An efficient recursive method for synthesis of correlation-immune Boolean functions is proposed. At the first stage, this method uses minimal correlation-immune functions. A classification of 6-variable minimal correl...
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An efficient recursive method for synthesis of correlation-immune Boolean functions is proposed. At the first stage, this method uses minimal correlation-immune functions. A classification of 6-variable minimal correlation-immune functions under the Jevons group is put forward. Newresults on minimal correlation-immune functions are given.
A classification of correlation-immune and minimal corelation-immune Boolean function of 4 and 5 variables with respect to the Jevons group is given. Representatives of the equivalence classes of correlation-immune fu...
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A classification of correlation-immune and minimal corelation-immune Boolean function of 4 and 5 variables with respect to the Jevons group is given. Representatives of the equivalence classes of correlation-immune functions of 4 and 5 variables are decomposed into minimal correlation-immune functions. Characteristics of various decompositions of the constant function 1 into minimal correlation-immune functions are presented.
We refine local limit theorems for the distribution of a part of the weight vector of subfunctions and for the distribution of a part of the vector of spectral coefficients of linear combinations of coordinate functio...
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We refine local limit theorems for the distribution of a part of the weight vector of subfunctions and for the distribution of a part of the vector of spectral coefficients of linear combinations of coordinate functions of a random binary mapping. These theorems are used to derive improved asymptotic estimates for the numbers of correlation-immune and k-resilient vectorial Boolean functions.
Le Bars and Viola have recently proposed an innovative recursive decomposition of the first-order correlation-immune Boolean functions. Based on their work this paper presents the design of an enumerative encoding of ...
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Le Bars and Viola have recently proposed an innovative recursive decomposition of the first-order correlation-immune Boolean functions. Based on their work this paper presents the design of an enumerative encoding of these Boolean functions. This is the first enumerative encoding of a class of Boolean functions defined by a cryptographic property. In this paper we study three major milestones to do this encoding: the conceptual computational tree, the use of normal classes and signed permutations, and a dynamic selection of the decomposition. Our enumerative encoding algorithm is practicable up to 8 variables which is the best result we may expect due to the combinatorial explosion of the numbers of classes. (C) 2013 Elsevier B.V. All rights reserved.
A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman ...
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ISBN:
(纸本)9781538692912
A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy t <= 2n/3 - 1;moreover, the (2n/3 - 1)-resilient (n,2)-functions correspond to the equitable partitions of the n-cube with the quotient matrix [[0, r, r, r], [r, 0, r, r], [r, r, 0, r], [r, r, r, 0]], r = n/3. We suggest constructions of such functions and corresponding partitions, show connections with Latin hypercubes and binary 1-perfect codes, characterize the non-full-rank and the reducible functions from the considered class, and discuss the possibility to make a complete characterization of the class.
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families...
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ISBN:
(纸本)9781424439867
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families of resilient functions with optimal nonlinearity which is particularly well-suited for combining linear feedback shift registers.
The Wire-Tap Channel II introduced by L. H. Ozarow, A.D. Wyner was the first instance of a Partial Exposure Problem. General Exposure-Resilient functions (l-ERF) are known to be appropriate to provide a solution to th...
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The Wire-Tap Channel II introduced by L. H. Ozarow, A.D. Wyner was the first instance of a Partial Exposure Problem. General Exposure-Resilient functions (l-ERF) are known to be appropriate to provide a solution to the Partial Exposure Problem as long as random secret chains are to be protected. It is known that a perfect l-ERF is nothing but a t-resilient function for t = n - l, where n is the length of the exposed symbol-chain and t the largest number of symbols that an adversary is able to observe. We here manage to adapt the use of t-resilient functions for protecting messages against partial exposure. A solution to that problem had been given by the perfect local pseudo-random generator introduced by Maurer and Massey which is based upon a t-resilient function, but its use needs a secret key shared by the sender and the receiver. We are able to provide solutions to protect messages against Partial Exposure without using secret keys, for various ranges of parameters. Moreover low complexity algorithms are devised to that end.
The binary vector-output correlation-immune functions are studied in this paper. Some important properties of vector-output correlation-immune functions are obtained. A number of methods for constructing new vector-ou...
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The binary vector-output correlation-immune functions are studied in this paper. Some important properties of vector-output correlation-immune functions are obtained. A number of methods for constructing new vector-output correlation-immune functions from old ones are discussed. The nonlinearity of the newly constructed vector-output correlation-immune functions is studied. For some cases we give the exact formulas for the nonlinearity of constructed vector-output correlation-immune functions. (C) 2003 Elsevier Inc. All rights reserved.
Bastd on the relationship between nonlinearity and resiliency of amulti-output function, we present a method for constructing noninterseeling linear codes frompacking design. Through these linear codes, we obtain n-va...
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Bastd on the relationship between nonlinearity and resiliency of amulti-output function, we present a method for constructing noninterseeling linear codes frompacking design. Through these linear codes, we obtain n-variable, m-output, t-resilient functionswith very high nonlinearity. Their nonlinearities are currently the best results for most of cases.
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