Sequential Random Sampling PIR with Multiple Colluding Servers in DNA-Based Data Storage

As DNA-based data storage evolves, protecting user privacy during data retrieval has become increasingly important. We study sequential random sampling DNA private information retrieval (SRS DNA PIR) with multiple colluding random sampling servers, where the database is partitioned into servers of equal size. We investigate the tradeoff between the download cost, defined as the expected number of queries, and the privacy leakage, measured by mutual information. We derive lower bounds on this tradeoff, including a bound given by an optimization problem. This bound is tight when each server stores two files, and we construct schemes that attain it. For servers of any size, we construct schemes that apply a single-server scheme to a randomly selected subset of servers.