139 research outputs found
Commitment and Oblivious Transfer in the Bounded Storage Model with Errors
The bounded storage model restricts the memory of an adversary in a
cryptographic protocol, rather than restricting its computational power, making
information theoretically secure protocols feasible. We present the first
protocols for commitment and oblivious transfer in the bounded storage model
with errors, i.e., the model where the public random sources available to the
two parties are not exactly the same, but instead are only required to have a
small Hamming distance between themselves. Commitment and oblivious transfer
protocols were known previously only for the error-free variant of the bounded
storage model, which is harder to realize
On the Oblivious Transfer Capacity of Generalized Erasure Channels against Malicious Adversaries
Noisy channels are a powerful resource for cryptography as they can be used
to obtain information-theoretically secure key agreement, commitment and
oblivious transfer protocols, among others. Oblivious transfer (OT) is a
fundamental primitive since it is complete for secure multi-party computation,
and the OT capacity characterizes how efficiently a channel can be used for
obtaining string oblivious transfer. Ahlswede and Csisz\'{a}r (\emph{ISIT'07})
presented upper and lower bounds on the OT capacity of generalized erasure
channels (GEC) against passive adversaries. In the case of GEC with erasure
probability at least 1/2, the upper and lower bounds match and therefore the OT
capacity was determined. It was later proved by Pinto et al. (\emph{IEEE Trans.
Inf. Theory 57(8)}) that in this case there is also a protocol against
malicious adversaries achieving the same lower bound, and hence the OT capacity
is identical for passive and malicious adversaries. In the case of GEC with
erasure probability smaller than 1/2, the known lower bound against passive
adversaries that was established by Ahlswede and Csisz\'{a}r does not match
their upper bound and it was unknown whether this OT rate could be achieved
against malicious adversaries as well. In this work we show that there is a
protocol against malicious adversaries achieving the same OT rate that was
obtained against passive adversaries.
In order to obtain our results we introduce a novel use of interactive
hashing that is suitable for dealing with the case of low erasure probability
()
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
Cryptography in the Bounded-Quantum-Storage Model
This thesis initiates the study of cryptographic protocols in the
bounded-quantum-storage model. On the practical side, simple protocols for
Rabin Oblivious Transfer, 1-2 Oblivious Transfer and Bit Commitment are
presented. No quantum memory is required for honest players, whereas the
protocols can only be broken by an adversary controlling a large amount of
quantum memory. The protocols are efficient, non-interactive and can be
implemented with today's technology.
On the theoretical side, new entropic uncertainty relations involving
min-entropy are established and used to prove the security of protocols
according to new strong security definitions. For instance, in the realistic
setting of Quantum Key Distribution (QKD) against quantum-memory-bounded
eavesdroppers, the uncertainty relation allows to prove the security of QKD
protocols while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries.Comment: PhD Thesis, BRICS, University of Aarhus, Denmark, 128 page
Distributed PCP Theorems for Hardness of Approximation in P
We present a new distributed model of probabilistically checkable proofs
(PCP). A satisfying assignment to a CNF formula is
shared between two parties, where Alice knows , Bob knows
, and both parties know . The goal is to have
Alice and Bob jointly write a PCP that satisfies , while
exchanging little or no information. Unfortunately, this model as-is does not
allow for nontrivial query complexity. Instead, we focus on a non-deterministic
variant, where the players are helped by Merlin, a third party who knows all of
.
Using our framework, we obtain, for the first time, PCP-like reductions from
the Strong Exponential Time Hypothesis (SETH) to approximation problems in P.
In particular, under SETH we show that there are no truly-subquadratic
approximation algorithms for Bichromatic Maximum Inner Product over
{0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate
Regular Expression Matching, and Diameter in Product Metric. All our
inapproximability factors are nearly-tight. In particular, for the first two
problems we obtain nearly-polynomial factors of ; only
-factor lower bounds (under SETH) were known before
Quantum oblivious transfer: a short review
Quantum cryptography is the field of cryptography that explores the quantum
properties of matter. Its aim is to develop primitives beyond the reach of
classical cryptography or to improve on existing classical implementations.
Although much of the work in this field is dedicated to quantum key
distribution (QKD), some important steps were made towards the study and
development of quantum oblivious transfer (QOT). It is possible to draw a
comparison between the application structure of both QKD and QOT primitives.
Just as QKD protocols allow quantum-safe communication, QOT protocols allow
quantum-safe computation. However, the conditions under which QOT is actually
quantum-safe have been subject to a great amount of scrutiny and study. In this
review article, we survey the work developed around the concept of oblivious
transfer in the area of theoretical quantum cryptography, with an emphasis on
some proposed protocols and their security requirements. We review the
impossibility results that daunt this primitive and discuss several quantum
security models under which it is possible to prove QOT security.Comment: 40 pages, 14 figure
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