Private Information Retrieval (PIR) schemes are communication protocols with low comnunication that allow a user to recover a single bit of information from a large database stored at multiple non-interacting servers without revealing any information about their query to any of the servers. PIRs have long been the subject of study with close relationships to locally decodable codes (LDCs). In this talk we describe new t-server PIR schemes with communication complexity subpolynomial in the previously best known, for all but finitely many t. Our results are based on combining the use of derivatives with "matching vectors". Both ingredients are well-used in the literature on PIRs and LDCs and in particular were used together in an ingenious way by Dvir and Gopi, using polynomials and derivatives over certain exotic rings, en route to their fundamental result giving the first 2-server PIR with subpolynomial communication. Our result gives a matching bound for 2-server PIRs with an arguably simple proof; and also leads to improvements for most other values of t, the number of servers. (Knowledge of previous works on PIRs or LDCs will not be assumed in the talk.)
Joint work with Fatemeh Ghasemi and Swastik Kopparty (U. Toronto).
Short Bio: Madhu Sudan is a Gordon McKay Professor in the John A. Paulson School of Engineering and Applied Sciences at Harvard University, where he has been since 2015. Madhu Sudan got his Bachelors degree from IIT Delhi in 1987 and his Ph.D. from U.C. Berkeley in 1992. Between 1992 and 2015, Madhu Sudan worked at IBM Research (Research Staff Member 1992-1997), at MIT (Associate Professor 1997-2000, Professor 2000-2011, Fujitsu Chair Professor 2003-2011, CSAIL Associate Director 2007-2009, Adjunct Professor 2011-2015), and at Microsoft Research (Principal Researcher, 2009-2015). Madhu Sudan is a recipient of the Nevanlinna Prize awarded by the International Mathematical Union for outstanding contributions to mathematics of computer and information science, and the Infosys Foundation Prize in Mathematical Sciences, and the IEEE Hamming Medal. Madhu Sudan is a fellow of the Association for Computing Machinery, the Institute of Electrical and Electronics Engineers and the American Mathematical Society. He is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.
Madhu Sudan's research interests revolve around mathematical studies of communication and computation. Specifically his research focusses on concepts of reliability and mechanisms that are, or can be, used by computers to interact reliably with each other. His research draws on tools from computational complexity, which studies efficiency of computation, and many areas of mathematics including algebra and probability theory. He is best known for his works on probabilistic checking of proofs, and on the design of list-decoding algorithms for error-correcting codes. His current research interests include property testing which is the study of sublinear time algorithms to estimate properties of massive data, and communication amid uncertainty, a mathematical study of the role of context in communication.
