1,911 research outputs found
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
Making Asynchronous Distributed Computations Robust to Channel Noise
We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating a maximal corruption level of Theta(1/n)-fraction of all messages. Our noise tolerance is optimal and is obtained with only a moderate overhead in the number of messages.
Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.
Overcoming this more realistic setting of an unknown topology leads to intriguing distributed problems, in which nodes try to learn sufficient information about the network topology in order to perform efficient coding and routing operations for coping with the noise. What makes these problems hard is that these topology exploration computations themselves must already be robust to noise
Noisy Beeping Networks
We introduce noisy beeping networks, where nodes have limited communication
capabilities, namely, they can only emit energy or sense the channel for
energy. Furthermore, imperfections may cause devices to malfunction with some
fixed probability when sensing the channel, which amounts to deducing a noisy
received transmission. Such noisy networks have implications for
ultra-lightweight sensor networks and biological systems.
We show how to compute tasks in a noise-resilient manner over noisy beeping
networks of arbitrary structure. In particular, we transform any algorithm that
assumes a noiseless beeping network (of size ) into a noise-resilient
version while incurring a multiplicative overhead of only in its
round complexity, with high probability. We show that our coding is optimal for
some tasks, such as node-coloring of a clique.
We further show how to simulate a large family of algorithms designed for
distributed networks in the CONGEST() model over a noisy beeping network.
The simulation succeeds with high probability and incurs an asymptotic
multiplicative overhead of in the
round complexity, where is the maximal degree of the network. The
overhead is tight for certain graphs, e.g., a clique. Further, this simulation
implies a constant overhead coding for constant-degree networks
Interactive Coding Resilient to an Unknown Number of Erasures
We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our setting is arbitrary and a priori unknown to the parties.
We develop interactive coding schemes that adapt to the actual level of noise and correctly execute any two-party computation. Namely, in case the channel erases T transmissions, the coding scheme will take N+2T transmissions using an alphabet of size 4 (alternatively, using 2N+4T transmissions over a binary channel) to correctly simulate any binary protocol that takes N transmissions assuming a noiseless channel. We can further reduce the communication to N+T by relaxing the communication model and allowing parties to remain silent rather than forcing them to communicate in every round of the coding scheme.
Our coding schemes are efficient, deterministic, have linear overhead both in their communication and round complexity, and succeed (with probability 1) regardless of the number of erasures T
Protecting Single-Hop Radio Networks from Message Drops
Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the n participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic message drops (i.e., erasures), where in every round, the message received by each party is erased (replaced by ?) with some small constant probability, independently.
Our main result is a constant rate coding scheme, allowing one to run protocols designed to work over the (noiseless) SHRN model over the SHRN model with erasures. Our scheme converts any protocol ? of length at most exponential in n over the SHRN model to a protocol ?\u27 that is resilient to constant fraction of erasures and has length linear in the length of ?.
We mention that for the special case where the protocol ? is non-adaptive, i.e., the order of communication is fixed in advance, such a scheme was known. Nevertheless, adaptivity is widely used and is known to hugely boost the power of wireless channels, which makes handling the general case of adaptive protocols ? both important and more challenging. Indeed, to the best of our knowledge, our result is the first constant rate scheme that converts adaptive protocols to noise resilient ones in any multi-party model
The Adversarial Noise Threshold for Distributed Protocols
We consider the problem of implementing distributed protocols, despite
adversarial channel errors, on synchronous-messaging networks with arbitrary
topology.
In our first result we show that any -party -round protocol on an
undirected communication network can be compiled into a robust simulation
protocol on a sparse ( edges) subnetwork so that the simulation
tolerates an adversarial error rate of ; the
simulation has a round complexity of , where is the number of edges in . (So the simulation is
work-preserving up to a factor.) The adversary's error rate is within a
constant factor of optimal. Given the error rate, the round complexity blowup
is within a factor of of optimal, where is the edge
connectivity of . We also determine that the maximum tolerable error rate on
directed communication networks is where is the number of
edges in a minimum equivalent digraph.
Next we investigate adversarial per-edge error rates, where the adversary is
given an error budget on each edge of the network. We determine the exact limit
for tolerable per-edge error rates on an arbitrary directed graph. However, the
construction that approaches this limit has exponential round complexity, so we
give another compiler, which transforms -round protocols into
-round simulations, and prove that for polynomial-query black
box compilers, the per-edge error rate tolerated by this last compiler is
within a constant factor of optimal.Comment: 23 pages, 2 figures. Fixes mistake in theorem 6 and various typo
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