In this manuscript, the problem of function computation with privacy constraints is considered. The problem consists of two legitimate nodes Alice and Bob, and an eavesdropper Eve. Bob would like to compute a function, and the arguments of the function are two source observation sequences that are distributed over the legitimate nodes respectively. To make the function computable at Bob, Alice is allowed to transmit a message to Bob via a public noiseless channel, which Eve has full access to. Under this model, we study the relationship among message rate, private information leakage to Bob and equivocation of Alice's source observations at Eve, and fully single-letter characterize the region of these achievable parameter tuples.
In this manuscript, the problem of function computation with privacy constraints is considered. The problem consists of two legitimate nodes Alice and Bob, and an eavesdropper Eve. Bob would like to compute a function, and the arguments of the function are two source observation sequences that are distributed over the legitimate nodes respectively. To make the function computable at Bob, Alice is allowed to transmit a message to Bob via a public noiseless channel, which Eve has full access to. Under this model, we study the relationship among message rate, private information leakage to Bob and equivocation of Alice's source observations at Eve, and fully single-letter characterize the region of these achievable parameter tuples.
In this paper, the problem of function computation with privacy and secrecy constraints is considered. The considered model consists of three legitimate nodes (i.e., two transmitters, Alice and Bob, and a fusion center that acts as the receiver) that observe correlated sources and are connected by noiseless public channels, and an eavesdropper Eve who has full access to the public channels and also has its own source observations. The fusion center would like to compute a function of the distributed sources within a prefixed distortion level under a certain distortion metric. To facilitate the function computation, Alice and Bob will send messages to the fusion center. Different from the existing setups in function computation, we assume that there is a privacy constraint on the sources at Alice and Bob. In particular, Alice and Bob would like to enable the fusion center to compute the function, but at same time, they do not want the fusion center to learn too much information about the source observations. We introduce a quantity to precisely measure the privacy leakage to the fusion center. In addition to this privacy constraint, we also have a secrecy constraint to Eve and use equivocation of sources to measure this quantity. Under this model, we study the tradeoffs among message rates, private information leakage, equivocation, and distortion. We first consider a scenario that has only one transmitter, i.e., the source at Bob is empty, and fully single-letter characterize the corresponding regions. Then, we consider the more general case and provide both outer and inner bounds on the corresponding regions.
The distributed binary hypothesis testing problem with communication and security constraints is investigated. A legitimate statistician (referred to as Bob) is interested in detecting the joint probability distribution of two remotely located sources. To this end, Bob has access to analog and coded data where the later is observed at another node (referred to as Alice) and communicated over a public noise-less channel of finite rate. An eavesdropper (referred to as Eve) has access to the encoded bits. In this framework, we study the tradeoff between the maximum achievable error exponent at Bob, i.e., the minimum Type II error probability for a fixed Type I probability of error, the rate and the equivocation rate. We first derive an achievable rate-exponent-equivocation region. Then, we investigate the special case of testing against independence for which we provide the optimal rate-exponent-equivocation region. An application example to binary sources is also considered.
We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary input symmetric output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions differing only in the Markov chain conditions imposed are characterized.
We consider secure computation of randomized functions by two users, where both the users (Alice and Bob) have inputs, Alice sends a message to Bob over a rate-limited, noise-free link, and then Bob produces the output. We study this problem when privacy is required only against Bob, i.e., from the message, Bob must not learn any information about Alice's input other than what can be inferred by his own input and output. We give a single-letter expression for the optimal rate. We also explicitly characterize securely computable randomized functions when input has full support, which leads to a much simpler expression for the optimal rate. Recently, Data (ISIT 2016) studied the other two cases (first, when privacy is required against both the users; and second, when privacy is required only against Alice) and obtained single-letter expressions for optimal rates in both the scenarios. Yassaee, Gohari, and Aref (IEEE Transactions on Information Theory 2015) studied the case when there is no privacy requirement and obtained a single-letter expression for the optimal rate, when Alice and Bob interact for arbitrary but finite number of rounds, and both of them may produce potentially different outputs.
We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also secrecy and privacy. Specifically, 1) the function computed should remainsecretfrom an eavesdropper observing the public communication and correlated observations, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used; 2) the remote source should remainprivatefrom the eavesdropper and the fusion center, measured in terms of the information leaked about the remote source itself. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary-input symmetric-output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions that differ only in the Markov chain conditions imposed are characterized.
We consider a two-user secure computation problem in which Alice and Bob communicate interactively in order to compute some deterministic functions of the inputs. The privacy requirement is that each user should not learn any additional information about a function of the inputs other than what can be inferred from its own input and output. For the distribution-free setting, i.e., when the protocol must be correct and private for any joint input distribution, we completely characterize the set of all securely computable functions. When privacy is required only against Bob who computes a function based on a single transmission from Alice, we show that asymptotically secure computability is equivalent to perfectly secure computability. Separately, we consider an eavesdropper who has access to all the communication and should not learn any information about some function of the inputs (possibly different from the functions to be computed by the users) and show that interaction may be necessary for secure computation.