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A highly nonlinear S-box based on a fractional linear transformation

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ABSTRACT

We study the structure of an S-box based on a fractional linear transformation applied on the Galois field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GF(2^{8})$$\end{document}GF(28). The algorithm followed is very simple and yields an S-box with a very high ability to create confusion in the data. The cryptographic strength of the new S-box is critically analyzed by studying the properties of S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.

No MeSH data available.


LP of different S-boxes
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Fig2: LP of different S-boxes

Mentions: The linear approximation probability determines the maximum value of imbalance in the event. Let and be the input and output masks respectively and X consists of all possible inputs with cardinality , the linear approximation probability for a given S-box is defined as;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} LP=\underset{\Gamma _{x},\Gamma _{y}\ne 0}{\max }\left/ \frac{ \#\{x/x.\Gamma _{x}=S(x).\Gamma _{y}\}}{2^{n}}-\frac{1}{2}\right/ \end{aligned}$$\end{document}LP=maxΓx,Γy≠0#{x/x.Γx=S(x).Γy}2n-12Table 4 and Fig. 2 show that the linear approximation probability of the newly structured S-box is much better than those for Skipjack, Xyi and Residue prime S-boxes.Fig. 2


A highly nonlinear S-box based on a fractional linear transformation
LP of different S-boxes
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037109&req=5

Fig2: LP of different S-boxes
Mentions: The linear approximation probability determines the maximum value of imbalance in the event. Let and be the input and output masks respectively and X consists of all possible inputs with cardinality , the linear approximation probability for a given S-box is defined as;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} LP=\underset{\Gamma _{x},\Gamma _{y}\ne 0}{\max }\left/ \frac{ \#\{x/x.\Gamma _{x}=S(x).\Gamma _{y}\}}{2^{n}}-\frac{1}{2}\right/ \end{aligned}$$\end{document}LP=maxΓx,Γy≠0#{x/x.Γx=S(x).Γy}2n-12Table 4 and Fig. 2 show that the linear approximation probability of the newly structured S-box is much better than those for Skipjack, Xyi and Residue prime S-boxes.Fig. 2

View Article: PubMed Central - PubMed

ABSTRACT

We study the structure of an S-box based on a fractional linear transformation applied on the Galois field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GF(2^{8})$$\end{document}GF(28). The algorithm followed is very simple and yields an S-box with a very high ability to create confusion in the data. The cryptographic strength of the new S-box is critically analyzed by studying the properties of S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.

No MeSH data available.