1. On CCZ-Equivalence of the Inverse Function.
- Author
-
Kolsch, Lukas
- Subjects
INVERSE functions ,BLOCK ciphers ,QUADRATIC forms ,COMBINATORICS ,PERMUTATIONS ,BOOLEAN functions - Abstract
The inverse function x → x
−1 on F2n, 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 L1 (x−1 ) + L2 (x) over F2n if n ≥ 5, where L1 ,L2 are nonzero linear functions. In the proof, we combine Kloosterman sums, quadratic forms and tools from additive combinatorics. [ABSTRACT FROM AUTHOR]- Published
- 2021
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