More differentially 6-uniform power functions

被引：34

作者：

Blondeau, Celine ^{[1
]}

Perrin, Leo ^{[2
]}

机构：

[1] Aalto Univ, Sch Sci, Dept Informat & Comp Sci, Espoo, Finland

[2] Univ Luxembourg, Luxembourg, Luxembourg

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2014年 / 73卷 / 02期

关键词：

Differential uniformity; Differential spectrum; Monomial; Kloosterman sum; Roots of trinomial; x bar right arrow x(2t-1); Dickson polynomial; WELCH; PROOF;

D O I：

10.1007/s10623-014-9948-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we study the differential spectra of differentially 6-uniform functions among the family of monomials defined in . We show that the functions when with odd have a differential spectrum similar to the one of the function which belongs to the same family. We also study the functions when with which are known to be differentially 6-uniform and show that their complete differential spectrum can be provided under an assumption related to a new formulation of the Kloosterman sum. 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 is widely used in this paper. A discussion regarding the non-linearity and the algebraic degree of the vectorial functions is also proposed.

引用

页码：487 / 505

页数：19

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