Capacity-Achieving PIR Schemes with Optimal Sub-Packetization

Suppose a database containing M records is replicated across 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 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 usually means simple realization. For general values of N, T,M , the only known capacity-achieving PIR scheme was designed by Sun and Jafar in 2016 with sub-packetization N . In this paper, we design a linear capacity-achieving PIR scheme with much smaller sub-packetization dn, where d = gcd(N,T ) and n = N/d. Furthermore, we prove that for any linear capacity-achieving PIR scheme it must have sub-packetization no less than dn, implying our scheme has the optimal sub-packetization. Moreover, comparing with Sun and Jafar’s scheme, our scheme reduces the field size by a factor of 1 NdM−2 .