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P.: When is a function securely computable
 IEEE Trans. Inf. Theory
, 2011
"... Abstract—A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public communication. It is required that the value of the function be concealed from an eavesdropper with access to the communication. We show that the function is securely comp ..."
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Cited by 18 (7 self)
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Abstract—A subset of a set of terminals that observe correlated signals seek to compute a function of the signals using public communication. It is required that the value of the function be concealed from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the capacity of a new secrecy generationmodel, for which a singleletter characterization is provided. Index Terms—Aided secret key, balanced coloring lemma, function computation, maximum common function, omniscience, secret key capacity, secure computability. I.
Distributed computing with privacy
 Proc. IEEE International Symposium on Information Theory
, 2012
"... Abstract—A set of terminals that observe correlated data seek to compute functions of the data using interactive public communication. At the same time it is required that this communication, observed by an eavesdropper, does not reveal the value of a private function of the data. In general, the pr ..."
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Cited by 3 (1 self)
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Abstract—A set of terminals that observe correlated data seek to compute functions of the data using interactive public communication. At the same time it is required that this communication, observed by an eavesdropper, does not reveal the value of a private function of the data. In general, the private function and the functions computed by the terminals can be all different. We show that a class of functions are securely computable if and only if the conditional entropy of data given the value of private function is greater than the least rate of interactive communication required for an appropriately chosen multiterminal source coding task. A singleletter formula is provided for this rate in special cases. I.
Common Randomness Principles of Secrecy
, 2013
"... This dissertation concerns the secure processing of distributed data by multiple terminals, using interactive public communication among themselves, in order to accomplish a given computational task. In the setting of a probabilistic multiterminal source model in which several terminals observe cor ..."
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Cited by 2 (2 self)
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This dissertation concerns the secure processing of distributed data by multiple terminals, using interactive public communication among themselves, in order to accomplish a given computational task. In the setting of a probabilistic multiterminal source model in which several terminals observe correlated random signals, we analyze secure distributed data processing protocols that harness the correlation in the data. The specific tasks considered are: computing functions of the data under secrecy requirements; generating secretly shared bits with minimal rate of public communication; and securely sharing bits in presence of a querying eavesdropper. In studying these various secure distributed processing tasks, we adopt a unified approach that entails examining the form of underlying common randomness (CR) that is generated at the terminals during distributed processing. We make the case that the exact form of established CR is linked inherently to the data processing task at hand, and its characterization can lead to a structural understanding of the associated algorithms. An identification of the underlying CR and its decomposition into independent components, each with a different operational significance, is
1Distributed Function Computation with Confidentiality
"... Abstract—A set of terminals observe correlated data and seek to compute functions of the data using interactive public communication. At the same time, it is required that the value of a private function of the data remains concealed from an eavesdropper observing this communication. In general, the ..."
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Cited by 1 (1 self)
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Abstract—A set of terminals observe correlated data and seek to compute functions of the data using interactive public communication. At the same time, it is required that the value of a private function of the data remains concealed from an eavesdropper observing this communication. In general, the private function and the functions computed by the nodes can be all different. We show that a class of functions are securely computable if and only if the conditional entropy of data given the value of private function is greater than the least rate of interactive communication required for a related multiterminal sourcecoding task. A singleletter formula is provided for this rate in special cases. Index Terms—Balanced coloring lemma, distributed computing, function computation, omniscience, secure computation. I.
INFORMATION AGGREGATION IN SENSOR NETWORKS
, 2011
"... In many sensor network applications, one is interested only in computing some relevant function of the sensor measurements. In this thesis, we study optimal strategies for innetwork computation and communication in such wireless sensor networks. We begin by considering a directed graph G = (V,E) on ..."
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In many sensor network applications, one is interested only in computing some relevant function of the sensor measurements. In this thesis, we study optimal strategies for innetwork computation and communication in such wireless sensor networks. We begin by considering a directed graph G = (V,E) on the sensor nodes, with a designated collector node, where the goal is to characterize the rate region in R E, i.e., the set of vector rates for which there exist feasible encoders and decoders which achieve zeroerror computation for large enough block length. For directed tree graphs, we determine a necessary and sufficient condition for each edge that yields the optimal alphabet, from which we then calculate the minimum worst case and average case complexity. For general directed acyclic graphs, we provide an outer bound on the rate region by finding the disambiguation requirements for each cut, and describe examples where this outer bound is tight. Next, we consider undirected tree networks, where each node has an integer measurement, and all nodes want to compute a symmetric Boolean function. For a class of functions called sumthreshold functions, we derive an optimal strategy which minimizes the worstcase number of bits exchanged on each edge. In the case of general graphs, we present a cutset lower bound, and an
From Secret Key Agreement to Matroidal Undirected Network
"... An undirected network link model is formulated, generalizing the usual undirected graphical model. The optimal direction for multicasting can be found in polynomial time with respect to the size of the network, despite the exponential number of possible directions. A more general problem is conside ..."
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An undirected network link model is formulated, generalizing the usual undirected graphical model. The optimal direction for multicasting can be found in polynomial time with respect to the size of the network, despite the exponential number of possible directions. A more general problem is considered where certain function of a distributed source is to be computed at multiple nodes. The converse results are derived, not from the usual cutset bound but through the related problem of secret key agreement and secure source coding by public discussion. A unifying model of partly directed network is also formulated, covering both the directed and undirected networks as special cases.