We study both the practical and theoretical efficiency of private information retrieval (PIR) protocols in a model wherein several untrusted servers work to obliviously service remote clients’ requests for data and yet no pair of servers colludes in a bid to violate said obliviousness. In exchange for such a strong security assumption, we obtain new PIR protocols exhibiting remarkable efficiency with respect to every cost metric—download, upload, computation, and round complexity—typically considered in the PIR literature.
The new constructions extend a multiserver PIR protocol of Shah, Rashmi, and Ramchandran (ISIT 2014), which exhibits a remarkable property of its own: to fetch a b-bit record from a collection of r such records, the client need only download b + 1 bits total. We find that allowing “a bit more” download (and optionally introducing computational assumptions) yields a family of protocols offering very attractive trade-offs. In addition to Shah et al.’s protocol, this family includes as special cases (2-server instances of) the seminal protocol of Chor, Goldreich, Kushilevitz, and Sudan (FOCS 1995) and the recent DPF-based protocol of Boyle, Gilboa, and Ishai (CCS 2016). An implicit “folklore” axiom that dogmatically permeates the research literature on multiserver PIR posits that the latter protocols are the “most efficient” protocols possible in the perfectly and computationally private settings, respectively. Yet our findings soundly refute this supposed axiom: These special cases are (by far) the least performant representatives of our family, with essentially all other parameter settings yielding instances that are significantly faster.
 Carlos Aguilar-Melchor and Philippe Gaborit. A fast private information retrieval protocol. In Proceedings of ISIT 2008, pages 1848–1852, Toronto, ON, Canada (July, 2008).
 Sebastian Angel, Hao Chen, Kim Laine, and Srinath T. V. Setty. PIR with compressed queries and amortized query processing. In Proceedings of IEEE S&P 2018, pages 962–979, San Francisco, CA, USA (May, 2018).
 Karim A. Banawan and Sennur Ulukus. Private information retrieval from Byzantine and colluding databases. In Proceedings of Allerton 2017, pages 1091–1098, Monticello, IL, USA (October, 2017).
 Amos Beimel, Yuval Ishai, and Tal Malkin. Reducing the servers’ computation in private information retrieval: PIR with preprocessing. Journal of Cryptology, 17(2):125–151 (March, 2004).
 Amos Beimel and Yoav Stahl. Robust information-theoretic private information retrieval. In Proceedings of SCN 2002, volume 2576 of LNCS, pages 326–341, Amalfi, Italy (September, 2002).
 Simon R. Blackburn, Tuvi Etzion, and Maura B. Paterson. PIR schemes with small download complexity and low storage requirements. In Proceedings of ISIT 2017, pages 146–150, Aachen, Germany (June, 2017).
 Elette Boyle, Niv Gilboa, and Yuval Ishai. Breaking the circuit size barrier for secure computation under DDH. In Advances in Cryptology: Proceedings of CRYPTO2016 (Part I), volume 9814 of LNCS, pages 509–539, Santa Barbara, CA, USA (August, 2016).
 Elette Boyle, Niv Gilboa, and Yuval Ishai. Function secret sharing: Improvements and extensions. In Proceedings of CCS 2016, pages 1292–1303, Vienna, Austria (October, 2016).
 Benny Chor and Niv Gilboa. Computationally private information retrieval (Extended abstract). In Proceedings of STOC1997, pages 304–313, El Paso, TX, USA (May, 1997).
 Benny Chor, Oded Goldreich, Eyal Kushilevitz, and Madhu Sudan. Private information retrieval. In Proceedings of FOCS 1995, pages 41–50, Milwaukee, WI, USA (October, 1995).
 Benny Chor, Eyal Kushilevitz, Oded Goldreich, and Madhu Sudan. Private information retrieval. Journal of the ACM (JACM), 45(6):965–981 (November, 1998).
 Henry Corrigan-Gibbs, Dan Boneh, and David Mazières. Riposte: An anonymous messaging system handling millions of users. In Proceedings of IEEE S&P 2015, pages 321–338, San Jose, CA, USA (May, 2015).
