Classification of cubic (n-4)-resilient Boolean functions

被引：5

作者：

Braeken, A ^{[1
]}

Borissov, Y

Nikova, S

Preneel, B

机构：

[1] Katholieke Univ Leuven, COSIC, SCD, ESAT,Dept Elect Engn, B-3001 Heverlee, Belgium

[2] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2006年 / 52卷 / 04期

关键词：

algebraic normal form (ANF); Boolean function; classification; cubic; linear space; resiliency;

D O I：

10.1109/TIT.2006.871063

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Carlet and Charpin classified the set of cubic (n - 4)-resilient Boolean functions into four different types with respect to the Walsh spectrum and the dimension of the linear space. Based on the classification of RM(3, 6)/RM(1, 6), we have completed this classification of cubic (n - 4)-resilient Boolean functions by deriving the corresponding algebraic normal form (ANF) and autocorrelation spectrum for each of the four types. At the same time, we have solved an open problem by proving that all plateaued cubic (n - 4)-resilient Boolean functions have dimension of the linear space equal either to a - 5 or n - 6.

引用

页码：1670 / 1676

页数：7

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