Abstract
Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or cloud without disclosing information about the identity of the data items retrieved. The area has received renewed attention in the context of PIR from coded storage. Here, the files are distributed over the servers according to a storage code instead of mere replication. Alongside with the basic principles of PIR, we will review recent capacity results and demonstrate the utility of the so-called star product PIR scheme. Accompanied with generalized Reed--Solomon codes and the concept of full support-rank, this scheme allows us to explain the key ingredients of proving a capacity conjecture from 2016 for full support-rank PIR. This brings us very close to the general capacity proof of coded PIR from colluding servers.
The talk is mainly based on the works https://ieeexplore.ieee.org/document/9570371 and https://epubs.siam.org/doi/10.1137/16M1102562.