The Capacity of Private Information Retrieval with Partially Known Private Side Information

2017/10/02 by Yi-Peng Wei, Wei, Yi-Peng, Karim Banawan +3 · 1 citation
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data

paper · pdf · doi:10.48550/arxiv.1710.00809

openalex publication_date 2017/10/02 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

We consider the problem of private information retrieval (PIR) of a single message out of K messages from N replicated and non-colluding databases where a cache-enabled user (retriever) of cache-size M possesses side information in the form of full messages that are partially known to the databases. In this model, the user and the databases engage in a two-phase scheme, namely, the prefetching phase where the user acquires side information and the retrieval phase where the user downloads desired information. In the prefetching phase, the user receives m_n full messages from the nth database, under the cache memory size constraint ∑_n=1^N m_n ≤ M. In the retrieval phase, the user wishes to retrieve a message such that no individual database learns anything about the identity of the desired message. In addition, the identities of the side information messages that the user did not prefetch from a database must remain private against that database. Since the side information provided by each database in the prefetching phase is known by the providing database and the side information must be kept private against the remaining databases, we coin this model as partially known private side information. We characterize the capacity of the PIR with partially known private side information to be C=(1+(1)/(N)+⋯+\frac1N^K-M-1)^-1=\frac1-(1)/(N)1-((1)/(N))^K-M. Interestingly, this result is the same if none of the databases knows any of the prefetched side information, i.e., when the side information is obtained externally, a problem posed by Kadhe et al. and settled by Chen-Wang-Jafar recently. Thus, our result implies that there is no loss in using the same databases for both prefetching and retrieval phases.

Citations

• Secure Symmetric Private Information Retrieval from Colluding Databases with Adversaries
• Linear Symmetric Private Information Retrieval for MDS Coded Distributed Storage with Colluding Servers
• Symmetric Private Information Retrieval For MDS Coded Distributed Storage

Cited by

• Cross Subspace Alignment and the Asymptotic Capacity of X-Secure T-Private Information Retrieval

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• The Capacity of Cache Aided Private Information Retrieval