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The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers
Zhang, Zhifang1,2; Xu, Jingke1,2
AbstractSuppose M records are replicated in N servers (each storing all M records), a user wants to privately retrieve one record by accessing the servers such that the identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T-private information retrieval (PIR) scheme. In practice, capacity-achieving and small sub-packetization are both desired for PIR schemes, because the former implies the highest download rate and the latter means simple realization. Meanwhile, sub-packetization is the key technique for achieving capacity. In this paper, we characterize the optimal sub-packetization for linear capacity-achieving T-PIR schemes. First, a lower bound on the sub-packetization L for linear capacity-achieving T-PIR schemes is proved, i.e., L >= dn(M-1), where d = gcd(N, T) and n = N/d. Then, for general values of M and N > T >= 1, a linear capacity-achieving T-PIR scheme with sub-packetization dnM-1 is designed. Comparing with the first capacity-achieving T-PIR scheme given by Sun and Jafar in 2016, our scheme reduces the sub-packetization from N-M to the optimal and further reduces the field size by a factor of NdM-2.
KeywordPrivate information retrieval capacity sub-packetization
Funding ProjectNational Natural Science Foundation of China[61872353]
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000466029900007
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Document Type期刊论文
Corresponding AuthorZhang, Zhifang
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Zhifang,Xu, Jingke. The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2019,65(5):2723-2735.
APA Zhang, Zhifang,&Xu, Jingke.(2019).The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers.IEEE TRANSACTIONS ON INFORMATION THEORY,65(5),2723-2735.
MLA Zhang, Zhifang,et al."The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers".IEEE TRANSACTIONS ON INFORMATION THEORY 65.5(2019):2723-2735.
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