2,163 research outputs found
On the Efficiency of Classical and Quantum Secure Function Evaluation
We provide bounds on the efficiency of secure one-sided output two-party
computation of arbitrary finite functions from trusted distributed randomness
in the statistical case. From these results we derive bounds on the efficiency
of protocols that use different variants of OT as a black-box. When applied to
implementations of OT, these bounds generalize most known results to the
statistical case. Our results hold in particular for transformations between a
finite number of primitives and for any error. In the second part we study the
efficiency of quantum protocols implementing OT. While most classical lower
bounds for perfectly secure reductions of OT to distributed randomness still
hold in the quantum setting, we present a statistically secure protocol that
violates these bounds by an arbitrarily large factor. We then prove a weaker
lower bound that does hold in the statistical quantum setting and implies that
even quantum protocols cannot extend OT. Finally, we present two lower bounds
for reductions of OT to commitments and a protocol based on string commitments
that is optimal with respect to both of these bounds
Strong connections between quantum encodings, non-locality and quantum cryptography
Encoding information in quantum systems can offer surprising advantages but
at the same time there are limitations that arise from the fact that measuring
an observable may disturb the state of the quantum system. In our work, we
provide an in-depth analysis of a simple question: What happens when we perform
two measurements sequentially on the same quantum system? This question touches
upon some fundamental properties of quantum mechanics, namely the uncertainty
principle and the complementarity of quantum measurements. Our results have
interesting consequences, for example they can provide a simple proof of the
optimal quantum strategy in the famous Clauser-Horne-Shimony-Holt game.
Moreover, we show that the way information is encoded in quantum systems can
provide a different perspective in understanding other fundamental aspects of
quantum information, like non-locality and quantum cryptography. We prove some
strong equivalences between these notions and provide a number of applications
in all areas.Comment: Version 3. Previous title: "Oblivious transfer, the CHSH game, and
quantum encodings
Converses for Secret Key Agreement and Secure Computing
We consider information theoretic secret key agreement and secure function
computation by multiple parties observing correlated data, with access to an
interactive public communication channel. Our main result is an upper bound on
the secret key length, which is derived using a reduction of binary hypothesis
testing to multiparty secret key agreement. Building on this basic result, we
derive new converses for multiparty secret key agreement. Furthermore, we
derive converse results for the oblivious transfer problem and the bit
commitment problem by relating them to secret key agreement. Finally, we derive
a necessary condition for the feasibility of secure computation by trusted
parties that seek to compute a function of their collective data, using an
interactive public communication that by itself does not give away the value of
the function. In many cases, we strengthen and improve upon previously known
converse bounds. Our results are single-shot and use only the given joint
distribution of the correlated observations. For the case when the correlated
observations consist of independent and identically distributed (in time)
sequences, we derive strong versions of previously known converses
Assisted Common Information: Further Results
We presented assisted common information as a generalization of
G\'acs-K\"orner (GK) common information at ISIT 2010. The motivation for our
formulation was to improve upperbounds on the efficiency of protocols for
secure two-party sampling (which is a form of secure multi-party computation).
Our upperbound was based on a monotonicity property of a rate-region (called
the assisted residual information region) associated with the assisted common
information formulation. In this note we present further results. We explore
the connection of assisted common information with the Gray-Wyner system. We
show that the assisted residual information region and the Gray-Wyner region
are connected by a simple relationship: the assisted residual information
region is the increasing hull of the Gray-Wyner region under an affine map.
Several known relationships between GK common information and Gray-Wyner system
fall out as consequences of this. Quantities which arise in other source coding
contexts acquire new interpretations. In previous work we showed that assisted
common information can be used to derive upperbounds on the rate at which a
pair of parties can {\em securely sample} correlated random variables, given
correlated random variables from another distribution. Here we present an
example where the bound derived using assisted common information is much
better than previously known bounds, and in fact is tight. This example
considers correlated random variables defined in terms of standard variants of
oblivious transfer, and is interesting on its own as it answers a natural
question about these cryptographic primitives.Comment: 8 pages, 3 figures, 1 appendix; to be presented at the IEEE
International Symposium on Information Theory, 201
Tight bounds for classical and quantum coin flipping
Coin flipping is a cryptographic primitive for which strictly better
protocols exist if the players are not only allowed to exchange classical, but
also quantum messages. During the past few years, several results have appeared
which give a tight bound on the range of implementable unconditionally secure
coin flips, both in the classical as well as in the quantum setting and for
both weak as well as strong coin flipping. But the picture is still incomplete:
in the quantum setting, all results consider only protocols with perfect
correctness, and in the classical setting tight bounds for strong coin flipping
are still missing. We give a general definition of coin flipping which unifies
the notion of strong and weak coin flipping (it contains both of them as
special cases) and allows the honest players to abort with a certain
probability. We give tight bounds on the achievable range of parameters both in
the classical and in the quantum setting.Comment: 18 pages, 2 figures; v2: published versio
Finite-state Strategies in Delay Games (full version)
What is a finite-state strategy in a delay game? We answer this surprisingly
non-trivial question by presenting a very general framework that allows to
remove delay: finite-state strategies exist for all winning conditions where
the resulting delay-free game admits a finite-state strategy. The framework is
applicable to games whose winning condition is recognized by an automaton with
an acceptance condition that satisfies a certain aggregation property. Our
framework also yields upper bounds on the complexity of determining the winner
of such delay games and upper bounds on the necessary lookahead to win the
game. In particular, we cover all previous results of that kind as special
cases of our uniform approach
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