A Capacity-Achieving T-PIR Scheme Based On MDS Array Codes
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Suppose a database containing M records is replicated in each of N servers, and a user wants to privately retrieve one record by accessing the servers such that 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 (T-PIR) scheme. In this paper we focus on the field size of T-PIR schemes. We design a generalcapacity-achieving T-PIR scheme whose queries are generated by using some MDS array codes. It only requires field size q≥√(N), where ℓ={t^M-2,(n-t)^M-2}, t=T/ gcd(N,T), n=N/ gcd(N,T) and has the optimal sub-packetization Nn^M-2. Comparing with existing capacity-achieving T-PIR schemes, our scheme has the following advantage, that is, its field size monotonically decreases as the number of records M grows. In particular, the binary field is sufficient for building a capacity-achieving T-PIR scheme as long as M≥ 2+_μ_2N, where μ={t,n-t}>1.
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