ALGEBRAICALLY DEGENERATE APPROXIMATIONS OF BOOLEAN FUNCTIONS

被引：1
|
作者：
Alekseychuk, A. N. [1 ]
Konyushok, S. N. [1 ]
机构：
[1] Natl Tech Univ Ukraine, Inst Special Commun & Informat Protect, Kyiv Polytech Inst, Kiev, Ukraine
来源：
CYBERNETICS AND SYSTEMS ANALYSIS | 2014年 / 50卷 / 06期
关键词：
correlation cryptanalysis; degenerate Boolean function; k-dimensional function; Walsh-Hadamard transform; finding k-dimensional approximations of Boolean functions;
D O I：
10.1007/s10559-014-9673-x
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
Properties of k-dimensional approximations of Boolean functions are investigated. One of main results is the theorem on the structure of k-dimensional functions whose degree equals d and whose distance from a given Boolean function of n variables is no longer than 2(n-d) (1-epsilon), 1 <= d <= k <= n, epsilon is an element of (0,1). This theorem considerably strengthens the well-known P. Gopalan result and makes it possible to considerably increase the efficiency of his algorithm for constructing all the mentioned k-dimensional Boolean functions.
引用
收藏
页码：817 / 828
页数：12
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