A New Construction of Boolean Functions with Maximum Algebraic Immunity

2009 ◽  
pp. 177-185 ◽  
Author(s):  
Deshuai Dong ◽  
Shaojing Fu ◽  
Longjiang Qu ◽  
Chao Li
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
New Construction

CONSTRUCTING 2m-VARIABLE BOOLEAN FUNCTIONSWITH OPTIMAL ALGEBRAIC IMMUNITY BASED ON POLAR DECOMPOSITION OF $\mathbb{F}^\ast_{2^{2m}}$

2014 ◽  
Vol 25 (05) ◽  
pp. 537-551 ◽  
Author(s):  
JIA ZHENG ◽  
BAOFENG WU ◽  
YUFU CHEN ◽  
ZHUOJUN LIU
Keyword(s):  
Boolean Functions ◽  
Polar Decomposition ◽  
Multiplicative Group ◽  
Slight Modification ◽  
Additive Group ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
New Construction ◽  
Fast Algebraic Attacks ◽  
Class Of Functions

Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field [Formula: see text] seems to be a promising approach since Tu and Deng's work. In this paper, we consider the same problem in a new way. Based on polar decomposition of the multiplicative group of [Formula: see text], we propose a new construction of Boolean functions with optimal algebraic immunity. By a slight modification of it, we obtain a class of balanced Boolean functions achieving optimal algebraic immunity, which also have optimal algebraic degree and high nonlinearity. Computer investigations imply that this class of functions also behaves well against fast algebraic attacks.

Sign in / Sign up

Export Citation Format

Share Document