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• W3044227546 abstract "Substitution box (S-Box) has a prominent significance being the fundamental nonlinear component of block cipher which fulfils confusion, one of the properties proposed by Claude Shannon in 1949. In this paper, we proposed an S-Box by using the action of modular group PSL <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$left ({2,mathbb {Z} }right)$ </tex-math></inline-formula> on projective line PL <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$left ({F_{257} }right)$ </tex-math></inline-formula> over Galois field GF <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$left ({2^{8} }right)$ </tex-math></inline-formula> . In the first step we obtained elements of GF <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$left ({2^{8} }right)$ </tex-math></inline-formula> by using powers of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$alpha $ </tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$alpha $ </tex-math></inline-formula> is the primitive root of irreducible polynomial <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$pleft ({x }right)$ </tex-math></inline-formula> of order 8 over field <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {Z}_{2}$ </tex-math></inline-formula> , then applied the generators of PSL <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$left ({2,mathbb {Z} }right)$ </tex-math></inline-formula> and followed steps to get rid of infinity from output. In the final step of proposed scheme, one of the permutations of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$S_{16}$ </tex-math></inline-formula> is applied which enhanced the possible number of S-Boxes obtained by any single specific irreducible polynomial <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$p(x)$ </tex-math></inline-formula> over field <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {Z}_{2}$ </tex-math></inline-formula> of order 8. We analyzed performance of the proposed <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$8times 8$ </tex-math></inline-formula> S-Box under cryptographic properties such as strict avalanche criterion, bit independence criterion, nonlinearity, differential approximation probability, linear approximation probability; and compared obtained results with a number of renowned S-Boxes. Lastly, we performed statistical analysis (which comprises of contrast analysis, homogeneity analysis, energy analysis, correlation analysis, entropy analysis and mean of absolute deviation analysis) on our proposed S-Box and obtained results have been compared with adequate number of S-Boxes." @default.
• W3044227546 created "2020-07-29" @default.
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• W3044227546 date "2020-01-01" @default.
• W3044227546 modified "2023-09-26" @default.
• W3044227546 title "Construction of Nonlinear Component of Block Cipher by Action of Modular Group PSL(2, Z) on Projective Line PL(GF(2⁸))" @default.
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• W3044227546 doi "https://doi.org/10.1109/access.2020.3010615" @default.
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