31. Isogeometric analysis with geometrically continuous functions on two-patch geometriesMario Kapl, Vito Vitrih, Bert Jüttler, Katharina Birner, 2015, izvirni znanstveni članek Opis: We study the linear space of Cs-smooth isogeometric functions defined on a multi-patch domain % % R2. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the Cs-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (Gs-smoothness) of their graph surfaces. This motivates us to call them Cs-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is analyzed in more detail. Numerical experiments with bicubic and biquartic functions for performing L2 approximation and for solving Poisson%s equation and the biharmonic equation on two-patch geometries are presented and indicate optimal rates of convergence.
Ključne besede: izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domain
Objavljeno v RUP: 15.10.2015; Ogledov: 3782; Prenosov: 192
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36. On cryptographically significant mappings over GF(2 [sup] n)Enes Pašalić, 2008, objavljeni znanstveni prispevek na konferenci Opis: In this paper we investigate the algebraic properties of important cryptographic primitives called substitution boxes (S-boxes). An S-box is a mapping that takes ▫$n$▫ binary inputs whose image is a binary ▫$m$▫-tuple; therefore it is represented as ▫$F:\text{GF}(2)^n \rightarrow \text{GF}(2)^m$▫. One of the most important cryptographic applications is the case ▫$n = m$▫, thus the S-box may be viewed as a function over ▫$\text{GF}(2^n)$▫. We show that certain classes of functions over ▫$\text{GF}(2^n)$▫ do not possess a cryptographic property known as APN (AlmostPerfect Nonlinear) permutations. On the other hand, when ▫$n$▫ is odd, an infinite class of APN permutations may be derived in a recursive manner, that is starting with a specific APN permutation on ▫$\text{GF}(2^k), k$▫ odd, APN permutations are derived over ▫$\text{GF}(2^{k+2i})$▫ for any ▫$i \geq 1$▫. Some theoretical results related to permutation polynomials and algebraic properties of the functions in the ring ▫$\text{GF}(q)[x,y]$▫ are also presented. For sparse polynomials over the field ▫$\text{GF}(2^n)$▫, an efficient algorithm for finding low degree I/O equations is proposed.
Ključne besede: cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties
Objavljeno v RUP: 15.10.2013; Ogledov: 3283; Prenosov: 74
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37. Collisions for variants of the BLAKE hash functionJanoš Vidali, Peter Nose, Enes Pašalić, 2010, izvirni znanstveni članek Ključne besede: BLAKE, BLOKE, BRAKE, collision, cryptography, fixed point, hash functions
Objavljeno v RUP: 15.10.2013; Ogledov: 3062; Prenosov: 64
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38. Further results on the relation between nonlinearity and resiliency for Boolean functionsEnes Pašalić, Thomas Johansson, 1999, objavljeni znanstveni prispevek na konferenci (vabljeno predavanje) Opis: A good design of a Boolean function used in a stream cipher requires that the function satisfies certain criteria in order to resist different attacks. In this paper we study the tradeoff between two such criteria, the nonlinearity and the resiliency. The results are twofold. Firstly, we establish the maximum nonlinearity for a fixed resiliency in certain cases. Secondly, we present a simple search algorithm for finding Boolean functions with good nonlinearity and some fixed resiliency.
Ključne besede: Boolean functions, cryptography, optimisation, search problems, stream cipher, attacks, maximum nonlinearity, search algorithm, fixed resiliency
Objavljeno v RUP: 15.10.2013; Ogledov: 2962; Prenosov: 132
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