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Constructing new differentially 4-uniform permutations from the inverse function. (English) Zbl 1305.94084
Summary: Two new families of differentially 4-uniform permutations over \(\mathbb F_{2^{2m}}\) are constructed by modifying the values of the inverse function on some subfield of \(\mathbb F_{2^{2m}}\) and by applying affine transformations on the function. The resulted 4-uniform permutations have high nonlinearity and algebraic degree. A family of differentially 6-uniform permutations with high nonlinearity and algebraic degree is also constructed by making the modification on an affine subspace of \(\mathbb F_{2^{2m}}\).

MSC:
94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14G50 Applications to coding theory and cryptography of arithmetic geometry
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