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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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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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creator	Xiangyong Zeng Carlet, Claude Jinyong Shan Lei Hu
description	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.
doi_str_mv	10.1109/TIT.2011.2109935
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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
title	More Balanced Boolean Functions With Optimal Algebraic Immunity and Good Nonlinearity and Resistance to Fast Algebraic Attacks
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