TY - GEN
T1 - On computational shortcuts for information-theoretic PIR
AU - Hong, Matthew M.
AU - Ishai, Yuval
AU - Kolobov, Victor I.
AU - Lai, Russell W.F.
N1 - Publisher Copyright:
© International Association for Cryptologic Research 2020.
PY - 2020
Y1 - 2020
N2 - Information-theoretic private information retrieval (PIR) schemes have attractive concrete efficiency features. However, in the standard PIR model, the computational complexity of the servers must scale linearly with the database size. We study the possibility of bypassing this limitation in the case where the database is a truth table of a “simple” function, such as a union of (multi-dimensional) intervals or convex shapes, a decision tree, or a DNF formula. This question is motivated by the goal of obtaining lightweight homomorphic secret sharing (HSS) schemes and secure multiparty computation (MPC) protocols for the corresponding families. We obtain both positive and negative results. For “first-generation” PIR schemes based on Reed-Muller codes, we obtain computational shortcuts for the above function families, with the exception of DNF formulas for which we show a (conditional) hardness result. For “third-generation” PIR schemes based on matching vectors, we obtain stronger hardness results that apply to all of the above families. Our positive results yield new information-theoretic HSS schemes and MPC protocols with attractive efficiency features for simple but useful function families. Our negative results establish new connections between information-theoretic cryptography and fine-grained complexity.
AB - Information-theoretic private information retrieval (PIR) schemes have attractive concrete efficiency features. However, in the standard PIR model, the computational complexity of the servers must scale linearly with the database size. We study the possibility of bypassing this limitation in the case where the database is a truth table of a “simple” function, such as a union of (multi-dimensional) intervals or convex shapes, a decision tree, or a DNF formula. This question is motivated by the goal of obtaining lightweight homomorphic secret sharing (HSS) schemes and secure multiparty computation (MPC) protocols for the corresponding families. We obtain both positive and negative results. For “first-generation” PIR schemes based on Reed-Muller codes, we obtain computational shortcuts for the above function families, with the exception of DNF formulas for which we show a (conditional) hardness result. For “third-generation” PIR schemes based on matching vectors, we obtain stronger hardness results that apply to all of the above families. Our positive results yield new information-theoretic HSS schemes and MPC protocols with attractive efficiency features for simple but useful function families. Our negative results establish new connections between information-theoretic cryptography and fine-grained complexity.
UR - http://www.scopus.com/inward/record.url?scp=85098248856&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-64375-1_18
DO - 10.1007/978-3-030-64375-1_18
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AN - SCOPUS:85098248856
SN - 9783030643744
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 504
EP - 534
BT - Theory of Cryptography - 18th International Conference, TCC 2020, Proceedings
A2 - Pass, Rafael
A2 - Pietrzak, Krzysztof
T2 - 18th International Conference on Theory of Cryptography, TCCC 2020
Y2 - 16 November 2020 through 19 November 2020
ER -