TY - JOUR
T1 - Bounds on the Capacity of Private Information Retrieval Over Graphs
AU - Sadeh, Bar
AU - Gu, Yujie
AU - Tamo, Itzhak
N1 - Publisher Copyright:
© 2005-2012 IEEE.
PY - 2023
Y1 - 2023
N2 - In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file's identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, implying an improved general lower bound on all graphs' PIR capacity.
AB - In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file's identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, implying an improved general lower bound on all graphs' PIR capacity.
KW - Private information retrieval (PIR)
KW - capacity
KW - edge-coloring
KW - graph-based replication system
UR - http://www.scopus.com/inward/record.url?scp=85141552378&partnerID=8YFLogxK
U2 - 10.1109/TIFS.2022.3220034
DO - 10.1109/TIFS.2022.3220034
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AN - SCOPUS:85141552378
SN - 1556-6013
VL - 18
SP - 261
EP - 273
JO - IEEE Transactions on Information Forensics and Security
JF - IEEE Transactions on Information Forensics and Security
ER -