scholarly journals Algebraic immunity of vectorial boolean functions and boolean groebner bases

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
A.N. Alekseychuk
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
Groebner Bases ◽  
Vectorial Boolean Functions

NEW CONSTRUCTIONS OF VECTORIAL BOOLEAN FUNCTIONS WITH GOOD CRYPTOGRAPHIC PROPERTIES

2012 ◽  
Vol 23 (03) ◽  
pp. 749-760
Author(s):  
DESHUAI DONG ◽  
LONGJIANG QU ◽  
SHAOJING FU ◽  
CHAO LI
Keyword(s):  
Boolean Functions ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
High Nonlinearity ◽  
Vectorial Boolean Functions ◽  
Very High

Vectorial Boolean functions play an important role in cryptography. How to construct vectorial Boolean functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper we present several constructions of balanced vectorial Boolean functions with high algebraic immunity, high(or optimum) algebraic degree, and very high nonlinearity. In some cases, the constructed functions also achieve optimum algebraic immunity.

VECTORIAL BOOLEAN FUNCTIONS WITH GOOD CRYPTOGRAPHIC PROPERTIES

2011 ◽  
Vol 22 (06) ◽  
pp. 1271-1282 ◽  
Author(s):  
KEQIN FENG ◽  
JING YANG
Keyword(s):  
Boolean Functions ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
Vectorial Boolean Functions

In this paper we generalize two remarkable results on cryptographic properties of Boolean functions given by Tu and Deng [8] to the vectorial case. Firstly we construct vectorial bent Boolean functions [Formula: see text] with good algebraic immunity for all cases 1 ⩽ m ⩽ n, and with maximum algebraic immunity for some cases (n,m). Then by modifying F, we get vectorial balanced functions [Formula: see text] with optimum algebraic degree, good nonlinearity and good algebraic immunity for all cases [Formula: see text], and with maximum algebraic immunity for some cases (n,m). Moreover, while Tu-Deng's results are valid under a combinatorial hypothesis, our results (Theorems 4 and 5) are true without this hypothesis.

scholarly journals Constructing vectorial Boolean functions with high algebraic immunity based on group decomposition

2014 ◽  
Vol 92 (3) ◽  
pp. 451-462 ◽  
Author(s):  
Yu Lou ◽  
Huiting Han ◽  
Chunming Tang ◽  
Zhangqing Wu ◽  
Maozhi Xu
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
Vectorial Boolean Functions
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