The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers

doi:10.1109/TIT.2018.2883283

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	The Optimal Sub-Packetization of Linear Capacity-Achieving PIR Schemes With Colluding Servers
	Zhang, Zhifang1,2 ; Xu, Jingke 1,2
	2019-05-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	65 期号:5 页码:2723-2735
摘要	Suppose 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.
关键词	Private information retrieval capacity sub-packetization
DOI	10.1109/TIT.2018.2883283
语种	英语
资助项目	National Natural Science Foundation of China[61872353]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000466029900007
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34690
专题	系统科学研究所
通讯作者	Zhang, Zhifang
作者单位	1.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
推荐引用方式 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.