809,080 research outputs found
Zero-Knowledge Functional Elementary Databases
Zero-knowledge elementary databases (ZK-EDBs) enable a prover to commit a database of key-value pairs and later provide a convincing answer to the query ``send me the value associated with \u27\u27 without revealing any extra knowledge (including the size of ). After its introduction, several works extended it to allow more expressive queries, but the expressiveness achieved so far is still limited: only a relatively simple queries--range queries over the keys and values-- can be handled by known constructions.
In this paper we introduce a new notion called zero knowledge functional elementary databases (ZK-FEDBs), which allows the most general functional queries. Roughly speaking, for any Boolean circuit , ZK-FEDBs allows the ZK-EDB prover to provide convincing answers to the queries of the form ``send me all records in satisfying ,\u27\u27 without revealing any extra knowledge (including the size of ). We present a construction of ZK-FEDBs in the random oracle model and generic group model, whose proof size is only linear in the length of record and the size of query circuit, and is independent of the size of input database .
Our technical constribution is two-fold. Firstly, we introduce a new variant of zero-knowledge sets (ZKS) which supports combined operations on sets, and present a concrete construction that is based on groups with unknown order. Secondly, we develop a tranformation that tranforms the query of Boolean circuit into a query of combined operations on related sets, which may be of independent interest
Instant Zero Knowledge Proof of Reserve
We present two zero knowledge protocols that allow one to assert solvency of a financial organization instantly with high throughput. The
scheme is enabled by the recent breakthrough in lookup argument, i.e., after a pre-processing step, the prover cost can be independent of the lookup
table size for subsequent queries. We extend the cq protocol [EFG22] and
develop an aggregated non-membership proof for zero knowledge sets.
Based on it, we design two instant proof-of-reserve protocols. One is non-
intrusive, which works for crypto-currencies such as BTC where transaction details are public. It has O(n log(n)) prover complexity and O(1)
proof size/verifier complexity, where n is the number of transactions assembled in a cycle. The other works for privacy preserving platforms
where the blockchain has no knowledge of transaction details. By sacrificing non-intrusiveness, the second protocol achieves O(1) complexity for both the prover and verifier
Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology
Context dependence is central to the description of complexity. Keying on the
pairwise definition of "set complexity" we use an information theory approach
to formulate general measures of systems complexity. We examine the properties
of multi-variable dependency starting with the concept of interaction
information. We then present a new measure for unbiased detection of
multi-variable dependency, "differential interaction information." This
quantity for two variables reduces to the pairwise "set complexity" previously
proposed as a context-dependent measure of information in biological systems.
We generalize it here to an arbitrary number of variables. Critical limiting
properties of the "differential interaction information" are key to the
generalization. This measure extends previous ideas about biological
information and provides a more sophisticated basis for study of complexity.
The properties of "differential interaction information" also suggest new
approaches to data analysis. Given a data set of system measurements
differential interaction information can provide a measure of collective
dependence, which can be represented in hypergraphs describing complex system
interaction patterns. We investigate this kind of analysis using simulated data
sets. The conjoining of a generalized set complexity measure, multi-variable
dependency analysis, and hypergraphs is our central result. While our focus is
on complex biological systems, our results are applicable to any complex
system.Comment: 44 pages, 12 figures; made revisions after peer revie
An Impossibility Result for High Dimensional Supervised Learning
We study high-dimensional asymptotic performance limits of binary supervised
classification problems where the class conditional densities are Gaussian with
unknown means and covariances and the number of signal dimensions scales faster
than the number of labeled training samples. We show that the Bayes error,
namely the minimum attainable error probability with complete distributional
knowledge and equally likely classes, can be arbitrarily close to zero and yet
the limiting minimax error probability of every supervised learning algorithm
is no better than a random coin toss. In contrast to related studies where the
classification difficulty (Bayes error) is made to vanish, we hold it constant
when taking high-dimensional limits. In contrast to VC-dimension based minimax
lower bounds that consider the worst case error probability over all
distributions that have a fixed Bayes error, our worst case is over the family
of Gaussian distributions with constant Bayes error. We also show that a
nontrivial asymptotic minimax error probability can only be attained for
parametric subsets of zero measure (in a suitable measure space). These results
expose the fundamental importance of prior knowledge and suggest that unless we
impose strong structural constraints, such as sparsity, on the parametric
space, supervised learning may be ineffective in high dimensional small sample
settings.Comment: This paper was submitted to the IEEE Information Theory Workshop
(ITW) 2013 on April 23, 201
Conditions for duality between fluxes and concentrations in biochemical networks
Mathematical and computational modelling of biochemical networks is often
done in terms of either the concentrations of molecular species or the fluxes
of biochemical reactions. When is mathematical modelling from either
perspective equivalent to the other? Mathematical duality translates concepts,
theorems or mathematical structures into other concepts, theorems or
structures, in a one-to-one manner. We present a novel stoichiometric condition
that is necessary and sufficient for duality between unidirectional fluxes and
concentrations. Our numerical experiments, with computational models derived
from a range of genome-scale biochemical networks, suggest that this
flux-concentration duality is a pervasive property of biochemical networks. We
also provide a combinatorial characterisation that is sufficient to ensure
flux-concentration duality. That is, for every two disjoint sets of molecular
species, there is at least one reaction complex that involves species from only
one of the two sets. When unidirectional fluxes and molecular species
concentrations are dual vectors, this implies that the behaviour of the
corresponding biochemical network can be described entirely in terms of either
concentrations or unidirectional fluxes
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