 Danniel Demmler, Amir Herzberg, and Thomas Schneider. RAIDPIR: Practical multi-server PIR. In Proceedings of CCSW2014, pages 45–56, Scottsdale, AZ, USA (November, 2014).
 Casey Devet, Ian Goldberg, and Nadia Heninger. Optimally robust private information retrieval. In Proceedings of USENIX Security 2012, pages 269–283, Bellevue, WA, USA (August, 2012).
 Yael Gertner, Yuval Ishai, Eyal Kushilevitz, and Tal Malkin. Protecting data privacy in private information retrieval schemes. Journal of Computer and System Science (JCSS), 60(3):592–629 (June, 2000).
 Niv Gilboa and Yuval Ishai. Distributed point functions and their applications. In Advances in Cryptology: Proceedings of EUROCRYPT 2014, volume 8441 of LNCS, pages 640–658, Copenhagen, Denmark (May, 2014).
 Ian Goldberg. Improving the robustness of private information retrieval. In Proceedings of IEEE S&P 2007, pages 131–148, Oakland, CA, USA (May, 2007).
 Ian Goldberg, Casey Devet, Wouter Lueks, Ann Yang, Paul Hendry, and Ryan Henry. Percy++ / PIR in C++; version 1.0 [computer software]. Available from: git://git-crysp.uwaterloo.ca/percy (October, 2014).
 Trinabh Gupta, Natacha Crooks, Whitney Mulhern, Srinath T. V. Setty, Lorenzo Alvisi, and Michael Walfish. Scalable and private media consumption with Popcorn. In Proceedings of NSDI 2016 (March, 2016).
 Ryan Henry. Polynomial batch codes for efficient IT-PIR. In Proceedings on Privacy Enhancing Technologies (PoPETS), volume 2016(4), pages 202–218, Darmstadt, Germany (July, 2016).
 Ryan Henry, Yizhou Huang, and Ian Goldberg. One (block) size fits all: PIR and SPIR with variable-length records via multi-block queries. In Proceedings of NDSS 2013, San Diego, CA, USA (February, 2013).
 Aggelos Kiayias, Nikos Leonardos, Helger Lipmaa, Kateryna Pavlyk, and Qiang Tang. Optimal rate private information retrieval from homomorphic encryption. In Proceedings of PETS 2015, volume 2, pages 222–243, Philadelphia, PA, USA (June–July, 2015).
 Wouter Lueks and Ian Goldberg. Sublinear scaling for multi-client private information retrieval. In Proceedings of FC 2015, volume 8975 of LNCS, pages 168–186, San Juan, Puerto Rico (January, 2015).
 Femi G. Olumofin and Ian Goldberg. Revisiting the computational practicality of private information retrieval. In Proceedings of FC 2011, volume 7035 of LNCS, pages 158–172, Gros Islet, St. Lucia (February, 2011).
 Nihar B. Shah, K. V. Rashmi, and Kannan Ramchandran. One extra bit of download ensures perfectly private information retrieval. In Proceedings of ISIT 2014, pages 856–860, Honolulu, HI, USA (June–July, 2014).
 Radu Sion and Bogdan Carbunar. On the practicality of private information retrieval. In Proceedings of NDSS 2007, San Diego, CA, USA (March, 2007).
 Hua Sun and Syed Ali Jafar. The capacity of private information retrieval with colluding databases. In Proceedings of GlobeCom 2016, pages 941–946, Washington, DC, USA (December, 2016).
 Hua Sun and Syed Ali Jafar. The capacity of private information retrieval. IEEE Transactions on Information Theory, 63(7):4075–4088, 2017.
 Hua Sun and Syed Ali Jafar. The capacity of robust private information retrieval with colluding databases. IEEE Transactions on Information Theory, 64(4):2361–2370, 2018.
 Luqin Wang, Trishank Karthik Kuppusamy, Yong Liu, and Justin Cappos. A fast multi-server, multi-block private information retrieval protocol. In Proceedings of GlobeCom 2015, pages 1–6, San Diego, CA, USA (December, 2015).
 Sergey Yekhanin. Private information retrieval. Communications of the ACM (CACM), 53(4):68–73 (April, 2010).