TY - GEN
T1 - Random-Index PIR and Applications
AU - Gentry, Craig
AU - Halevi, Shai
AU - Magri, Bernardo
AU - Nielsen, Jesper Buus
AU - Yakoubov, Sophia
N1 - Publisher Copyright:
© 2021, International Association for Cryptologic Research.
PY - 2021
Y1 - 2021
N2 - Private information retrieval (PIR) lets a client retrieve an entry from a database without the server learning which entry was retrieved. Here we study a weaker variant that we call random-index PIR (RPIR), where the retrieved index is an output rather than an input of the protocol, and is chosen at random. RPIR is clearly weaker than PIR, but it suffices for some interesting applications and may be realized more efficiently than full-blown PIR. We report here on two lines of work, both tied to RPIR but otherwise largely unrelated. The first line of work studies RPIR as a primitive on its own. Perhaps surprisingly, we show that RPIR is in fact equivalent to PIR when there are no restrictions on the number of communication rounds. On the other hand, RPIR can be implemented in a “noninteractive” setting (with pre-processing), which is clearly impossible for PIR. For two-server RPIR we even show a truly noninteractive solution, offering information-theoretic security without any pre-processing. The other line of work, which was the original motivation for our work, uses RPIR to improve on the recent work of Benhamouda et al. (TCC’20) for maintaining secret values on public blockchains. Their solution depends on a method for selecting many random public keys from a PKI while hiding most of the selected keys from an adversary. However, the method they proposed is vulnerable to a double-dipping attack, limiting its resilience. Here we observe that a RPIR protocol, where the client is implemented via secure MPC, can eliminate that vulnerability. We thus get a secrets-on-blockchain protocol (and more generally large-scale MPC) which is resilient to any fraction f< 1 / 2 of corrupted parties, resolving the main open problem left from the work of Benhamouda et al. As the client in this solution is implemented via secure MPC, it really brings home the need to make it as efficient as possible. We thus strive to explore whatever efficiency gains we can get by using RPIR rather than PIR. We achieve more gains by using batch RPIR where multiple indexes are retrieved at once. Lastly, we observe that this application can make do with a weaker security guarantee than full RPIR, and show that this weaker variant can be realized even more efficiently. We discuss one protocol in particular that may be attractive for practical implementations.
AB - Private information retrieval (PIR) lets a client retrieve an entry from a database without the server learning which entry was retrieved. Here we study a weaker variant that we call random-index PIR (RPIR), where the retrieved index is an output rather than an input of the protocol, and is chosen at random. RPIR is clearly weaker than PIR, but it suffices for some interesting applications and may be realized more efficiently than full-blown PIR. We report here on two lines of work, both tied to RPIR but otherwise largely unrelated. The first line of work studies RPIR as a primitive on its own. Perhaps surprisingly, we show that RPIR is in fact equivalent to PIR when there are no restrictions on the number of communication rounds. On the other hand, RPIR can be implemented in a “noninteractive” setting (with pre-processing), which is clearly impossible for PIR. For two-server RPIR we even show a truly noninteractive solution, offering information-theoretic security without any pre-processing. The other line of work, which was the original motivation for our work, uses RPIR to improve on the recent work of Benhamouda et al. (TCC’20) for maintaining secret values on public blockchains. Their solution depends on a method for selecting many random public keys from a PKI while hiding most of the selected keys from an adversary. However, the method they proposed is vulnerable to a double-dipping attack, limiting its resilience. Here we observe that a RPIR protocol, where the client is implemented via secure MPC, can eliminate that vulnerability. We thus get a secrets-on-blockchain protocol (and more generally large-scale MPC) which is resilient to any fraction f< 1 / 2 of corrupted parties, resolving the main open problem left from the work of Benhamouda et al. As the client in this solution is implemented via secure MPC, it really brings home the need to make it as efficient as possible. We thus strive to explore whatever efficiency gains we can get by using RPIR rather than PIR. We achieve more gains by using batch RPIR where multiple indexes are retrieved at once. Lastly, we observe that this application can make do with a weaker security guarantee than full RPIR, and show that this weaker variant can be realized even more efficiently. We discuss one protocol in particular that may be attractive for practical implementations.
KW - Batch PIR
KW - Large-scale MPC
KW - Private information retrieval
KW - Random ORAM
KW - Random PIR
KW - Secrets on blockchain
UR - https://www.scopus.com/pages/publications/85120076697
U2 - 10.1007/978-3-030-90456-2_2
DO - 10.1007/978-3-030-90456-2_2
M3 - Article in proceedings
AN - SCOPUS:85120076697
SN - 9783030904555
T3 - Lecture Notes in Computer Science
SP - 32
EP - 61
BT - Theory of Cryptography
A2 - Nissim, Kobbi
A2 - Waters, Brent
PB - Springer
T2 - 19th International Conference on Theory of Cryptography, TCC 2021
Y2 - 8 November 2021 through 11 November 2021
ER -