More differentially 6-uniform power functions
نویسندگان
چکیده
We provide the differential spectra of differentially 6-uniform functions among the family of power functions x 7→ x −1 defined in F2n . We show that the functions x 7→ x −1 when t = n−1 2 , n+3 2 with odd n and when t = kn+1 3 , (3−k)n+2 3 with kn ≡ 2 mod 3 have differential spectra similar to the one of the function x 7→ x which belongs to the same family. To provide the differential spectra for these functions, a recent result of Helleseth and Kholosha regarding the number of roots of polynomials of the form x +1 + x+ a is used. A discussion regarding the non-linearity and the algebraic degree of this family of exponents is provided.
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 73 شماره
صفحات -
تاریخ انتشار 2014