Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
One-way functions are essential for single-server private information retrieval
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computing with Very Weak Random Sources
SIAM Journal on Computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Lower bounds on the efficiency of encryption and digital signature schemes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Limits on the Efficiency of One-Way Permutation-Based Hash Functions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Lower bounds on the efficiency of generic cryptographic constructions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The relationship between public key encryption and oblivious transfer
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
On the Compressibility of NP Instances and Cryptographic Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Statistical Zero-Knowledge Arguments for NP from Any One-Way Function
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Succinct Non-Interactive Zero-Knowledge Proofs with Preprocessing for LOGSNP
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Single database private information retrieval implies oblivious transfer
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
One-way permutations, interactive hashing and statistically hiding commitments
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Bounds on the efficiency of “black-box” commitment schemes
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Single-database private information retrieval with constant communication rate
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Sufficient conditions for collision-resistant hashing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
An oblivious transfer protocol with log-squared communication
ISC'05 Proceedings of the 8th international conference on Information Security
Private predictions on hidden Markov models
Artificial Intelligence Review
Limits on the power of zero-knowledge proofs in cryptographic constructions
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Private coins versus public coins in zero-knowledge proof systems
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
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We study the communication complexity of single-server Private Information Retrieval (PIR) protocols that are based on fundamental cryptographic primitives in a black-box manner. In this setting, we establish a tight lower bound on the number of bits communicated by the server in any polynomially-preserving construction that relies on trapdoor permutations. More specifically, our main result states that in such constructions Ω(n) bits must be communicated by the server, where n is the size of the server's database, and this improves the Ω(n/ log n) lower bound due to Haitner, Hoch, Reingold and Segev (FOCS '07). Therefore, in the setting under consideration, the naive solution in which the user downloads the entire database turns out to be optimal up to constant multiplicative factors. We note that the lower bound we establish holds for the most generic form of trapdoor permutations, including in particular enhanced trapdoor permutations. Technically speaking, this paper consists of two main contributions from which our lower bound is obtained. First, we derive a tight lower bound on the number of bits communicated by the sender during the commit stage of any black-box construction of a statistically-hiding bitcommitment scheme from a family of trapdoor permutations. This lower bound asymptotically matches the upper bound provided by the scheme of Naor, Ostrovsky, Venkatesan and Yung (CRYPTO '92). Second, we improve the efficiency of the reduction of statistically-hiding commitment schemes to low-communication single-server PIR, due to Beimel, Ishai, Kushilevitz and Malkin (STOC '99). In particular, we present a reduction that essentially preserves the communication complexity of the underlying single-server PIR protocol.