Fast Actively Secure OT Extension for Short Secrets

Oblivious Transfer (OT) is one of the most fundamental cryptographic primitives with wide-spread application in general secure multi-party computation (MPC) as well as in a number of tailored and special-purpose problems of interest such as private set intersection (PSI), private information retrieval (PIR), contract signing to name a few. Often the instantiations of OT require prohibitive communication and computation complexity. OT extension protocols are introduced to compute a very large number of OTs referred to as extended OTs at the cost of a small number of OTs referred to as seed OTs. We present a fast OT extension protocol for small secrets in the active setting. Our protocol when used to produce 1-out-of-n OTs outperforms all the known actively secure OT extensions. Our protocol is built on the semi-honest secure extension protocol of Kolesnikov and Kumaresan of CRYPTO'13 (referred to as KK13 protocol henceforth) which is the best known OT extension for short secrets.

[1]  Alex J. Malozemoff,et al.  Amortizing Garbled Circuits , 2015, IACR Cryptol. ePrint Arch..

[2]  Paul G. Spirakis,et al.  Space Efficient Hash Tables with Worst Case Constant Access Time , 2003, Theory of Computing Systems.

[3]  Moni Naor,et al.  Backyard Cuckoo Hashing: Constant Worst-Case Operations with a Succinct Representation , 2009, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

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

[5]  Yuval Ishai,et al.  Extending Oblivious Transfers Efficiently , 2003, CRYPTO.

[6]  Benny Pinkas,et al.  Phasing: Private Set Intersection Using Permutation-based Hashing , 2015, USENIX Security Symposium.

[7]  Moni Naor,et al.  Computationally Secure Oblivious Transfer , 2004, Journal of Cryptology.

[8]  Donald Beaver,et al.  Correlated pseudorandomness and the complexity of private computations , 1996, STOC '96.

[9]  Changyu Dong,et al.  When private set intersection meets big data: an efficient and scalable protocol , 2013, CCS.

[10]  Silvio Micali,et al.  A Completeness Theorem for Protocols with Honest Majority , 1987, STOC 1987.

[11]  Mikkel Lambæk.  Breaking and Fixing Private Set Intersection Protocols , 2016, IACR Cryptol. ePrint Arch..

[12]  Yehuda Lindell,et al.  More efficient oblivious transfer and extensions for faster secure computation , 2013, CCS.

[13]  Marcel Keller,et al.  Actively Secure OT Extension with Optimal Overhead , 2015, CRYPTO.

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

[15]  Russell Impagliazzo,et al.  Limits on the provable consequences of one-way permutations , 1988, STOC '89.

[16]  Jesper Buus Nielsen,et al.  Extending Oblivious Transfers Efficiently - How to get Robustness Almost for Free , 2007, IACR Cryptol. ePrint Arch..

[17]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

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

[19]  Claudio Orlandi,et al.  MiniLEGO: Efficient Secure Two-Party Computation from General Assumptions , 2013, EUROCRYPT.

[20]  Yehuda Lindell.  Fast Cut-and-Choose-Based Protocols for Malicious and Covert Adversaries , 2015, Journal of Cryptology.

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

[22]  Yehuda Lindell,et al.  On the Feasibility of Extending Oblivious Transfer , 2013, Journal of Cryptology.

[23]  Abhi Shelat,et al.  Fast two-party secure computation with minimal assumptions , 2013, CCS.

[24]  Rudolf Ahlswede,et al.  Founding Cryptography on Oblivious Transfer , 2016 .

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

[26]  Yehuda Lindell,et al.  More Efficient Oblivious Transfer Extensions with Security for Malicious Adversaries , 2015, IACR Cryptol. ePrint Arch..

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

[28]  Andrew Chi-Chih Yao,et al.  How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[29]  Enrique Larraia,et al.  Extending Oblivious Transfer Efficiently - or - How to Get Active Security with Constant Cryptographic Overhead , 2014, LATINCRYPT.

[30]  Vladimir Kolesnikov,et al.  Improved OT Extension for Transferring Short Secrets , 2013, CRYPTO.

[31]  Yehuda Lindell,et al.  An Efficient Protocol for Secure Two-Party Computation in the Presence of Malicious Adversaries , 2007, Journal of Cryptology.

[32]  Claudio Orlandi,et al.  A New Approach to Practical Active-Secure Two-Party Computation , 2012, IACR Cryptol. ePrint Arch..

[33]  Michael Mitzenmacher,et al.  More Robust Hashing: Cuckoo Hashing with a Stash , 2008, ESA.

[34]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

[35]  Claudio Orlandi,et al.  LEGO for Two-Party Secure Computation , 2009, TCC.

[36]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[37]  Oded Goldreich,et al.  How to Solve any Protocol Problem - An Efficiency Improvement , 1987, CRYPTO.

[38]  Yehuda Lindell,et al.  Blazing Fast 2PC in the Offline/Online Setting with Security for Malicious Adversaries , 2015, IACR Cryptol. ePrint Arch..

[39]  Benny Pinkas,et al.  Faster Private Set Intersection Based on OT Extension , 2014, USENIX Security Symposium.