VECTORIAL BOOLEAN FUNCTIONS WITH GOOD CRYPTOGRAPHIC PROPERTIES

被引：8
|
作者：
Feng, Keqin [1 ]
Yang, Jing [1 ,2 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore
来源：
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE | 2011年 / 22卷 / 06期
关键词：
Boolean function; bent function; nonlinearity; algebraic immunity; stream and block cipher; ALGEBRAIC IMMUNITY; GOOD NONLINEARITY; INFINITE CLASS;
D O I：
10.1142/S0129054111008702
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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 F:F(2)(n) -> F(2)(m) 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 F':F(2)(n) -> F(2)(m) with optimum algebraic degree, good nonlinearity and good algebraic immunity for all cases 1 <= m <= n/2, 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.
引用
收藏
页码：1271 / 1282
页数：12
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