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• W3135372254 abstract "The inverse function x → x <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-1</sup> on mathbb F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2ⁿ</sub> is one of the most studied functions in cryptography due to its widespread use as an S-box in block ciphers like AES. In this paper, we show that, if n ≥ 5, every function that is CCZ-equivalent to the inverse function is already EA-equivalent to it. This confirms a conjecture by Budaghyan, Calderini and Villa. We also prove that every permutation that is CCZ-equivalent to the inverse function is already affine equivalent to it. The majority of the paper is devoted to proving that there is no permutation polynomial of the form L <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> (x <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-1</sup> )+L <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> (x) over mathbb F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2ⁿ</sub> if n ≥ 5, where L <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> ,L <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> are nonzero linear functions. In the proof, we combine Kloosterman sums, quadratic forms and tools from additive combinatorics." @default.
• W3135372254 created "2021-03-15" @default.
• W3135372254 creator A5077216045 @default.
• W3135372254 date "2021-07-01" @default.
• W3135372254 modified "2023-09-23" @default.
• W3135372254 title "On CCZ-Equivalence of the Inverse Function" @default.
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• W3135372254 doi "https://doi.org/10.1109/tit.2021.3065068" @default.
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