Nonlinearity bounds and constructions of resilient Boolean functions

被引:0
|
作者
Sarkar, P
Maitra, S
机构
[1] Indian Stat Inst, Appl Stat Unit, Kolkata 700035, W Bengal, India
[2] Indian Stat Inst, Comp & Stat Serv Ctr, Kolkata 700035, W Bengal, India
来源
ADVANCES IN CRYPTOLOGY-CRYPTO 2000, PROCEEDINGS | 2000年 / 1880卷
关键词
Boolean functions; balancedness; algebraic degree; nonlinearity; correlation immunity; resiliency; stream ciphers; combinatorial cryptography;
D O I
暂无
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known Xiao-Massey characterization. As a consequence, a nontrivial upper bound on the nonlinearity of resilient functions is obtained. This result coupled with Siegenthaler's inequality leads to the notion of best possible tradeoff among the parameters: number of variables, order of resiliency, nonlinearity and algebraic degree. We further show that functions achieving the best possible trade-off can be constructed by the Maiorana-McFarland like technique. Also we provide constructions of some previously unknown functions.
引用
收藏
页码:515 / 532
页数:18
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