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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
Construction of nonlinear Boolean functions with important cryptographic properties
 In Advances in Cryptology  EUROCRYPT 2000, number 1807 in Lecture Notes in Computer Science
, 2000
"... Abstract. This paper addresses the problem of obtaining new construction methods for cryptographically significant Boolean functions. We show that for each positive integer m, there are infinitely many integers n (both odd and even), such that it is possible to construct nvariable, mresilient func ..."
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Cited by 46 (14 self)
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Wiedemann functions to construct balanced Boolean functions on nvariables having nonlinearity strictly greater than 2 n−1 − 2 n−1 2 for all odd n ≥ 15. In addition, we consider the properties strict avalanche criteria and propagation characteristics which are important for design of Sboxes in block ciphers
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
Propagation Characteristics and CorrelationImmunity of Highly Nonlinear Boolean Functions
 EUROCRYPT 2000, LECTURE NOTES IN COMP. SCI
, 2000
"... We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with resp ..."
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Cited by 23 (8 self)
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We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion
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 3526 (46 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
Symbolic Boolean manipulation with ordered binarydecision diagrams
 ACM COMPUTING SURVEYS
, 1992
"... Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as grap ..."
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Cited by 1036 (13 self)
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Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented
Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks. Cryptology ePrint Archive, Report 2011/366
, 2011
"... In this paper, we present a new combinatorial conjecture about binary strings. Based on the new conjecture, two classes of Boolean functions of 2k variables with optimal algebraic immunity are proposed, where k ≥ 2. The first class contains unbalanced functions having high algebraic degree and nonli ..."
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Cited by 13 (0 self)
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and nonlinearity. The functions in the second one are balanced and have maximal algebraic degree and high nonlinearity. It is checked that, at least for small numbers of variables, both classes of functions have a good behavior against fast algebraic attacks. Compared with the known Boolean functions resisting
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1573 (83 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate
Results 1  10
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