论文标题
具有最大差异均匀性和特殊APN猜想的多项式
Polynomials with maximal differential uniformity and the exceptional APN conjecture
论文作者
论文摘要
我们通过表明M = 2 R的多项式（2 {\ Ell} + 1）为特殊的APN猜想做出了贡献，其中GCD（R，{\ Ell}）2，R 2，r 2，{\ Ell} 1具有非零第二个领先系数，可以在无限的基础场上的许多扩展上apn。更确切地说，我们证明，对于n个足够大的f 2 n [x]的所有多项式，具有非零第二个领先系数的程度具有等于m -2的差异均匀性。
We contribute to the exceptional APN conjecture by showing that no polynomial of degree m = 2 r (2 {\ell} + 1) where gcd(r, {\ell}) 2, r 2, {\ell} 1 with a nonzero second leading coefficient can be APN over infinitely many extensions of the base field. More precisely, we prove that for n sufficiently large, all polynomials of F 2 n [x] of such a degree with a nonzero second leading coefficient have a differential uniformity equal to m -- 2.
