Single-Server Private Linear Transformation: The Joint Privacy Case

This paper introduces the problem of Private Linear Transformation (PLT) which generalizes the problems of private information retrieval and private linear computation. The PLT problem includes one or more remote server(s) storing (identical copies of) <inline-formula> <tex-math notation=&q...

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Veröffentlicht in:IEEE journal on selected areas in communications Jg. 40; H. 3; S. 899 - 911
Hauptverfasser: Heidarzadeh, Anoosheh, Esmati, Nahid, Sprintson, Alex
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Codes
Computation
Computational modeling
Correlation
Data privacy
Dimensionality reduction
Information retrieval
Information theory
information-theoretic privacy
linear transformation
Linear transformations
Mathematical analysis
maximum distance separable codes
Messages
Privacy
private function computation
Private information retrieval
Servers
single server
ISSN:0733-8716, 1558-0008
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Zusammenfassung:This paper introduces the problem of Private Linear Transformation (PLT) which generalizes the problems of private information retrieval and private linear computation. The PLT problem includes one or more remote server(s) storing (identical copies of) <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> messages and a user who wants to compute <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> independent linear combinations of a <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula>-subset of messages. The objective of the user is to perform the computation by downloading minimum possible amount of information from the server(s), while protecting the identities of the <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> messages required for the computation. In this work, we focus on the single-server setting of the PLT problem when the identities of the <inline-formula> <tex-math notation="LaTeX">D </tex-math></inline-formula> messages required for the computation must be protected jointly. We consider two different models, depending on whether the coefficient matrix of the required <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> linear combinations generates a Maximum Distance Separable (MDS) code. We prove that the capacity for both models is given by <inline-formula> <tex-math notation="LaTeX">L/(K-D+L) </tex-math></inline-formula>, where the capacity is defined as the supremum of all achievable download rates. Our converse proofs are based on linear-algebraic and information-theoretic arguments. For each model, we also present an achievability scheme that relies on MDS codes.
Bibliographie:ObjectType-Article-1
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ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.2022.3142293