One (Block) Size Fits All: PIR and SPIR with Variable-Length Records via Multi-Block Queries

We propose a new, communication-efficient way for users to fetch multiple blocks simultaneously in Goldberg’s robust information-theoretic private information retrieval (IT-PIR) scheme. Our new multi-block IT-PIR trades off some Byzantine robustness to improve throughput without affecting user privacy. By taking advantage of the recent Cohn-Heninger multi-polynomial list decoding algorithm, we show how realistic parameter choices enable the user to retrieve several blocks without increasing the communication or computation costs beyond what is required to retrieve a single block, and argue that the resulting scheme still maintains essentially optimal Byzantine robustness in practice. We also derive optimal parameters for our construction, which yields communication costs within a small factor of the lowest possible. With our new multi-block IT-PIR protocol as a starting point, we construct four new symmetric PIR (SPIR) protocols that each support variable-length database records. By decoupling the PIR block size from the lengths of individual database records, we are free to fix the block size to its communication-optimal value without artificially restricting the contents and layout of the records. Moreover, it is straightforward to augment three of our four new SPIR constructions with efficient zero-knowledge proofs about the particular records a user is requesting in a given query; this makes it easy to implement pricing and access control structures over the records using standard techniques from the literature. The resulting SPIR protocols are therefore well suited to privacy-preserving e-commerce applications, such as privacy-friendly sales of e-books, music, movies, or smart phone and tablet apps.