TY - JOUR
AB - A robust combiner for hash functions takes two candidate implementations and constructs a hash function which is secure as long as at least one of the candidates is secure. So far, hash function combiners only aim at preserving a single property such as collision-resistance or pseudorandomness. However, when hash functions are used in protocols like TLS they are often required to provide several properties simultaneously. We therefore put forward the notion of robust multi-property combiners and elaborate on different definitions for such combiners. We then propose a combiner that provably preserves (target) collision-resistance, pseudorandomness, and being a secure message authentication code. This combiner satisfies the strongest notion we propose, which requires that the combined function satisfies every security property which is satisfied by at least one of the underlying hash function. If the underlying hash functions have output length n, the combiner has output length 2 n. This basically matches a known lower bound for black-box combiners for collision-resistance only, thus the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the property of being indifferentiable from a random oracle, slightly increasing the output length to 2 n+ω(log n). Moreover, we show how to augment our constructions in order to make them also robust for the one-wayness property, but in this case require an a priory upper bound on the input length.
AU - Fischlin, Marc
AU - Lehmann, Anja
AU - Pietrzak, Krzysztof Z
ID - 2852
IS - 3
JF - Journal of Cryptology
TI - Robust multi-property combiners for hash functions
VL - 27
ER -
TY - CONF
AB - Persistent homology is a recent grandchild of homology that has found use in
science and engineering as well as in mathematics. This paper surveys the method as well
as the applications, neglecting completeness in favor of highlighting ideas and directions.
AU - Edelsbrunner, Herbert
AU - Morozovy, Dmitriy
ID - 2905
TI - Persistent homology: Theory and practice
ER -
TY - BOOK
AB - This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
AU - Edelsbrunner, Herbert
ID - 6853
SN - 2191-530X
TI - A Short Course in Computational Geometry and Topology
ER -
TY - GEN
AU - Huszár, Kristóf
AU - Rolinek, Michal
ID - 7038
TI - Playful Math - An introduction to mathematical games
ER -
TY - JOUR
AB - We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.
AU - Guerrero, Paul
AU - Jeschke, Stefan
AU - Wimmer, Michael
AU - Wonka, Peter
ID - 1629
IS - 2
JF - ACM Transactions on Graphics
TI - Edit propagation using geometric relationship functions
VL - 33
ER -