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On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
 In Progress in Cryptology INDOCRYPT 2001
, 2001
"... . In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound 1 log 2 ( p 5+1) = 0:5902::: for the important ratio t t+k of its parameters and poi ..."
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Cited by 5 (0 self)
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and point out that there exists a sequence of matrices for which the limit of ratio of these parameters is equal to lower bound. By means of these matrices we construct mresilient nvariable functions with maximum possible nonlinearity 2 n 1 2 m+1 for m = 0:5902 : : : n+O (log 2 n). This result
New constructions of resilient Boolean functions with maximal nonlinearity
 Proceedings of FSE 2000, to appear in the Lecture Notes in Computer Science Series
, 2000
"... . In this paper we develop a technique that allows to obtain new eective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound 2 ..."
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Cited by 10 (0 self)
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. In this paper we develop a technique that allows to obtain new eective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound 2
On Balanced Nonlinear Boolean Functions
, 2007
"... This paper surveys techniques for studying and constructing balanced Boolean functions that exhibit desirable nonlinear properties including high nonlinearity, good avalanche characteristics and high orders of correlation immunity. Emphasis is placed on techniques that are of combinatorial nature, e ..."
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This paper surveys techniques for studying and constructing balanced Boolean functions that exhibit desirable nonlinear properties including high nonlinearity, good avalanche characteristics and high orders of correlation immunity. Emphasis is placed on techniques that are of combinatorial nature
The constructing of 3resilient Boolean functions of 9 variables with nonlinearity 240.
"... In this work we present a new way to construct 3resilient Boolean functions of 9 variables with nonlinearity 240. Such function have been discovered very recently in [1] and [2] by heuristic search. We find these functions by exhaustive search in the class of functions symmetric under cyclic shifts ..."
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In this work we present a new way to construct 3resilient Boolean functions of 9 variables with nonlinearity 240. Such function have been discovered very recently in [1] and [2] by heuristic search. We find these functions by exhaustive search in the class of functions symmetric under cyclic
Nonlinearity bounds and constructions of resilient Boolean functions
 LNCS 1880, M. Bellare, Ed
, 2000
"... Abstract. In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for ReedMuller codes as applied to resilient functions, which also generalizes the well known XiaoMassey characte ..."
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Cited by 34 (8 self)
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Abstract. In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for ReedMuller codes as applied to resilient functions, which also generalizes the well known Xiao
A New Construction of Resilient Boolean Functions with High Nonlinearity
"... In this paper we develop a technique that allows us to obtain new effective construction of 1resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1resilient function is based on modifying a bent function, by toggling some of its output bits. Two ..."
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In this paper we develop a technique that allows us to obtain new effective construction of 1resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1resilient function is based on modifying a bent function, by toggling some of its output bits. Two
Construction of 1Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
, 2010
"... Abstract This paper presents a construction for a class of 1resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1resilient functions with maximum a ..."
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algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler’s upper bound of algebraic degree. Also a class of 1resilient functions on any number n> 2 of variables with at least suboptimal algebraic immunity
Construction of 1Resilient Boolean Functions with Very Good Nonlinearity
"... Abstract. In this paper we present a strategy to construct 1resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in t ..."
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Abstract. In this paper we present a strategy to construct 1resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise
New constructions for resilient and highly nonlinear boolean functions
 Lecture Notes in Computer Science 2727
, 2003
"... Abstract. We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1resilient functions of n Boolean variables with nonlinearity 2 n−1 −2 (n−1)/2, n odd. The Hadamard transform of these functions is 3valued, which limits the efficien ..."
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Cited by 6 (2 self)
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Abstract. We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1resilient functions of n Boolean variables with nonlinearity 2 n−1 −2 (n−1)/2, n odd. The Hadamard transform of these functions is 3valued, which limits
Construction of 1Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
, 2010
"... This paper presents a construction for a class of 1resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying the generating ..."
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This paper presents a construction for a class of 1resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying
Results 1  10
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493,086