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.
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.
We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet. A previous result due to Gopalakrishnan and Stinson is generalized as we give an orthogonal array ch...
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We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet. A previous result due to Gopalakrishnan and Stinson is generalized as we give an orthogonal array characterization, a Fourier transform and a matrix characterization for correlation-immune and resilient functions over any finite alphabet endowed with the structure of an Abelian group. We then point out the existence of a tradeoff between the degree of the algebraic normal form and the correlation-immunity order of any function defined on a finite field and we construct some infinite families of t-resilient functions with optimal nonlinearity which are particularly well-suited for combining linear feedback shift registers. We also point out the link between correlation-immune functions and some cryptographic objects as perfect local randomizers and multipermutations.
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.
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.
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.
This correspondence studies resilient functions which have applications in fault-tolerant distributed computing, quantum cryptographic key distribution, and random sequence generation for stream ciphers. We present a ...
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This correspondence studies resilient functions which have applications in fault-tolerant distributed computing, quantum cryptographic key distribution, and random sequence generation for stream ciphers. We present a number of new methods for synthesizing resilient functions. An interesting aspect of these methods is that they are applicable both to linear and nonlinear resilient functions. Our second major contribution is to show that every Linear resilient function can be transformed into a Large number of nonlinear resilient functions with the same parameters. As a result, we obtain resilient functions that are highly nonlinear and have a high algebraic degree.
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.
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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