Parallel private information retrieval protocol with index anonymity for untrusted databases

Private information retrieval (PIR) enables a client to search data from a single (or multiple) untrusted server, without revealing which entry was queried. PIR can be divided into two categories: information -theoretic PIR (IT-PIR) and computational PIR (CPIR). However, there is a deployment challenge with IT-PIR because the non -collusion assumption is difficult to implement in practice. Meanwhile, due to the fact that CPIR involves performing cryptographic operations on each element, its performance significantly decreases as the size and number of database entries increase. To overcome these problems, based on homomorphic encryption, this paper presents a parallel PIR (ParPIR) with index anonymity for untrusted databases, which uses the batch encoding to compress request size. Furthermore, our ParPIR eliminates computationally expensive ciphertext multiplication operations, which improves the response time. Moreover, our ParPIR packs multiple responses through rotation column operations on ciphertext, thereby reducing the response size. Compared to previous PIR protocols, the offline time in our ParPIR has almost 1 similar to 63x improvement; the online time in our ParPIR decreases by at least 49.9 similar to 98.9%. Meanwhile, although the request size of our ParPIR has a 0 similar to 31x increase, the response size of our ParPIR has a 0 similar to 4095x improvement.