4,624 research outputs found
Lattice-Based proof of a shuffle
In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft
A discrete, unitary, causal theory of quantum gravity
A discrete model of Lorentzian quantum gravity is proposed. The theory is
completely background free, containing no reference to absolute space, time, or
simultaneity. The states at one slice of time are networks in which each vertex
is labelled with two arrows, which point along an adjacent edge, or to the
vertex itself. The dynamics is specified by a set of unitary replacement rules,
which causally propagate the local degrees of freedom. The inner product
between any two states is given by a sum over histories. Assuming it converges
(or can be Abel resummed), this inner product is proven to be hermitian and
fully gauge-degenerate under spacetime diffeomorphisms. At least for states
with a finite past, the inner product is also positive. This allows a Hilbert
space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4
expanded prospects sectio
Overlapping stochastic block models with application to the French political blogosphere
Complex systems in nature and in society are often represented as networks,
describing the rich set of interactions between objects of interest. Many
deterministic and probabilistic clustering methods have been developed to
analyze such structures. Given a network, almost all of them partition the
vertices into disjoint clusters, according to their connection profile.
However, recent studies have shown that these techniques were too restrictive
and that most of the existing networks contained overlapping clusters. To
tackle this issue, we present in this paper the Overlapping Stochastic Block
Model. Our approach allows the vertices to belong to multiple clusters, and, to
some extent, generalizes the well-known Stochastic Block Model [Nowicki and
Snijders (2001)]. We show that the model is generically identifiable within
classes of equivalence and we propose an approximate inference procedure, based
on global and local variational techniques. Using toy data sets as well as the
French Political Blogosphere network and the transcriptional network of
Saccharomyces cerevisiae, we compare our work with other approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS382 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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