Construction of nonlinear resilient boolean functions using "small" affine functions

被引：22

作者：

Sarkar, P ^{[1
]}

Maitra, S ^{[1
]}

机构：

[1] Indian Stat Inst, Appl Stat Unit, Kolkata 700108, W Bengal, India

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2004年 / 50卷 / 09期

关键词：

algebraic degree; balancedness; Boolean functions; correlation immunity; nonlinearity; resiliency;

D O I：

10.1109/TIT.2004.833366

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this correspondence, we use affine functions on a small number of variables to construct resilient functions on a large number of variables. We show that by properly combining these functions it is possible to achieve high nonlinearity and high algebraic degree. An important contribution of the correspondence is to show that for each order of resiliency m, it is possible to find infinitely many odd and even positive integers n, such that it is possible to construct (maximum degree) n-variable, m-resilient functions having nonlinearity strictly greater than 2(n-1) - 2([n/2]). We also present construction of some important functions on a small number of variables.

引用

页码：2185 / 2193

页数：9

共 21 条

[1]

[Anonymous], 1991, LECT NOTES COMPUTER

[2]

CAMION P, 1992, LECT NOTES COMPUT SC, V576, P86

[3]

Carlet C, 2002, LECT NOTES COMPUT SC, V2442, P549

[4]

Chee S., 1997, LECT NOTES COMPUTER, V1163, P232

[5]

CLARK J, 2003, CEC 2003 2003 C EV C, V3, P2173

[6]

FEDOROVA M, 2001, LECT NOTES COMPUTER, V2247, P254

[7]

GUOZHEN X, 1988, IEEE T INFORM THEORY, V34, P569

[8]

Gupta KC, 2002, LECT NOTES COMPUT SC, V2501, P466

[9] Further constructions of resilient Boolean functions with very high nonlinearity [J].

Maitra, S ;

Pasalic, E .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (07) :1825-1834

[10] Maximum nonlinearity of symmetric Boolean functions on odd number of variables [J].

Maitra, S ;

Sarkar, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (09) :2626-2630

← 1 2 3 →