Generalized Construction of Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation

Shaojing FU  Chao LI  Longjiang QU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.1   pp.360-362
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.360
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
cryptography,  Boolean function,  algebraic immunity,  

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Summary: 
Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In 2011, X.Y. Zeng et al. proposed three constructions of balanced Boolean functions with maximum algebraic immunity, the constructions are based on univariate polynomial representation of Boolean functions. In this paper, we will improve X.Y. Zeng et al.' constructions to obtain more even-variable Boolean functions with maximum algebraic immunity. It is checked that, our new functions can have as high nonlinearity as X.Y. Zeng et al.' functions.