Error-Tolerant Combiners for Oblivious Primitives

A robust combineris a construction that combines several implementations of a primitive based on different assumptions, and yields an implementation guaranteed to be secure if at least someassumptions (i.e. sufficiently many but not necessarily all) are valid. In this paper we generalize this concept by introducing error-tolerantcombiners, which in addition to protection against insecure implementations provide tolerance to functionality failures: an error-tolerant combiner guarantees a secure and correct implementation of the output primitive even if some of the candidates are insecure or faulty. We present simple constructions of error-tolerant robust combiners for oblivious linear function evaluation. The proposed combiners are also interesting in the regular (not error-tolerant) case, as the construction is much more efficient than the combiners known for oblivious transfer.

[1]  Miklos Santha,et al.  On the Reversibility of Oblivious Transfer , 1991, EUROCRYPT.

[2]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[3]  Stefan Wolf,et al.  Oblivious Transfer Is Symmetric , 2006, EUROCRYPT.

[4]  Oded Goldreich,et al.  On the power of cascade ciphers , 1985, TOCS.

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

[6]  Jürg Wullschleger,et al.  Robuster Combiners for Oblivious Transfer , 2007, TCC.

[7]  J. Rinehart.  U . S . Patent , 2006 .

[8]  Moni Naor,et al.  On Robust Combiners for Oblivious Transfer and Other Primitives , 2005, EUROCRYPT.

[9]  Moni Naor.  Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007, Proceedings , 2007, EUROCRYPT.

[10]  Anna Lysyanskaya,et al.  How to Securely Outsource Cryptographic Computations , 2005, TCC.

[11]  InitializerRonald L. RivestLaboratory.  Unconditionally Secure Commitment and Oblivious Transfer Schemes Using Private Channels and a Trusted Initializer , 1999 .

[12]  Ueli Maurer,et al.  Cascade ciphers: The importance of being first , 1993, Journal of Cryptology.

[13]  Michael O. Rabin,et al.  How To Exchange Secrets with Oblivious Transfer , 2005, IACR Cryptol. ePrint Arch..

[14]  Joe Kilian,et al.  Achieving Oblivious Transfer Using Weakened Security Assumptions (Extended Abstract) , 1988, FOCS 1988.

[15]  Alfred Menezes,et al.  Topics in Cryptology – CT-RSA 2005 , 2005 .

[16]  Amir Herzberg,et al.  On Tolerant Cryptographic Constructions , 2005, CT-RSA.

[17]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[18]  Ronald Cramer,et al.  Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings , 2005, EUROCRYPT.

[19]  Moni Naor,et al.  Oblivious Polynomial Evaluation , 2006, SIAM J. Comput..

[20]  Andrew Chi-Chih Yao,et al.  How to Generate and Exchange Secrets (Extended Abstract) , 1986, FOCS.

[21]  Jonathan Katz,et al.  Chosen-Ciphertext Security of Multiple Encryption , 2005, TCC.

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

[23]  Serge Vaudenay,et al.  Advances in Cryptology - EUROCRYPT 2006 , 2006, Lecture Notes in Computer Science.

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

[25]  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.

[26]  Ivan Damgård,et al.  On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions , 1998, EUROCRYPT.

[27]  Jürg Wullschleger.  Oblivious-transfer amplification , 2007, Ausgezeichnete Informatikdissertationen.

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

[29]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

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

[31]  Yuval Ishai,et al.  OT-Combiners via Secure Computation , 2008, TCC.

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

[33]  G. Blakley,et al.  An efficient algorithm for constructing a cryptosystem which is harder to break than two other cryptosystems , 1981 .

[34]  Joe Kilian,et al.  Achieving oblivious transfer using weakened security assumptions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[35]  Donald W. Davies,et al.  Advances in Cryptology — EUROCRYPT ’91 , 2001, Lecture Notes in Computer Science.

[36]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.