577 research outputs found
How Long It Takes for an Ordinary Node with an Ordinary ID to Output?
In the context of distributed synchronous computing, processors perform in
rounds, and the time-complexity of a distributed algorithm is classically
defined as the number of rounds before all computing nodes have output. Hence,
this complexity measure captures the running time of the slowest node(s). In
this paper, we are interested in the running time of the ordinary nodes, to be
compared with the running time of the slowest nodes. The node-averaged
time-complexity of a distributed algorithm on a given instance is defined as
the average, taken over every node of the instance, of the number of rounds
before that node output. We compare the node-averaged time-complexity with the
classical one in the standard LOCAL model for distributed network computing. We
show that there can be an exponential gap between the node-averaged
time-complexity and the classical time-complexity, as witnessed by, e.g.,
leader election. Our first main result is a positive one, stating that, in
fact, the two time-complexities behave the same for a large class of problems
on very sparse graphs. In particular, we show that, for LCL problems on cycles,
the node-averaged time complexity is of the same order of magnitude as the
slowest node time-complexity.
In addition, in the LOCAL model, the time-complexity is computed as a worst
case over all possible identity assignments to the nodes of the network. In
this paper, we also investigate the ID-averaged time-complexity, when the
number of rounds is averaged over all possible identity assignments. Our second
main result is that the ID-averaged time-complexity is essentially the same as
the expected time-complexity of randomized algorithms (where the expectation is
taken over all possible random bits used by the nodes, and the number of rounds
is measured for the worst-case identity assignment).
Finally, we study the node-averaged ID-averaged time-complexity.Comment: (Submitted) Journal versio
A new method for constructing small-bias spaces from Hermitian codes
We propose a new method for constructing small-bias spaces through a
combination of Hermitian codes. For a class of parameters our multisets are
much faster to construct than what can be achieved by use of the traditional
algebraic geometric code construction. So, if speed is important, our
construction is competitive with all other known constructions in that region.
And if speed is not a matter of interest the small-bias spaces of the present
paper still perform better than the ones related to norm-trace codes reported
in [12]
Unifying computational entropies via Kullback-Leibler divergence
We introduce hardness in relative entropy, a new notion of hardness for
search problems which on the one hand is satisfied by all one-way functions and
on the other hand implies both next-block pseudoentropy and inaccessible
entropy, two forms of computational entropy used in recent constructions of
pseudorandom generators and statistically hiding commitment schemes,
respectively. Thus, hardness in relative entropy unifies the latter two notions
of computational entropy and sheds light on the apparent "duality" between
them. Additionally, it yields a more modular and illuminating proof that
one-way functions imply next-block inaccessible entropy, similar in structure
to the proof that one-way functions imply next-block pseudoentropy (Vadhan and
Zheng, STOC '12)
Privacy-Preserving Distance Computation and Proximity Testing on Earth, Done Right
In recent years, the availability of GPS-enabled smartphones have made location-based services extremely popular. A multitude of applications rely on location information to provide a wide range of services. Location information is, however, extremely sensitive and can be easily abused. In this paper, we introduce the first protocols for secure computation of distance and for proximity testing over a sphere. Our secure distance protocols allow two parties, Alice and Bob, to determine their mutual distance without disclosing any additional information about their location. Through our secure proximity testing protocols, Alice only learns if Bob is in close proximity, i.e., within some arbitrary distance. Our techniques rely on three different representations of Earth, which provide different trade-os between accuracy and performance. We show, via experiments on a prototype implementation, that our protocols are practical on resource- constrained smartphone devices. Our distance computation protocols runs, in fact, in 54 to 78 ms on a commodity Android smartphone. Similarly, our proximity tests require between 1.2 s and 2.8 s on the same platform. The imprecision introduced by our protocols is very small, i.e., between 0.1% and 3% on average, depending on the distance
Pseudorandomness for Regular Branching Programs via Fourier Analysis
We present an explicit pseudorandom generator for oblivious, read-once,
permutation branching programs of constant width that can read their input bits
in any order. The seed length is , where is the length of the
branching program. The previous best seed length known for this model was
, which follows as a special case of a generator due to
Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of
for arbitrary branching programs of size ). Our techniques
also give seed length for general oblivious, read-once branching
programs of width , which is incomparable to the results of
Impagliazzo et al.Our pseudorandom generator is similar to the one used by
Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite
different; ours is based on Fourier analysis of branching programs. In
particular, we show that an oblivious, read-once, regular branching program of
width has Fourier mass at most at level , independent of the
length of the program.Comment: RANDOM 201
Nonlinear spectral calculus and super-expanders
Nonlinear spectral gaps with respect to uniformly convex normed spaces are
shown to satisfy a spectral calculus inequality that establishes their decay
along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to
behave sub-multiplicatively under zigzag products. These results yield a
combinatorial construction of super-expanders, i.e., a sequence of 3-regular
graphs that does not admit a coarse embedding into any uniformly convex normed
space.Comment: Typos fixed based on referee comments. Some of the results of this
paper were announced in arXiv:0910.2041. The corresponding parts of
arXiv:0910.2041 are subsumed by the current pape
Public-Key Encryption Schemes with Auxiliary Inputs
7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland, February 9-11, 2010. ProceedingsWe construct public-key cryptosystems that remain secure even when the adversary is given any computationally uninvertible function of the secret key as auxiliary input (even one that may reveal the secret key information-theoretically). Our schemes are based on the decisional Diffie-Hellman (DDH) and the Learning with Errors (LWE) problems.
As an independent technical contribution, we extend the Goldreich-Levin theorem to provide a hard-core (pseudorandom) value over large fields.National Science Foundation (U.S.) (Grant CCF-0514167)National Science Foundation (U.S.) (Grant CCF-0635297)National Science Foundation (U.S.) (Grant NSF-0729011)Israel Science Foundation (700/08)Chais Family Fellows Progra
A Framework for Adversarially Robust Streaming Algorithms
We investigate the adversarial robustness of streaming algorithms. In this
context, an algorithm is considered robust if its performance guarantees hold
even if the stream is chosen adaptively by an adversary that observes the
outputs of the algorithm along the stream and can react in an online manner.
While deterministic streaming algorithms are inherently robust, many central
problems in the streaming literature do not admit sublinear-space deterministic
algorithms; on the other hand, classical space-efficient randomized algorithms
for these problems are generally not adversarially robust. This raises the
natural question of whether there exist efficient adversarially robust
(randomized) streaming algorithms for these problems.
In this work, we show that the answer is positive for various important
streaming problems in the insertion-only model, including distinct elements and
more generally -estimation, -heavy hitters, entropy estimation, and
others. For all of these problems, we develop adversarially robust
-approximation algorithms whose required space matches that of
the best known non-robust algorithms up to a multiplicative factor (and in some cases even up to a constant
factor). Towards this end, we develop several generic tools allowing one to
efficiently transform a non-robust streaming algorithm into a robust one in
various scenarios.Comment: Conference version in PODS 2020. Version 3 addressing journal
referees' comments; improved exposition of sketch switchin
Efficient online weighted multi-level paging
We study the writeback-aware caching problem, a variant of classic paging where paging requests that modify data and requests that leave data intact are treated differently. We give an O(log^2 k) competitive randomized algorithm, answering an open question of Beckmann et al. [8] and Even et
Chosen-ciphertext security from subset sum
We construct a public-key encryption (PKE) scheme whose
security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012
- …