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A Bound For Multiparty Secret Key Agreement And Implications For A Problem Of Secure Computing
"... Abstract. We consider secret key agreement by multiple parties observing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a singleshot upper bound on the length of the secret keys that can be generated, without making any assumptions ..."
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Abstract. We consider secret key agreement by multiple parties observing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a singleshot upper bound on the length of the secret keys that can be generated, without making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of “how far ” is the joint distribution of the initial observations of the parties and the eavesdropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper’s side information. The closeness of the two distributions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypothesis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers
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
Converses For Secret Key Agreement and Secure Computing
, 2015
"... 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 ..."
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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 singleshot 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.
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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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.
INTERACTIVE FUNCTION COMPUTATION VIA POLAR CODING
"... ABSTRACT. In a series of papers N. Ma and P. Ishwar (201113) considered a range of distributed source coding problems that arise in the context of iterative computation of functions, characterizing the region of achievable communication rates. We consider the problems of interactive computation of ..."
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ABSTRACT. In a series of papers N. Ma and P. Ishwar (201113) considered a range of distributed source coding problems that arise in the context of iterative computation of functions, characterizing the region of achievable communication rates. We consider the problems of interactive computation of functions by two terminals and interactive computation in a collocated network, showing that the rate regions for both these problems can be achieved using several rounds of polarcoded transmissions. 1.
Impossibility Bounds for Secure Computing
"... Abstract—We derive impossibility (converse) bounds for the efficiency of implementing information theoretically secure oblivious transfer and bit commitment using correlated observations. Our approach is based on relating these problems to that of testing if the observations of the parties are cond ..."
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Abstract—We derive impossibility (converse) bounds for the efficiency of implementing information theoretically secure oblivious transfer and bit commitment using correlated observations. Our approach is based on relating these problems to that of testing if the observations of the parties are conditionally independent given the adversary’s observation. The resulting bounds strengthen and improve upon several previously known results. I.
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.