More Balanced Boolean Functions With Optimal Algebraic Immunity and Good Nonlinearity and Resistance to Fast Algebraic Attacks

In this paper, three constructions of balanced Boolean functions with optimal algebraic immunity are proposed. It is checked that, at least for small numbers of input variables, these functions have good behavior against fast algebraic attacks as well. Other cryptographic properties such as algebrai...

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Bibliographic Details
Published in:IEEE transactions on information theory 2011-09, Vol.57 (9), p.6310-6320
Main Authors: Xiangyong Zeng, Carlet, Claude, Jinyong Shan, Lei Hu
Format: Article
Language:English
Subjects:
Algebra
Algebraic degree
algebraic immunity
Applied sciences
balance
Boolean function
Boolean functions
Cryptography
Exact sciences and technology
fast algebraic attack
Generators
Hamming weight
Information theory
Information, signal and communications theory
Mathematical functions
nonlinearity
Polynomials
Resistance
Resists
Signal and communications theory
stream cipher
Telecommunications and information theory
Variables
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Summary:In this paper, three constructions of balanced Boolean functions with optimal algebraic immunity are proposed. It is checked that, at least for small numbers of input variables, these functions have good behavior against fast algebraic attacks as well. Other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed. Lower bounds on the nonlinearity are proved, which are similar to the best bounds obtained for known Boolean functions resisting algebraic attacks and fast algebraic attacks. Moreover, it is checked that for the number n of variables with 5 ≤ n ≤ 19, the proposed n -variable Boolean functions have in fact very good nonlinearity.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2109935