A Survey of Single-Database Private Information Retrieval: Techniques and Applications

In this paper we survey the notion of Single-Database Private Information Retrieval (PIR). The first Single-Database PIR was constructed in 1997 by Kushilevitz and Ostrovsky and since then Single-Database PIR has emerged as an important cryptographic primitive. For example, Single-Database PIR turned out to be intimately connected to collision-resistant hash functions, oblivious transfer and public-key encryptions with additional properties. In this survey, we give an overview of many of the constructions for Single-Database PIR (including an abstract construction based upon homomorphic encryption) and describe some of the connections of PIR to other primitives.

[1]  Rafail Ostrovsky,et al.  Algebraic Lower Bounds for Computing on Encrypted Data , 2007, Electron. Colloquium Comput. Complex..

[2]  Oded Goldreich,et al.  A randomized protocol for signing contracts , 1985, CACM.

[3]  Rafail Ostrovsky,et al.  Software protection and simulation on oblivious RAMs , 1996, JACM.

[4]  Moni Naor,et al.  On the Compressibility of NP Instances and Cryptographic Applications , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[5]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[6]  Rafail Ostrovsky,et al.  Private Searching on Streaming Data , 2005, Journal of Cryptology.

[7]  Moni Naor,et al.  Communication Complexity and Secure Function Evaluation , 2001, Electron. Colloquium Comput. Complex..

[8]  Arto Salomaa,et al.  Public-Key Cryptography , 1991, EATCS Monographs on Theoretical Computer Science.

[9]  Rafail Ostrovsky,et al.  Universal service-providers for database private information retrieval (extended abstract) , 1998, PODC '98.

[10]  Yan-Cheng Chang,et al.  Single Database Private Information Retrieval with Logarithmic Communication , 2004, ACISP.

[11]  Gilles Brassard,et al.  All-or-Nothing Disclosure of Secrets , 1986, CRYPTO.

[12]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[13]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[14]  Ivan Damgård,et al.  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System , 2001, Public Key Cryptography.

[15]  Rafail Ostrovsky,et al.  Single Database Private Information Retrieval Implies Oblivious Transfer , 2000, EUROCRYPT.

[16]  Victor Shoup.  Advances in Cryptology - CRYPTO 2005: 25th Annual International Cryptology Conference, Santa Barbara, California, USA, August 14-18, 2005, Proceedings , 2005, CRYPTO.

[17]  Andrew Odlyzko,et al.  Advances in Cryptology — CRYPTO’ 86 , 2000, Lecture Notes in Computer Science.

[18]  Silvio Micali,et al.  Computationally Private Information Retrieval with Polylogarithmic Communication , 1999, EUROCRYPT.

[19]  Ueli Maurer,et al.  On Generating the Initial Key in the Bounded-Storage Model , 2004, EUROCRYPT.

[20]  Rafail Ostrovsky,et al.  Private Information Storage , 1996, IACR Cryptol. ePrint Arch..

[21]  Rafail Ostrovsky,et al.  Cryptography from Anonymity , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[22]  Moni Naor,et al.  Universal one-way hash functions and their cryptographic applications , 1989, STOC '89.

[23]  Yuval Ishai,et al.  One-way functions are essential for single-server private information retrieval , 1999, STOC '99.

[24]  Claude Crépeau,et al.  Equivalence Between Two Flavours of Oblivious Transfers , 1987, CRYPTO.

[25]  Yael Tauman Kalai,et al.  Succinct Non-Interactive Zero-Knowledge Proofs with Preprocessing for LOGSNP , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[26]  Rafail Ostrovsky,et al.  One-Way Trapdoor Permutations Are Sufficient for Non-trivial Single-Server Private Information Retrieval , 2000, EUROCRYPT.

[27]  Cynthia Dwork,et al.  Advances in Cryptology – CRYPTO 2020: 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, August 17–21, 2020, Proceedings, Part III , 2020, Annual International Cryptology Conference.

[28]  Eyal Kushilevitz,et al.  Private information retrieval , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[29]  Claude Cripeaut.  Equivalence Between Two Flavours of Oblivious Transfers , 1988 .

[30]  Rafail Ostrovsky,et al.  Fair Games against an All-Powerful Adversary , 1990, Advances In Computational Complexity Theory.

[31]  Moni Naor,et al.  Oblivious transfer and polynomial evaluation , 1999, STOC '99.

[32]  Rafail Ostrovsky,et al.  Replication is not needed: single database, computationally-private information retrieval , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[33]  Yuval Ishai,et al.  Protecting data privacy in private information retrieval schemes , 1998, STOC '98.

[34]  Craig Gentry,et al.  Single-Database Private Information Retrieval with Constant Communication Rate , 2005, ICALP.

[35]  Rafail Ostrovsky,et al.  Public Key Encryption That Allows PIR Queries , 2007, CRYPTO.

[36]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

[37]  Rafail Ostrovsky,et al.  Batch codes and their applications , 2004, STOC '04.

[38]  Rafail Ostrovsky,et al.  Public Key Encryption with Keyword Search , 2004, EUROCRYPT.

[39]  Rafail Ostrovsky,et al.  Searchable symmetric encryption: improved definitions and efficient constructions , 2006, CCS '06.

[40]  Bartosz Przydatek,et al.  On Robust Combiners for Private Information Retrieval and Other Primitives , 2006, CRYPTO.

[41]  Carl Pomerance,et al.  Advances in Cryptology — CRYPTO ’87 , 2000, Lecture Notes in Computer Science.

[42]  Aggelos Kiayias,et al.  Advances in Cryptology - EUROCRYPT 2004 , 2004 .

[43]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[44]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[45]  Rafail Ostrovsky,et al.  Private information storage (extended abstract) , 1997, STOC '97.

[46]  Helger Lipmaa,et al.  An Oblivious Transfer Protocol with Log-Squared Communication , 2005, ISC.

[47]  Yuval Ishai,et al.  Sufficient Conditions for Collision-Resistant Hashing , 2005, TCC.