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 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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IEEE
01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0733-8716, 1558-0008 |
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| Abstract | 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. |
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| AbstractList | 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) [Formula Omitted] messages and a user who wants to compute [Formula Omitted] independent linear combinations of a [Formula Omitted]-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 [Formula Omitted] messages required for the computation. In this work, we focus on the single-server setting of the PLT problem when the identities of the [Formula Omitted] messages required for the computation must be protected jointly. We consider two different models, depending on whether the coefficient matrix of the required [Formula Omitted] linear combinations generates a Maximum Distance Separable (MDS) code. We prove that the capacity for both models is given by [Formula Omitted], 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. 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. |
| Author | Esmati, Nahid Sprintson, Alex Heidarzadeh, Anoosheh |
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| SubjectTerms | 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 |
| Title | Single-Server Private Linear Transformation: The Joint Privacy Case |
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