7,448 research outputs found
The Optimal Single Copy Measurement for the Hidden Subgroup Problem
The optimization of measurements for the state distinction problem has
recently been applied to the theory of quantum algorithms with considerable
successes, including efficient new quantum algorithms for the non-abelian
hidden subgroup problem. Previous work has identified the optimal single copy
measurement for the hidden subgroup problem over abelian groups as well as for
the non-abelian problem in the setting where the subgroups are restricted to be
all conjugate to each other. Here we describe the optimal single copy
measurement for the hidden subgroup problem when all of the subgroups of the
group are given with equal a priori probability. The optimal measurement is
seen to be a hybrid of the two previously discovered single copy optimal
measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe
Hash First, Argue Later: Adaptive Verifiable Computations on Outsourced Data
Proof systems for verifiable computation (VC) have the potential to make cloud outsourcing more trustworthy. Recent schemes enable a verifier with limited resources to delegate large computations and verify their outcome based on succinct arguments: verification complexity is linear in the size of the inputs and outputs (not the size of the computation). However, cloud computing also often involves large amounts of data, which may exceed the local storage and I/O capabilities of the verifier, and thus limit the use of VC.
In this paper, we investigate multi-relation hash & prove schemes for verifiable computations that operate on succinct data hashes. Hence, the verifier delegates both storage and computation to an untrusted worker. She uploads data and keeps hashes; exchanges hashes with other parties; verifies arguments that consume and produce hashes; and selectively downloads the actual data she needs to access.
Existing instantiations that fit our definition either target restricted classes of computations or employ relatively inefficient techniques. Instead, we propose efficient constructions that lift classes of existing arguments schemes for fixed relations to multi-relation hash & prove schemes. Our schemes (1) rely on hash algorithms that run linearly in the size of the input; (2) enable constant-time verification of arguments on hashed inputs; (3) incur minimal overhead for the prover. Their main benefit is to amortize the linear cost for the verifier across all relations with shared I/O. Concretely, compared to solutions that can be obtained from prior work, our new hash & prove constructions yield a 1,400x speed-up for provers. We also explain how to further reduce the linear verification costs by partially outsourcing the hash computation itself, obtaining a 480x speed-up when applied to existing VC schemes, even on single-relation executions
Provenance Views for Module Privacy
Scientific workflow systems increasingly store provenance information about
the module executions used to produce a data item, as well as the parameter
settings and intermediate data items passed between module executions. However,
authors/owners of workflows may wish to keep some of this information
confidential. In particular, a module may be proprietary, and users should not
be able to infer its behavior by seeing mappings between all data inputs and
outputs. The problem we address in this paper is the following: Given a
workflow, abstractly modeled by a relation R, a privacy requirement \Gamma and
costs associated with data. The owner of the workflow decides which data
(attributes) to hide, and provides the user with a view R' which is the
projection of R over attributes which have not been hidden. The goal is to
minimize the cost of hidden data while guaranteeing that individual modules are
\Gamma -private. We call this the "secureview" problem. We formally define the
problem, study its complexity, and offer algorithmic solutions
Every Bit Counts in Consensus
Consensus enables n processes to agree on a common valid L-bit value, despite
t < n/3 processes being faulty and acting arbitrarily. A long line of work has
been dedicated to improving the worst-case communication complexity of
consensus in partial synchrony. This has recently culminated in the worst-case
word complexity of O(n^2). However, the worst-case bit complexity of the best
solution is still O(n^2 L + n^2 kappa) (where kappa is the security parameter),
far from the \Omega(n L + n^2) lower bound. The gap is significant given the
practical use of consensus primitives, where values typically consist of
batches of large size (L > n).
This paper shows how to narrow the aforementioned gap while achieving optimal
linear latency. Namely, we present a new algorithm, DARE (Disperse, Agree,
REtrieve), that improves upon the O(n^2 L) term via a novel dispersal
primitive. DARE achieves O(n^{1.5} L + n^{2.5} kappa) bit complexity, an
effective sqrt{n}-factor improvement over the state-of-the-art (when L > n
kappa). Moreover, we show that employing heavier cryptographic primitives,
namely STARK proofs, allows us to devise DARE-Stark, a version of DARE which
achieves the near-optimal bit complexity of O(n L + n^2 poly(kappa)). Both DARE
and DARE-Stark achieve optimal O(n) latency
Hidden Translation and Translating Coset in Quantum Computing
We give efficient quantum algorithms for the problems of Hidden Translation
and Hidden Subgroup in a large class of non-abelian solvable groups including
solvable groups of constant exponent and of constant length derived series. Our
algorithms are recursive. For the base case, we solve efficiently Hidden
Translation in , whenever is a fixed prime. For the induction
step, we introduce the problem Translating Coset generalizing both Hidden
Translation and Hidden Subgroup, and prove a powerful self-reducibility result:
Translating Coset in a finite solvable group is reducible to instances of
Translating Coset in and , for appropriate normal subgroups of
. Our self-reducibility framework combined with Kuperberg's subexponential
quantum algorithm for solving Hidden Translation in any abelian group, leads to
subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in
any solvable group.Comment: Journal version: change of title and several minor update
Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I
Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded
prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009.
The main aims of this contribution are: (i) To suggest a procedure for the
designation of detected EM anomalies as seismogenic ones. We do not expect to
be possible to provide a succinct and solid definition of a pre-seismic EM
emission. Instead, we attempt, through a multidisciplinary analysis, to provide
elements of a definition. (ii) To link the detected MHz and kHz EM anomalies
with equivalent last stages of the L'Aquila earthquake preparation process.
(iii) To put forward physically meaningful arguments to support a way of
quantifying the time to global failure and the identification of distinguishing
features beyond which the evolution towards global failure becomes
irreversible. The whole effort is unfolded in two consecutive parts. We clarify
we try to specify not only whether or not a single EM anomaly is pre-seismic in
itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can
be characterized as pre-seismic one
Breaking the -Bit Barrier: Byzantine Agreement with Polylog Bits Per Party
Byzantine agreement (BA), the task of parties to agree on one of their
input bits in the face of malicious agents, is a powerful primitive that lies
at the core of a vast range of distributed protocols. Interestingly, in
protocols with the best overall communication, the demands of the parties are
highly unbalanced: the amortized cost is bits per party, but some
parties must send bits. In best known balanced protocols, the
overall communication is sub-optimal, with each party communicating . In this work, we ask whether asymmetry is inherent for optimizing
total communication. Our contributions in this line are as follows:
1) We define a cryptographic primitive, succinctly reconstructed distributed
signatures (SRDS), that suffices for constructing balanced BA. We
provide two constructions of SRDS from different cryptographic and Public-Key
Infrastructure (PKI) assumptions.
2) The SRDS-based BA follows a paradigm of boosting from "almost-everywhere"
agreement to full agreement, and does so in a single round. We prove that PKI
setup and cryptographic assumptions are necessary for such protocols in which
every party sends messages.
3) We further explore connections between a natural approach toward attaining
SRDS and average-case succinct non-interactive argument systems (SNARGs) for a
particular type of NP-Complete problems (generalizing Subset-Sum and
Subset-Product).
Our results provide new approaches forward, as well as limitations and
barriers, towards minimizing per-party communication of BA. In particular, we
construct the first two BA protocols with balanced communication,
offering a tradeoff between setup and cryptographic assumptions, and answering
an open question presented by King and Saia (DISC'09)
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