level of confusion introduced in the ciphertext, emphasizing the importance of this technique in guaranteeing robust data security (Chen et al, 2022) (Mahboob et al, 2022). The cryptographic robustness of the Scryptographic box itself determines the efficacy of a block cipher employing an Sbox (Khompysh, Kapalova, Algazy, Dyusenbayev, & Sakan, 2022). Extensive study has been conducted to generate high-quality S-boxes and evaluate their strength against known criteria such as nonlinearity, bijection, SAC (Khompysh et al, 2022), BIC, linear and differential probability(Y.…”

Section: Introductionmentioning

confidence: 99%

“…The cryptographic robustness of the Scryptographic box itself determines the efficacy of a block cipher employing an Sbox (Khompysh, Kapalova, Algazy, Dyusenbayev, & Sakan, 2022). Extensive study has been conducted to generate high-quality S-boxes and evaluate their strength against known criteria such as nonlinearity, bijection, SAC (Khompysh et al, 2022), BIC, linear and differential probability(Y. Zheng et al, 2023).…”

Section: Introductionmentioning

confidence: 99%

An innovative design of substitution-box using Trigonometric-Multiplicative Functions Using Square Root Arguments: A Data-driven study.

Shirazi,

Shah,

Wahab

et al. 2024

ABBDM

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In the evolving landscape of digital technology, the imperative for robust data security mechanisms has escalated, given the increasing sophistication of cyber threats. This abstract delineates a study focused on enhancing cryptographic defenses through the innovation of a Substitution box (S-Box), which is pivotal in the architecture of modern encryption algorithms. The proposed S-Box, deriving its foundation from chaotic maps integrated with trigonometric-multiplicative functions, represents a novel approach in cryptographic design, utilizing square root arguments to instigate dynamic characteristics. The evaluation of the proposed S-Box was methodically conducted using a comprehensive set of cryptographic benchmarks including Nonlinearity (NL), Strict Avalanche Criterion (SAC), Bit Independence Criterion (BIC), Linear Approximation Probability (LP), and Differential Approximation Probability (DP), to ascertain its defensive robustness against cryptanalytic attacks. The comparative analysis delineated in this study reveals that the cryptographic strength of the proposed S-Box transcends that of other contemporaneously designed S-Boxes thereby underscoring its potential applicability in real-world security scenarios. The findings of this research not only contribute to the theoretical underpinnings of cryptographic security but also have practical implications in the development of more secure digital environments fortifying data against unauthorized access and ensuring the integrity of confidential information in digital communications.

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Möbius Transformation and Permutation Based S-Box to Enhance IoT Multimedia Security

Aribilola,

Lee,

Naveed Asghar

2024

IEEE Access

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Design of substitution nodes (S-Boxes) of a block cipher intended for preliminary encryption of confidential information

Cited by 8 publications

References 12 publications

Study of the Cryptographic Strength of the S-Box Obtained on the Basis of Exponentiation Modulo

Study of the Cryptographic Strength of the S-Box Obtained on the Basis of Exponentiation Modulo

An innovative design of substitution-box using Trigonometric-Multiplicative Functions Using Square Root Arguments: A Data-driven study.

Möbius Transformation and Permutation Based S-Box to Enhance IoT Multimedia Security

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