565 research outputs found

    From Graphs to Keyed Quantum Hash Functions

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    We present two new constructions of quantum hash functions: the first based on expander graphs and the second based on extractor functions and estimate the amount of randomness that is needed to construct them. We also propose a keyed quantum hash function based on extractor function that can be used in quantum message authentication codes and assess its security in a limited attacker model

    Offline Signature Verification by Combining Graph Edit Distance and Triplet Networks

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    Biometric authentication by means of handwritten signatures is a challenging pattern recognition task, which aims to infer a writer model from only a handful of genuine signatures. In order to make it more difficult for a forger to attack the verification system, a promising strategy is to combine different writer models. In this work, we propose to complement a recent structural approach to offline signature verification based on graph edit distance with a statistical approach based on metric learning with deep neural networks. On the MCYT and GPDS benchmark datasets, we demonstrate that combining the structural and statistical models leads to significant improvements in performance, profiting from their complementary properties

    Computational complexity of reconstruction and isomorphism testing for designs and line graphs

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    Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line graphs of tt-(v,k,λ)(v,k,\lambda) designs. For this class of highly regular graphs, we obtain a worst-case running time of O(vlogv+O(1))O(v^{\log v + O(1)}) for bounded parameters t,k,λt,k,\lambda. In a first step, our approach makes use of the Babai--Luks algorithm to compute canonical forms of tt-designs. In a second step, we show that tt-designs can be reconstructed from their line graphs in polynomial-time. The first is algebraic in nature, the second purely combinatorial. For both, profound structural knowledge in design theory is required. Our results extend earlier complexity results about isomorphism testing of graphs generated from Steiner triple systems and block designs.Comment: 12 pages; to appear in: "Journal of Combinatorial Theory, Series A

    Perfectly Secure Communication, based on Graph-Topological Addressing in Unique-Neighborhood Networks

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    We consider network graphs G=(V,E)G=(V,E) in which adjacent nodes share common secrets. In this setting, certain techniques for perfect end-to-end security (in the sense of confidentiality, authenticity (implying integrity) and availability, i.e., CIA+) can be made applicable without end-to-end shared secrets and without computational intractability assumptions. To this end, we introduce and study the concept of a unique-neighborhood network, in which nodes are uniquely identifiable upon their graph-topological neighborhood. While the concept is motivated by authentication, it may enjoy wider applicability as being a technology-agnostic (yet topology aware) form of addressing nodes in a network

    On 1-factorizations of Bipartite Kneser Graphs

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    It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph H(v,t)H(v,t), which contains as vertices all tt-element and (vt)(v-t)-element subsets of [v]:={1,,v}[v]:=\{1,\ldots,v\} and an edge between any two vertices when one is a subset of the other. In this paper, we propose a new framework for designing such 1-factorizations, by which we solve a nontrivial case where t=2t=2 and vv is an odd prime power. We also revisit two classic constructions for the case v=2t+1v=2t+1 --- the \emph{lexical factorization} and \emph{modular factorization}. We provide their simplified definitions and study their inner structures. As a result, an optimal algorithm is designed for computing the lexical factorizations. (An analogous algorithm for the modular factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a odd prime powe

    Distance-regular graphs

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    This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
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