4,640 research outputs found
Practical sharing of quantum secrets over untrusted channels
In this work we address the issue of sharing a quantum secret over untrusted
channels between the dealer and players. Existing methods require entanglement
over a number of systems which scales with the security parameter, quickly
becoming impractical. We present protocols (interactive and a non-interactive)
where single copy encodings are sufficient. Our protocols work for all quantum
secret sharing schemes and access structures, and are implementable with
current experimental set ups. For a single authorised player, our protocols act
as quantum authentication protocols
Matroids and Quantum Secret Sharing Schemes
A secret sharing scheme is a cryptographic protocol to distribute a secret
state in an encoded form among a group of players such that only authorized
subsets of the players can reconstruct the secret. Classically, efficient
secret sharing schemes have been shown to be induced by matroids. Furthermore,
access structures of such schemes can be characterized by an excluded minor
relation. No such relations are known for quantum secret sharing schemes. In
this paper we take the first steps toward a matroidal characterization of
quantum secret sharing schemes. In addition to providing a new perspective on
quantum secret sharing schemes, this characterization has important benefits.
While previous work has shown how to construct quantum secret sharing schemes
for general access structures, these schemes are not claimed to be efficient.
In this context the present results prove to be useful; they enable us to
construct efficient quantum secret sharing schemes for many general access
structures. More precisely, we show that an identically self-dual matroid that
is representable over a finite field induces a pure state quantum secret
sharing scheme with information rate one
Key Generation in Wireless Sensor Networks Based on Frequency-selective Channels - Design, Implementation, and Analysis
Key management in wireless sensor networks faces several new challenges. The
scale, resource limitations, and new threats such as node capture necessitate
the use of an on-line key generation by the nodes themselves. However, the cost
of such schemes is high since their secrecy is based on computational
complexity. Recently, several research contributions justified that the
wireless channel itself can be used to generate information-theoretic secure
keys. By exchanging sampling messages during movement, a bit string can be
derived that is only known to the involved entities. Yet, movement is not the
only possibility to generate randomness. The channel response is also strongly
dependent on the frequency of the transmitted signal. In our work, we introduce
a protocol for key generation based on the frequency-selectivity of channel
fading. The practical advantage of this approach is that we do not require node
movement. Thus, the frequent case of a sensor network with static motes is
supported. Furthermore, the error correction property of the protocol mitigates
the effects of measurement errors and other temporal effects, giving rise to an
agreement rate of over 97%. We show the applicability of our protocol by
implementing it on MICAz motes, and evaluate its robustness and secrecy through
experiments and analysis.Comment: Submitted to IEEE Transactions on Dependable and Secure Computin
How to share a quantum secret
We investigate the concept of quantum secret sharing. In a ((k,n)) threshold
scheme, a secret quantum state is divided into n shares such that any k of
those shares can be used to reconstruct the secret, but any set of k-1 or fewer
shares contains absolutely no information about the secret. We show that the
only constraint on the existence of threshold schemes comes from the quantum
"no-cloning theorem", which requires that n < 2k, and, in all such cases, we
give an efficient construction of a ((k,n)) threshold scheme. We also explore
similarities and differences between quantum secret sharing schemes and quantum
error-correcting codes. One remarkable difference is that, while most existing
quantum codes encode pure states as pure states, quantum secret sharing schemes
must use mixed states in some cases. For example, if k <= n < 2k-1 then any
((k,n)) threshold scheme must distribute information that is globally in a
mixed state.Comment: 5 pages, REVTeX, submitted to PR
Belief-Invariant and Quantum Equilibria in Games of Incomplete Information
Drawing on ideas from game theory and quantum physics, we investigate
nonlocal correlations from the point of view of equilibria in games of
incomplete information. These equilibria can be classified in decreasing power
as general communication equilibria, belief-invariant equilibria and correlated
equilibria, all of which contain the familiar Nash equilibria. The notion of
belief-invariant equilibrium has appeared in game theory before, in the 1990s.
However, the class of non-signalling correlations associated to
belief-invariance arose naturally already in the 1980s in the foundations of
quantum mechanics.
Here, we explain and unify these two origins of the idea and study the above
classes of equilibria, and furthermore quantum correlated equilibria, using
tools from quantum information but the language of game theory. We present a
general framework of belief-invariant communication equilibria, which contains
(quantum) correlated equilibria as special cases. It also contains the theory
of Bell inequalities, a question of intense interest in quantum mechanics, and
quantum games where players have conflicting interests, a recent topic in
physics.
We then use our framework to show new results related to social welfare.
Namely, we exhibit a game where belief-invariance is socially better than
correlated equilibria, and one where all non-belief-invariant equilibria are
socially suboptimal. Then, we show that in some cases optimal social welfare is
achieved by quantum correlations, which do not need an informed mediator to be
implemented. Furthermore, we illustrate potential practical applications: for
instance, situations where competing companies can correlate without exposing
their trade secrets, or where privacy-preserving advice reduces congestion in a
network. Along the way, we highlight open questions on the interplay between
quantum information, cryptography, and game theory
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