Private Sequential Function Computation

Tahmasebi, Behrooz; Maddah-Ali, Mohammad Ali

doi:10.1109/isit.2019.8849524

Cited by 16 publications

(3 citation statements)

References 52 publications

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“…The problem in Fig. 2 is related to private information retrieval (PIR), introduced in [29] and widely studied in recent years, e.g., [30]- [39]. In the PIR problem, the master server wishes to retrieve a message within some library from a set of distributed databases, each of which stores all the messages.…”

Section: B Related Workmentioning

confidence: 99%

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Aliasgari

Simeone

Kliewer

2020

IEEE Trans.Inform.Forensic Secur.

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Large matrix multiplications are central to largescale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, i.e., the total amount of data to be downloaded from the workers. In this paper, in addition to exact recovery requirements, we impose security and privacy constraints on the data matrices, and study the recovery threshold as a function of the communication load. We first assume that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, we introduce a novel class of secure codes, referred to as secure generalized PolyDot (SGPD) codes, that generalize state-of-the-art non-secure codes for matrix multiplication. SGPD codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. We then assume that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, we present a variant of generalized PolyDot codes that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.

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Section: B Related Workmentioning

confidence: 99%

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Aliasgari

Simeone

Kliewer

2020

IEEE Trans.Inform.Forensic Secur.

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“…Private function evaluation, at first glance, might seem related to private computation [10]- [12] and private information retrieval [13], [14]. However, in private function evaluation, the objective is not to hide the function to be computed (cf., private computation) or the datasets on which the function is evaluated (cf., private information retrieval).…”

Section: Introductionmentioning

confidence: 99%

Non-Stochastic Private Function Evaluation

Farokhi¹,

Nair²

2020

Preprint

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We consider private function evaluation to provide query responses based on private data of multiple untrusted entities in such a way that each cannot learn something substantially new about the data of others. First, we introduce perfect non-stochastic privacy in a two-party scenario. Perfect privacy amounts to conditional unrelatedness of the query response and the private uncertain variable of other individuals conditioned on the uncertain variable of a given entity. We show that perfect privacy can be achieved for queries that are functions of the common uncertain variable, a generalization of the common random variable. We compute the closest approximation of the queries that do not take this form. To provide a trade-off between privacy and utility, we relax the notion of perfect privacy. We define almost perfect privacy and show that this new definition equates to using conditional disassociation instead of conditional unrelatedness in the definition of perfect privacy. Then, we generalize the definitions to multi-party function evaluation (more than two data entities). We prove that uniform quantization of query responses, where the quantization resolution is a function of privacy budget and sensitivity of the query (cf., differential privacy), achieves function evaluation privacy.

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“…. , ω 10 }, H can be thought of as the parity-check matrix of a[10,7] GRS code with the multipliers {α 1 , . .…”

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confidence: 99%

Private Linear Transformation: The Joint Privacy Case

Esmati¹,

Heidarzadeh²,

Sprintson³

2021

Preprint

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We introduce the problem of Private Linear Transformation (PLT). This problem includes a single (or multiple) remote server(s) storing (identical copies of) K messages and a user who wants to compute L linear combinations of a D-subset of these messages by downloading the minimum amount of information from the server(s) while protecting the privacy of the entire set of D messages. This problem generalizes the Private Information Retrieval and Private Linear Computation problems. In this work, we focus on the single-server case. For the setting in which the coefficient matrix of the required L linear combinations generates a Maximum Distance Separable (MDS) code, we characterize the capacity-defined as the supremum of all achievable download rates, for all parameters K, D, L.In addition, we present lower and/or upper bounds on the capacity for the settings with non-MDS coefficient matrices and the settings with a prior side information. I. INTRODUCTIONThis work introduces the problem of Private Linear Transformation (PLT). This problem includes a single (or multiple non-colluding or with limited collusion capability) remote server(s) storing (identical copies of) a dataset consisting of K data items; and a user who is interested in computing L linear combinations of a D-subset of data items. The goal of the user is to perform the computation privately so that the identities of the data items required for the computation are protected (to some degree) from the server(s), while minimizing the total amount of information being downloaded from the server(s). The PLT problem generalizes the problems of Private Information Retrieval (PIR) (see, e.g., [1]-[7]) and Private Linear Computation (PLC) (see, e.g., [8]-[10]), which have recently received a significant attention from the information and coding theory community. In particular, PLT reduces to PIR or PLC when L = D or L = 1, respectively. In this work, we focus on the single-server setting of PLT.This problem setup appears in several practical scenarios such as linear transformation for dimensionality reduction in Machine Learning (ML), see, e.g., [11] and references therein. Consider a dataset with N data samples, each with K attributes. Consider a user that wishes to implement an ML algorithm on a subset of D selected attributes, while protecting the privacy of the selected attributes. When D is large, the D-dimensional feature space is typically mapped onto a new subspace of lower dimension, say, L, and the ML algorithm operates on the new L-dimensional subspace instead. A commonly-used technique for dimensionality reduction is linear transformation, where an L×D matrix is multiplied by the D × N data submatrix (the submatrix of the original K × N data matrix restricted to the D selected attributes). Thinking of the rows of the K × N data matrix as the K messages, the labels of the The authors are with the

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Private Sequential Function Computation

Cited by 16 publications

References 52 publications

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Non-Stochastic Private Function Evaluation

Private Linear Transformation: The Joint Privacy Case

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