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A New Class of Hyperbent Boolean Functions with Multiple Trace Terms
, 2011
"... Introduced by Rothaus in 1976 as interesting combinatorial objects, bent functions are maximally nonlinear Boolean functions with even numbers of variables whose Hamming distance to the set of all affine functions equals 2 n−1 ± 2 n 2 −1. Not only bent functions are applied in cryptography, such as ..."
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Cited by 4 (2 self)
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, such as applications in components of Sbox, block cipher and stream cipher, but also they have relations to coding theory. Hence a lot of research have been paid on them. Youssef and Gong introduced a new class of bent functions the socalled hyperbent functions which have stronger properties and rarer elements
Hyperbent Functions
 In Advances in Cryptology, Eurocrypt 2001, Lecture Notes in Computer Science, Number 2045, Pages
, 2001
"... Abstract. Bent functions have maximal minimum distance to the set of affine functions. In other words, they achieve the maximal minimum distance to all the coordinate functions of affine monomials. In this paper we introduce a new class of bent functions which we call hyperbent functions. Functions ..."
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Cited by 17 (2 self)
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Abstract. Bent functions have maximal minimum distance to the set of affine functions. In other words, they achieve the maximal minimum distance to all the coordinate functions of affine monomials. In this paper we introduce a new class of bent functions which we call hyperbent functions
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
A note on hyperbent functions via Dillonlike exponents
, 2012
"... This note is devoted to hyperbent functions with multiple trace terms (including binomial functions) via Dillonlike exponents. We show how the approach developed by Mesnager to extend the Charpin–Gong family and subsequently extended by Wang et al. fits in a much more general setting. To this end, ..."
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Cited by 4 (1 self)
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these results not only to reprove straightforwardly the results of Mesnager and Wang et al., but also to characterize the hyperbentness of new infinite classes of Boolean functions.
Dickson polynomials, hyperelliptic curves and hyperbent functions
, 2012
"... In this paper, we study the action of Dickson polynomials on subsets of finite fields of even characteristic related to the trace of the inverse of an element and provide an alternate proof of a not so wellknown result. Such properties are then applied to the study of a family of Boolean functions ..."
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Cited by 2 (0 self)
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and a characterization of their hyperbentness in terms of exponential sums recently proposed by Wang et al. Finally, we extend previous works of Lisoněk and Flori and Mesnager to reformulate this characterization in terms of the number of points on hyperelliptic curves and present some numerical
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
Efficient implementation of a BDD package
 In Proceedings of the 27th ACM/IEEE conference on Design autamation
, 1991
"... Efficient manipulation of Boolean functions is an important component of many computeraided design tasks. This paper describes a package for manipulating Boolean functions based on the reduced, ordered, binary decision diagram (ROBDD) representation. The package is based on an efficient implementat ..."
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Cited by 500 (9 self)
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Efficient manipulation of Boolean functions is an important component of many computeraided design tasks. This paper describes a package for manipulating Boolean functions based on the reduced, ordered, binary decision diagram (ROBDD) representation. The package is based on an efficient
Results 1  10
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193,614