565 research outputs found
From Graphs to Keyed Quantum Hash Functions
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
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
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 - designs. For this class of
highly regular graphs, we obtain a worst-case running time of for bounded parameters . In a first step, our approach
makes use of the Babai--Luks algorithm to compute canonical forms of
-designs. In a second step, we show that -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
We consider network graphs 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
It is a challenging open problem to construct an explicit 1-factorization of
the bipartite Kneser graph , which contains as vertices all -element
and -element subsets of 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 and is an odd prime power. We also revisit two classic
constructions for the case --- 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
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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