The Capacity of Private Information Retrieval

In the private information retrieval (PIR) problem, a user wishes to retrieve, as efficiently as possible, one out of K messages from N non-communicating databases (each holds all K messages) while revealing nothing about the identity of the desired message index to any individual database. The info...

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Published in:	IEEE transactions on information theory Vol. 63; no. 7; pp. 4075 - 4088
Main Authors:	Hua Sun, Jafar, Syed Ali
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.07.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Capacity Communication Data privacy Distributed databases Encoding Indexes Information retrieval Information theory Messages private information retrieval Upper bound
ISSN:	0018-9448, 1557-9654
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Abstract	In the private information retrieval (PIR) problem, a user wishes to retrieve, as efficiently as possible, one out of K messages from N non-communicating databases (each holds all K messages) while revealing nothing about the identity of the desired message index to any individual database. The information theoretic capacity of PIR is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. For K messages and N databases, we show that the PIR capacity is (1+1/N+1/N 2 +· · ·+1/N K-1 ) -1 . A remarkable feature of the capacity achieving scheme is that if we eliminate any subset of messages (by setting the message symbols to zero), the resulting scheme also achieves the PIR capacity for the remaining subset of messages.
AbstractList	In the private information retrieval (PIR) problem, a user wishes to retrieve, as efficiently as possible, one out of K messages from N non-communicating databases (each holds all K messages) while revealing nothing about the identity of the desired message index to any individual database. The information theoretic capacity of PIR is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. For K messages and N databases, we show that the PIR capacity is (1+1/N+1/N2+· · ·+1/NK-1)-1. A remarkable feature of the capacity achieving scheme is that if we eliminate any subset of messages (by setting the message symbols to zero), the resulting scheme also achieves the PIR capacity for the remaining subset of messages. In the private information retrieval (PIR) problem, a user wishes to retrieve, as efficiently as possible, one out of K messages from N non-communicating databases (each holds all K messages) while revealing nothing about the identity of the desired message index to any individual database. The information theoretic capacity of PIR is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. For K messages and N databases, we show that the PIR capacity is (1+1/N+1/N 2 +· · ·+1/N K-1 ) -1 . A remarkable feature of the capacity achieving scheme is that if we eliminate any subset of messages (by setting the message symbols to zero), the resulting scheme also achieves the PIR capacity for the remaining subset of messages.
Author	Jafar, Syed Ali Hua Sun
Author_xml	– sequence: 1 surname: Hua Sun fullname: Hua Sun email: huas2@uci.edu organization: Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Irvine, Irvine, CA, USA – sequence: 2 givenname: Syed Ali surname: Jafar fullname: Jafar, Syed Ali email: syed@uci.edu organization: Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Irvine, Irvine, CA, USA
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SubjectTerms	Capacity Communication Data privacy Distributed databases Encoding Indexes Information retrieval Information theory Messages private information retrieval Upper bound
Title	The Capacity of Private Information Retrieval
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