Distributed Vector-OLE: Improved Constructions and Implementation

We investigate concretely efficient protocols for distributed oblivious linear evaluation over vectors (Vector-OLE). Boyle et al. (CCS 2018) proposed a protocol for secure distributed pseudorandom Vector-OLE generation using sublinearcommunication, but they did not provide an implementation. Their construction is based on a variant of the LPN assumption and assumes a distributed key generation protocol for single-point Function Secret Sharing (FSS), as well as an efficient batching scheme to obtain multi-point FSS. We show that this requirement can be relaxed, resulting in a weaker variant of FSS, for which we give an efficient protocol. This allows us to use efficient probabilistic batch codes that were also recently used for batched PIR by Angel et al. (S&P 2018). We construct a full Vector-OLE generator from our protocols, and compare it experimentally with alternative approaches. Our implementation parallelizes very well, and has low communication overhead in practice. For generating a VOLE of size $2^20 $, our implementation only takes $0.52$s on 32 cores.

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

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

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

[4]  Yuval Ishai,et al.  Function Secret Sharing , 2015, EUROCRYPT.

[5]  Marcel Keller,et al.  Overdrive: Making SPDZ Great Again , 2018, IACR Cryptol. ePrint Arch..

[6]  L. Dagum,et al.  OpenMP: an industry standard API for shared-memory programming , 1998 .

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

[8]  Rasmus Pagh,et al.  Cuckoo Hashing , 2001, Encyclopedia of Algorithms.

[9]  KirschAdam,et al.  More Robust Hashing: Cuckoo Hashing with a Stash , 2009 .

[10]  N. S. Barnett,et al.  Private communication , 1969 .

[11]  Dan Boneh,et al.  Constraining Pseudorandom Functions Privately , 2015, Public Key Cryptography.

[12]  Ivan Damgård,et al.  Multiparty Computation from Somewhat Homomorphic Encryption , 2012, IACR Cryptol. ePrint Arch..

[13]  Yuval Ishai,et al.  Founding Cryptography on Oblivious Transfer - Efficiently , 2008, CRYPTO.

[14]  Alex J. Malozemoff,et al.  Efficiently Enforcing Input Validity in Secure Two-party Computation , 2016, IACR Cryptol. ePrint Arch..

[15]  Yuval Ishai,et al.  Compressing Vector OLE , 2018, CCS.

[16]  Nico Döttling,et al.  TinyOLE: Efficient Actively Secure Two-Party Computation from Oblivious Linear Function Evaluation , 2017, IACR Cryptol. ePrint Arch..

[17]  Niv Gilboa,et al.  Two Party RSA Key Generation , 1999, CRYPTO.

[18]  Yuval Ishai,et al.  Efficient Pseudorandom Correlation Generators: Silent OT Extension and More , 2019, IACR Cryptol. ePrint Arch..

[19]  Payman Mohassel,et al.  SecureML: A System for Scalable Privacy-Preserving Machine Learning , 2017, 2017 IEEE Symposium on Security and Privacy (SP).

[20]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

[21]  Marcel Keller,et al.  Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits , 2013, ESORICS.

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

[23]  Yuval Ishai,et al.  Secure Arithmetic Computation with Constant Computational Overhead , 2017, CRYPTO.

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

[25]  Yuval Ishai,et al.  Function Secret Sharing: Improvements and Extensions , 2016, CCS.

[26]  Yehuda Lindell,et al.  A Proof of Security of Yao’s Protocol for Two-Party Computation , 2009, Journal of Cryptology.

[27]  Donald Beaver,et al.  Efficient Multiparty Protocols Using Circuit Randomization , 1991, CRYPTO.

[28]  Yehuda Lindell,et al.  Introduction to Modern Cryptography , 2004 .

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

[30]  Abhi Shelat,et al.  Scaling ORAM for Secure Computation , 2017, IACR Cryptol. ePrint Arch..

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

[32]  Michael Zohner,et al.  ABY - A Framework for Efficient Mixed-Protocol Secure Two-Party Computation , 2015, NDSS.

[33]  Nico Döttling,et al.  David & Goliath Oblivious Affine Function Evaluation - Asymptotically Optimal Building Blocks for Universally Composable Two-Party Computation from a Single Untrusted Stateful Tamper-Proof Hardware Token , 2012, IACR Cryptol. ePrint Arch..

[34]  Tobias Nilges,et al.  An Algebraic Approach to Maliciously Secure Private Set Intersection , 2019, IACR Cryptol. ePrint Arch..

[35]  Benny Pinkas,et al.  Efficient Set Intersection with Simulation-Based Security , 2014, Journal of Cryptology.

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

[37]  Benny Pinkas,et al.  Scalable Private Set Intersection Based on OT Extension , 2018, IACR Cryptol. ePrint Arch..

[38]  Abraham Waksman,et al.  A Permutation Network , 1968, JACM.

[39]  Hao Chen,et al.  Fast Private Set Intersection from Homomorphic Encryption , 2017, CCS.

[40]  Christof Paar,et al.  Lapin: An Efficient Authentication Protocol Based on Ring-LPN , 2012, FSE.

[41]  Yuval Ishai,et al.  Efficient Two-Round OT Extension and Silent Non-Interactive Secure Computation , 2019, IACR Cryptol. ePrint Arch..

[42]  Benny Pinkas,et al.  Make Some ROOM for the Zeros: Data Sparsity in Secure Distributed Machine Learning , 2019, IACR Cryptol. ePrint Arch..

[43]  Peter Rindal,et al.  PIR-PSI: Scaling Private Contact Discovery , 2018, IACR Cryptol. ePrint Arch..

[44]  Yehuda Lindell,et al.  Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series) , 2007 .

[45]  Vladimir Kolesnikov,et al.  Efficient Batched Oblivious PRF with Applications to Private Set Intersection , 2016, CCS.

[46]  Robert S. Winternitz.  A Secure One-Way Hash Function Built from DES , 1984, 1984 IEEE Symposium on Security and Privacy.

[47]  Ivan Damgård,et al.  Is Public-Key Encryption Based on LPN Practical? , 2012, IACR Cryptol. ePrint Arch..

[48]  Srinath T. V. Setty,et al.  PIR with Compressed Queries and Amortized Query Processing , 2018, 2018 IEEE Symposium on Security and Privacy (SP).

[49]  Mariana Raykova,et al.  Privacy-Preserving Distributed Linear Regression on High-Dimensional Data , 2017, Proc. Priv. Enhancing Technol..

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

[51]  Benny Pinkas,et al.  Keyword Search and Oblivious Pseudorandom Functions , 2005, TCC.

[52]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

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

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

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