A highly nonlinear S-box based on a fractional linear transformation View Article: PubMed Central - PubMed ABSTRACTWe 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. © Copyright Policy - OpenAccess Related In: Results  -  Collection License getmorefigures.php?uid=PMC5037109&req=5 .flowplayer { width: px; height: px; } Fig3: DP of different S-boxes Mentions: The differential approximation probability 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} DP=\left[ \frac{\#\{x\in X/S(x)\oplus S(x\oplus \Delta x)=\Delta y\}}{2^{n}}\right] , \end{aligned}\end{document}DP=#{x∈X/S(x)⊕S(x⊕Δx)=Δy}2n,where and are input and output differentials respectively. In ideal conditions, the S-box shows differential uniformity (Biham and Shamir 1991). The smaller the differential uniformity, the stronger is the S-box. It is evident from the Table 4 and Fig. 3 that the differential approximation probability of the proposed S-box is similar to those of the AES, APA and Gray S-boxes and much better than the Skipjack, Xyi and Residue Prime S-boxes.Fig. 3

A highly nonlinear S-box based on a fractional linear transformation
Related In: Results  -  Collection

Mentions: The differential approximation probability 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} DP=\left[ \frac{\#\{x\in X/S(x)\oplus S(x\oplus \Delta x)=\Delta y\}}{2^{n}}\right] , \end{aligned}\end{document}DP=#{x∈X/S(x)⊕S(x⊕Δx)=Δy}2n,where and are input and output differentials respectively. In ideal conditions, the S-box shows differential uniformity (Biham and Shamir 1991). The smaller the differential uniformity, the stronger is the S-box. It is evident from the Table 4 and Fig. 3 that the differential approximation probability of the proposed S-box is similar to those of the AES, APA and Gray S-boxes and much better than the Skipjack, Xyi and Residue Prime S-boxes.Fig. 3
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&nbsp;and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.