1,235 research outputs found
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
Secure and linear cryptosystems using error-correcting codes
A public-key cryptosystem, digital signature and authentication procedures
based on a Gallager-type parity-check error-correcting code are presented. The
complexity of the encryption and the decryption processes scale linearly with
the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted
by Bob, whereas a private-noise added by Alice to a given fraction of the
ciphertext of each encrypted plaintext serves to increase the secure channel
and is the cornerstone for digital signatures and authentication. Various
scenarios are discussed including the possible actions of the opponent Oscar as
an eavesdropper or as a disruptor
On Unconditionally Secure Distributed Oblivious Transfer.
This paper is about the Oblivious Transfer in the distributed model proposed by M.
Naor and B. Pinkas. In this setting a Sender has n secrets and a Receiver is interested
in one of them. During a set up phase, the Sender gives information about the secrets to
m Servers. Afterwards, in a recovering phase, the Receiver can compute the secret she
wishes by interacting with any k of them. More precisely, from the answers received she
computes the secret in which she is interested but she gets no information on the others
and, at the same time, any coalition of k â 1 Servers can neither compute any secret nor
ïŹgure out which one the Receiver has recovered.
We present an analysis and new results holding for this model: lower bounds on
the resources required to implement such a scheme (i.e., randomness, memory storage,
communication complexity); some impossibility results for one-round distributed oblivi-
ous transfer protocols; two polynomial-based constructions implementing 1-out-of-n dis-
tributed oblivious transfer, which generalize and strengthen the two constructions for
1-out-of-2 given by Naor and Pinkas; as well as new one-round and two-round distributed
oblivious transfer protocols, both for threshold and general access structures on the set
of Servers, which are optimal with respect to some of the given bounds. Most of these
constructions are basically combinatorial in nature
Secure exchange of information by synchronization of neural networks
A connection between the theory of neural networks and cryptography is
presented. A new phenomenon, namely synchronization of neural networks is
leading to a new method of exchange of secret messages. Numerical simulations
show that two artificial networks being trained by Hebbian learning rule on
their mutual outputs develop an antiparallel state of their synaptic weights.
The synchronized weights are used to construct an ephemeral key exchange
protocol for a secure transmission of secret data. It is shown that an opponent
who knows the protocol and all details of any transmission of the data has no
chance to decrypt the secret message, since tracking the weights is a hard
problem compared to synchronization. The complexity of the generation of the
secure channel is linear with the size of the network.Comment: 11 pages, 5 figure
Quantum Nondemolition Monitoring of Universal Quantum Computers
The halt scheme for quantum Turing machines, originally proposed by Deutsch,
is reformulated precisely and is proved to work without spoiling the
computation. The ``conflict'' pointed out recently by Myers in the definition
of a universal quantum computer is shown to be only apparent. In the context of
quantum nondemolition (QND) measurement, it is also shown that the output
observable, an observable representing the output of the computation, is a QND
observable and that the halt scheme is equivalent to the QND monitoring of the
output observable.Comment: 5 pages, RevTeX, no figures, revised, to appear in Phys. Rev. Let
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Responses of non-native earthworms to experimental eradication of garlic mustard and implications for native vegetation
Recent studies in invasion biology suggest that positive feedback among two or more introduced organisms facilitate establishment within a new range and drive changes in native plant communities. Here, we experimentally tested for relationships between native plants and two nonânative organisms invading forest habitats in North America: garlic mustard (Alliaria petiolata, Brassicaceae) and earthworms. In two forested sites, we compared understory vegetation and earthworm biomass in plots where garlic mustard was removed for three years, plots without garlic mustard invasion, and plots invaded by garlic mustard that was not removed. Earthworm biomass was highest in the plots with garlic mustard, and longâterm eradication of garlic mustard reduced earthworm biomass to levels similar to those observed in the uninvaded control plots. Invasion treatment, and the interactions between earthworm biomass and treatment, explained most of the variation in plant community composition and diversityâsuggesting that earthworms alone do not necessarily drive forest understory floristic patterns. In contrast to broader geographic patterns indicating earthworms as the main driver of vegetation change in the presence of nonânative plants, we show that garlic mustard solely, or in conjunction with earthworm biomass, drives changes in native plant composition and diversity at the scale of individual forests. From a local management perspective, our data suggest that garlic mustard eradication can directly assist in the conservation of native plant communities and simultaneously reduce earthworm biomass
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance
Implementing Shor's algorithm on Josephson Charge Qubits
We investigate the physical implementation of Shor's factorization algorithm
on a Josephson charge qubit register. While we pursue a universal method to
factor a composite integer of any size, the scheme is demonstrated for the
number 21. We consider both the physical and algorithmic requirements for an
optimal implementation when only a small number of qubits is available. These
aspects of quantum computation are usually the topics of separate research
communities; we present a unifying discussion of both of these fundamental
features bridging Shor's algorithm to its physical realization using Josephson
junction qubits. In order to meet the stringent requirements set by a short
decoherence time, we accelerate the algorithm by decomposing the quantum
circuit into tailored two- and three-qubit gates and we find their physical
realizations through numerical optimization.Comment: 12 pages, submitted to Phys. Rev.
Bounded-Collusion IBE from Key Homomorphism
In this work, we show how to construct IBE schemes that are secure against a bounded number of collusions, starting with underlying PKE schemes which possess linear homomorphisms over their keys. In particular, this enables us to exhibit a new (bounded-collusion) IBE construction based on the quadratic residuosity assumption, without any need to assume the existence of random oracles. The new IBEâs public parameters are of size O(tλlogI) where I is the total number of identities which can be supported by the system, t is the number of collusions which the system is secure against, and λ is a security parameter. While the number of collusions is bounded, we note that an exponential number of total identities can be supported.
More generally, we give a transformation that takes any PKE satisfying Linear Key Homomorphism, Identity Map Compatibility, and the Linear Hash Proof Property and translates it into an IBE secure against bounded collusions. We demonstrate that these properties are more general than our quadratic residuosity-based scheme by showing how a simple PKE based on the DDH assumption also satisfies these properties.National Science Foundation (U.S.) (NSF CCF-0729011)National Science Foundation (U.S.) (NSF CCF-1018064)United States. Defense Advanced Research Projects Agency (DARPA FA8750-11-2-0225
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