On Subspaces of Kloosterman Zeros and Permutation of the Form

Abstrakt

ermutations of the form F(x) = L1(x-1) + L2(x) with linear functions L1, L2 are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that F cannot be a permutation on binary fields if the kernel of L1 or L2 is large.

A key step of our proof is an observation on the maximal size of a subspace V of F2n that consists of Kloosterman zeros, i.e. a subspace V such that Kn(v) = 0 for every v ELEMENT OF V where Kn(v) denotes the Kloosterman sum of v.

Klíčová slova

• Subspaces
• Kloosterman
• Zeros
• Permutation
• Form