756 research outputs found
Statistical Multiparty Computation Based on Random Walks on Graphs
With respect to a special class of access structures based on connectivity of graphs, we start from a linear secret sharing scheme
and turn it into a secret sharing scheme with perfect security and exponentially small error probability by randomizing the
reconstruction algorithm through random walks on graphs. It reduces the polynomial work space to logarithmic. Then we build the corresponding statistical multiparty computation protocol by using the secret sharing scheme. The results of this paper also imply the inherent connections and influences among secret sharing, randomized algorithms, and secure multi-party computation
Interconnection network with a shared whiteboard: Impact of (a)synchronicity on computing power
In this work we study the computational power of graph-based models of
distributed computing in which each node additionally has access to a global
whiteboard. A node can read the contents of the whiteboard and, when activated,
can write one message of O(log n) bits on it. When the protocol terminates,
each node computes the output based on the final contents of the whiteboard. We
consider several scheduling schemes for nodes, providing a strict ordering of
their power in terms of the problems which can be solved with exactly one
activation per node. The problems used to separate the models are related to
Maximal Independent Set, detection of cycles of length 4, and BFS spanning tree
constructions
On total communication complexity of collapsing protocols for pointer jumping problem
This paper focuses on bounding the total communication complexity of
collapsing protocols for multiparty pointer jumping problem (). Brody
and Chakrabati in \cite{bc08} proved that in such setting one of the players
must communicate at least bits. Liang in \cite{liang} has
shown protocol matching this lower bound on maximum complexity. His protocol,
however, was behaving worse than the trivial one in terms of total complexity
(number of bits sent by all players). He conjectured that achieving total
complexity better then the trivial one is impossible. In this paper we prove
this conjecture. Namely, we show that for a collapsing protocol for ,
the total communication complexity is at least which closes the gap
between lower and upper bound for total complexity of in collapsing
setting
Localizing genuine multiparty entanglement in noisy stabilizer states
Characterizing large noisy multiparty quantum states using genuine multiparty
entanglement is a challenging task. In this paper, we calculate lower bounds of
genuine multiparty entanglement localized over a chosen multiparty subsystem of
multi-qubit stabilizer states in the noiseless and noisy scenario. In the
absence of noise, adopting a graph-based technique, we perform the calculation
for arbitrary graph states as representatives of the stabilizer states, and
show that the graph operations required for the calculation has a polynomial
scaling with the system size. As demonstrations, we compute the localized
genuine multiparty entanglement over subsystems of large graphs having linear,
ladder, and square structures. We also extend the calculation for graph states
subjected to single-qubit Markovian or non-Markovian Pauli noise on all qubits,
and demonstrate, for a specific lower bound of the localizable genuine
multiparty entanglement corresponding to a specific Pauli measurement setup,
the existence of a critical noise strength beyond which all of the post
measured states are biseparable. The calculation is also useful for arbitrary
large stabilizer states under noise due to the local unitary connection between
stabilizer states and graph states. We demonstrate this by considering a toric
code defined on a square lattice, and computing a lower bound of localizable
genuine multiparty entanglement over a non-trivial loop of the code. Similar to
the graph states, we show the existence of the critical noise strength in this
case also, and discuss its interesting features.Comment: 36 pages, 21 figures, 2 table
Exploring Differential Obliviousness
In a recent paper, Chan et al. [SODA \u2719] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM \u2796] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures.
In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness
Liquidity in Credit Networks with Constrained Agents
In order to scale transaction rates for deployment across the global web,
many cryptocurrencies have deployed so-called "Layer-2" networks of private
payment channels. An idealized payment network behaves like a Credit Network, a
model for transactions across a network of bilateral trust relationships.
Credit Networks capture many aspects of traditional currencies as well as new
virtual currencies and payment mechanisms. In the traditional credit network
model, if an agent defaults, every other node that trusted it is vulnerable to
loss. In a cryptocurrency context, trust is manufactured by capital deposits,
and thus there arises a natural tradeoff between network liquidity (i.e. the
fraction of transactions that succeed) and the cost of capital deposits.
In this paper, we introduce constraints that bound the total amount of loss
that the rest of the network can suffer if an agent (or a set of agents) were
to default - equivalently, how the network changes if agents can support
limited solvency guarantees.
We show that these constraints preserve the analytical structure of a credit
network. Furthermore, we show that aggregate borrowing constraints greatly
simplify the network structure and in the payment network context achieve the
optimal tradeoff between liquidity and amount of escrowed capital.Comment: To be published in TheWebConf 202
- âŠ