Improving the Lower Bound on the Higher Order Nonlinearity of Boolean Functions With Prescribed Algebraic Immunity

The recent algebraic attacks have received a lot of attention in cryptographic literature. The algebraic immunity of a Boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function. Very few results...

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Vydáno v:	IEEE transactions on information theory Ročník 54; číslo 8; s. 3656 - 3662
Hlavní autor:	Mesnager, S.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.08.2008 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algebra Algebraic attack algebraic degree algebraic immunity annihilator Applied sciences block cipher Blocking Boolean function Boolean functions Codes Cryptography Data encryption Detection, estimation, filtering, equalization, prediction Exact sciences and technology Filtering Hamming weight higher order nonlinearity Immunity Information theory Information, signal and communications theory Linear feedback shift registers Lower bounds Mathematics Nonlinear equations Nonlinear filters Nonlinearity Polynomials Signal and communications theory Signal, noise stream cipher Telecommunications and information theory algebraic immunity Lower bound block cipher Stream ciphering Algebraic attack stream cipher algebraic degree Boolean function Non linear phenomenon higher order nonlinearity Non linear filtering Private key First order Block ciphering Security of data annihilator Cryptography Non linear effect
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	The recent algebraic attacks have received a lot of attention in cryptographic literature. The algebraic immunity of a Boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function. Very few results have been found concerning its relation with the other cryptographic parameters or with the r th-order nonlinearity. As recalled by Carlet at CRYPTO'06, many papers have illustrated the importance of the r th-order nonlinearity profile (which includes the first-order nonlinearity). The role of this parameter relatively to the currently known attacks has been also shown for block ciphers. Recently, two lower bounds involving the algebraic immunity on the r th-order nonlinearity have been shown by Carlet . None of them improves upon the other one in all situations. In this paper, we prove a new lower bound on the r th-order nonlinearity profile of Boolean functions, given their algebraic immunity, that improves significantly upon one of these lower bounds for all orders and upon the other one for low orders.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2008.926360