On Nonlinear Resilient Functions

Zhang, Xian-Mo; Zheng, Yuliang

doi:10.1007/3-540-49264-x_22

Cited by 16 publications

(13 citation statements)

References 19 publications

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“…-To prevent from fast correlation attacks, the nonzero correlation coefficients of f to linear functions (both unconditional and conditioned on its binary output) should be relatively small and mutually close in magnitude. To accomplish this, n should be large enough, and one can use a composition of a linear vectorial boolean function based on a linear error-correcting code with a specified minimum distance and a random balanced boolean function of less than n input variables (e.g., see [25], [27], [26]). -The number of nonzero terms in the LFSR feedback polynomial and in any of its r degree polynomial multiples should not be ~sma]l'.…”

Section: (O)mentioning

confidence: 99%

On the security of nonlinear filter generators

Golić

1996

Fast Software Encryption

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Abstract. By regarding a nonlinear filter keystream generator as a finite input memory combiner, it is observed that a recent, important attack introduced by Anderson can be viewed as a conditional correlation attack. Necessary and sufficient conditions for the output sequence to be purely random given than the input sequence is such are pointed out and a new, so-cMled inversion attack is introduced, which may work for larger input memory sizes in comparison with the Anderson's attack. Large input memory size and use of full positive difference sets and correlation immune nonlinear filter functions are proposed as new design criteria to ensure the security against the considered attacks.

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Section: (O)mentioning

confidence: 99%

On the security of nonlinear filter generators

Golić

1996

Fast Software Encryption

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“…This corollary is the result of Corollary 11 in [2]. This shows that the method used in Theorem 11 is more general than that in [-2].…”

Section: Notementioning

confidence: 58%

“…By use of the decomposition formulas described above we can give some construction FOr w (1) EGF"(2),w (2) EGF' (2). if W(w (1) ,w(2))~t, then W(w(a))~t.…”

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confidence: 99%

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On construction of a class of nonlinear resilient functions

Liu

Shi-qu

1999

Appl. Math. Chin. Univ.

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In this paper the decomposition formula of Walsh spectrum of boolean functions is used to construct a class of nonlinear resilient functions. § 1 Introduction A (n ,m,t)-resilient function (fl,. • • ,f.~) is an m-dimension t-th order correlation immune and balanced vector function. The concept was introduced firstly by Chor, et al. ~13 Resilient functions were originally applied respectively to the generation of random strings in presence of faulty processors and to key distribution especially for quantum cryptography. Several other applications afterwards emerged and the theory of resilient functions is now almost omnipresent in cryptography and communication. Researchers have concentrated themselves on linear resilient functions, but recent advances in cryptanalyses show that these functions cannot resist the best affine approximation (BAA) attack. So many researchers pay attention to investigate highly nonlinear resilient functions. E2-43 In [-23, it gives a method to construct new resilient functions by permutations, but its application is difficult. In [33 and E43, the constructions of balanced and correlation immune functions are introduced mainly by the composition of maps. In this paper we give some new construction methods of resilient functions on the basis of the decomposition formula of Walsh spectrum of a class of boolean functions. The resilient functions constructed in this paper have higher algebraic degrees and higher nonlinearity. The results are easily applied and can be extended to field Fp or ring Z~. § The Definition and Equivalent Condition of Resilient FunctionGiven a sample space O=GF"(2) and a a algebra F= {A:ACO}, we have a probability measure over a measurable space (g~,F) satisfying

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“…In fact, there exist actually only two main constructions of a large set of resilient highly nonlinear mappings: the Maiorana-MacFarland construction recalled in Section 3.2 and a second one proposed by Zhang and Zheng in [43,44]. Zhang and Zheng's construction consists in the composition of a linear resilient (n, m, t)-function with a highly nonlinear permutation on F m 2 and it is based on the second part of Remark 1.…”

Section: Other Constructions Of Highly Nonlinear Resilient Vectorial mentioning

confidence: 98%

Vectorial Functions and Covering Sequences

Carlet

Prouff

2004

Lecture Notes in Computer Science

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Abstract. The design of large classes of highly nonlinear resilient vectorial functions (mappings from F n 2 into F m 2 , also called S-boxes) is needed for iterated block ciphers and for pseudo-random generators with multiple output. In this paper, we recall the diverse known constructions of such S-boxes, and we show that those which provide good candidate functions are, in fact, all in the same class. This class corresponds to a generalization of a well known construction due to Maiorana and MacFarland. We study in detail this construction and we specify it to obtain good S-boxes. In a second part, we generalize to S-boxes the notion of covering sequence. We show that this generalization has the same properties as for Boolean functions, and that it has nice additional properties of stability. We study how this notion can be used to design attacks, and we explain why some functions, including the elements of the new class, cannot be involved in the construction of iterated block ciphers.

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On Nonlinear Resilient Functions

Cited by 16 publications

References 19 publications

On the security of nonlinear filter generators

On the security of nonlinear filter generators

On construction of a class of nonlinear resilient functions

Vectorial Functions and Covering Sequences

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