Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes

Isa, Herman; Aljunid, Syed Alwee; Z’aba, Muhammad Reza; Endut, R.; Ammar, Syed Mohammad; Ali, Noraziah

doi:10.3390/math11020446

Cited by 9 publications

(5 citation statements)

References 64 publications

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“…The article [14] focuses only on the differential properties of S-boxes, which is clearly not enough. Articles [15] and [16] also offer quite complex and time-consuming algorithms for generating S-boxes.…”

Section: Review Of the Literaturementioning

confidence: 99%

The influence of S-boxes on the arrival of the cipher to the state of random substitution

Lysytska,

Lysytskyi,

Nariezhnii

et al. 2023

reks

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The subject of this study is the process of developing block symmetric ciphers with improved cryptographic stability indicators for solving the problems of information protection in information and communication systems. The goal of this study is to develop a mathematical model of the optimal s-box design (non-linear substitution block) for modern block symmetric ciphers. Task: to show that the stability of block symmetric ciphers does not significantly depend on the indicators of the s-boxes included in these ciphers; to justify their use without reducing the stability of random substitutions as s-box constructions of modern block symmetric ciphers; and to prove the futility of searching for s-boxes with special properties. The methods used are: methods of probability theory; mathematical statistics; combinatorics and system analysis; methods of statistical tests; and methods of Boolean algebra. The following results were obtained. In modern ciphers, nonlinear substitution transformations are used as S-boxes (in most ciphers, byte substitutions are used). S-boxes perform the main function of encryption transformation - mixing of text bits. Dynamic indicators of the arrival of the cipher in the state of random substitution depend on their effectiveness. The presented results confirm that the indicators of cipher stability do not significantly depend on the indicators of the S-boxes included in the ciphers. It is not the individual properties of substitutions, but the results of their sequential interactions decisive for achieving stability indicators. It is shown that the fee for encryption is chosen to be three to four times greater than the depth of the avalanche effect - the minimum number of cycles of the cipher’s arrival to the state of random substitution) is hardly noticeable. Conclusions. The scientific novelty of the obtained results is as follows. This work represents a generalization of the transition to the use of random permutations as S-boxes is an increase of only one cycle in the number of cycles of the arrival of the cipher to the state of random permutations, and this is hardly noticeable against the background of the stability margin used in modern ciphers. The result of this generalization is a scientific statement that can be described as follows: random S-boxes can be used in all known modern ciphers without reducing stability. That is, the task of finding S-boxes with special properties loses any meaning, which means that the scientific direction related to the search for S-boxes with special properties becomes redundant.

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Section: Review Of the Literaturementioning

confidence: 99%

The influence of S-boxes on the arrival of the cipher to the state of random substitution

Lysytska,

Lysytskyi,

Nariezhnii

et al. 2023

reks

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“…A. ), the authors [46] created a series of mathematical functions. This approach prevented random production of S-Box and its attributes such as BIC and DP were 106.32 and 0.015625, while NL, SAC, and LP were 108, 0.5001, and 0.1545 respectively.…”

Section: Introductionmentioning

confidence: 99%

Innovative Transformation of S-Box Through Chaotic Map Using a Pragmatic Approach

Qazi,

Zahid,

Baz

et al. 2024

IEEE Access

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In present-day data communication, the imperative to safeguard information and shield it from a multitude of potential threats and attacks has gained significant prominence. One of the pivotal tools employed in the pursuit of data protection is the design of robust substitution boxes (S-Boxes). These S-Boxes often find their roots in the realm of chaotic maps, leveraging the inherent unpredictability and complexity of these mathematical constructs. An S-Box is an integral and critical component in the design of modern ciphers offering a means to enhance the security of data by introducing non-linearity and confusion into the encryption process. In this research endeavor, we propose the development of a novel chaotic map to create an S-Box that exhibits a notably high nonlinear score making it more formidable for potential adversaries to decrypt the ciphertext. To substantiate the efficacy of the proposed S-Box, a comprehensive analysis is done by comparing its performance using standard criteria including nonlinearity (NL), strict avalanche criterion (SAC), bit independence criterion (BIC), presence of fixed points (FP), linear probability (LP), differential probability (DP), etc. to other state-of-the-art S-Boxes. The comparative analysis reinforces the security fortitude of the proposed S-Box in meeting the rigorous demands of modern data security and presents a vital contribution to the ever-evolving field of cryptographic techniques and data protection in the digital age.

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“…More than 100 sbox generation algorithms have been proposed using many approaches from the past to the present. Among these approaches, the most; mathematical transformations [3][4][5][6][7][8], chaotic systems [9][10][11][12][13][14] and optimization techniques [15][16][17][18][19][20][21][22] are used. In addition, hybrid approaches have been developed [23][24][25] by combining DNA coding, cellular automata, and the benefits of existing approaches.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Nonlinearity Value of Substitution Box Generation Approaches

Artuğer

Karakuş

Özkaynak

2023

ICRAS

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Substitution box (s-box) is one of the important structures that perform the mixing process for encryption algorithms. Therefore, strong s-box structures are needed to develop effective encryption algorithms. The most important feature of the S-box is that it has a nonlinear structure. In this way, it can effectively scramble the data to be encrypted. More than a hundred new algorithms have been proposed using many approaches to obtain s-box structures with high nonlinearity. In this study, the performances of the s-box generation approaches in recent years were compared according to their non-linearity values. In addition, the advantages and disadvantages of these approaches have been discussed and suggestions have been made especially for researchers who will just start in this field.

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Enhancement of Non-Permutation Binomial Power Functions to Construct Cryptographically Strong S-Boxes

Cited by 9 publications

References 64 publications

The influence of S-boxes on the arrival of the cipher to the state of random substitution

The influence of S-boxes on the arrival of the cipher to the state of random substitution

Innovative Transformation of S-Box Through Chaotic Map Using a Pragmatic Approach

Comparison of Nonlinearity Value of Substitution Box Generation Approaches

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