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• W3089062277 abstract "Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem. In block ciphers, the S-boxes create confusion and add valuable strength. The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field. For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256. Conventionally, construction of affine power affine S-box is based on Galois field of order 256, depending on a single degree <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mn>8</mml:mn></mml:math> primitive irreducible polynomial over <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℤ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>. In this manuscript, we study affine power affine S-boxes for all the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mn>16</mml:mn></mml:math> distinct degree <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mn>8</mml:mn></mml:math> primitive irreducible polynomials over <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℤ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> to propose 16 different <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mn>8</mml:mn><mml:mo>×</mml:mo><mml:mn>8</mml:mn></mml:math> substitution boxes. To perform this idea, we introduce 16 affine power affine transformations and, for fixed parameters, we obtained 16 distinct S-boxes. Here, we thoroughly study S-boxes with all possible primitive irreducible polynomials and their algebraic properties. All of these boxes are evaluated with the help of nonlinearity test, strict avalanche criterion, bit independent criterion, and linear and differential approximation probability analyses to measure the algebraic and statistical strength of the proposed substitution boxes. Majority logic criterion results indicate that the proposed substitution boxes are well suited for the techniques of secure communication." @default.
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• W3089062277 date "2020-09-24" @default.
• W3089062277 modified "2023-10-17" @default.
• W3089062277 title "The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers" @default.
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• W3089062277 doi "https://doi.org/10.1155/2020/8883884" @default.
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