At a high level, our goal is to realize the following picture: the client sends one ciphertext containing an encryption of its desired index i to the server, and the server inexpensively evaluates a function EXPAND that outputs n ciphertexts containing an encryption of 0 or 1 (where the i th ciphertext encrypts 1 and others encrypt 0). The server can then use these n ciphertexts as a query and execute the protocol as before. [1]
Query vector compression and expansion for PIR
[1] PIR with Compressed Queries and Amortized Query Processing (https://ieeexplore.ieee.org/document/8418648)