Maximal values of generalized algebraic immunity

被引：48

作者：

Feng, Keqin ^{[1
]}

Liao, Qunying ^{[1
,2
]}

Yang, Jing ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2009年 / 50卷 / 02期

关键词：

Algebraic immunity; Reed-Muller codes; Finite field; Cryptography; BOOLEAN FUNCTIONS; ATTACKS;

D O I：

10.1007/s10623-008-9228-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions and/or over arbitrary finite fields and reasonable upper bounds for such generalized algebraic immunities has been proved in Armknecht and Krause (Proceedings of ICALP 2006, LNCS, vol. 4052, pp 180-191, 2006), Ars and Faugere (Algebraic immunity of functions over finite fields, INRIA, No report 5532, 2005) and Batten (Canteaut, Viswanathan (eds.) Progress in Cryptology-INDOCRYPT 2004, LNCS, vol. 3348, pp 84-91, 2004). In this paper we show that the upper bounds can be reached as the maximal values of algebraic immunities for most of generalizations by using properties of Reed-Muller codes.

引用

页码：243 / 252

页数：10