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Lecture 11 Private Information Retrieval Stefan Dziembowski University of Rome La Sapienza
Plan 1. Motivation and definition 2. Information‐theoretic impossibility 3. A construction of Kushilevitz and Ostrovsky 4. Overview of some other related results
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Observation The owners of databases know a lot about the users! This poses a risk to users’ privacy. E.g. consider database with stock prices…
problematic!
Can we do something about it? problematic
We can: • trust them that they will protect our secrecy, or • use cryptography!
How can crypto help?
user U
database D
Note: this problem has nothing to do with secure communication!
Our settings
user U
database D
A new primitive: Private Information Retrieval (PIR)
Plan 1. 2. 3. 4.
Definition of PIR An ideal PIR doesn’t exist Construction of a computational PIR Open problems Literature: • B. Chor, E. Kushilevitz, O. Goldreich and M. Sudan, Private Information Retrieval, Journal of ACM, 1998 • E. Kushilevitz and R. Ostrovsky Replication Is NOT Needed: SINGLE Database, Computationally‐Private Information Retrieval, FOCS 1997
Question How to protect privacy of queries?
user U wants to retrieve some data from D
database D shouldn’t learn what U retrieved
Let’s make things simple!
? database B: index i = 1,…,w
the user should learn Bi (he may also learn other Bi’s)
B1 B2
… Bi
Bw each Bi є {0,1}
Trivial solution
B1 B2
…
Bw
The database simply sends everything to the user!
Non‐triviality The previous solution has a drawback: the communication complexity is huge! Therefore we introduce the following requirement: “Non‐triviality”: the number of bits communicated between U and D has to be smaller than w.
Private Information Retrieval (PIR) polynomial time randomized interactive algorithms
input:
input: index i = 1,…,w
B1
B2
…
This property needs to be defined more formally • at the end the user learns Bi
correctness
• the database does not learn i
secrecy (of the user)
• the total communication is 0 Take some T’, and look where it is possible:
databases B
T’
T’
T’
T’
indices i
PIR doesn’t exists [2/4]
databases B
Observation: secrecy →
if T’ is possible for some B and i then it is possible for B and all the other i’s
