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Journal of Cryptology

, Volume 30, Issue 3, pp 805–858 | Cite as

More Efficient Oblivious Transfer Extensions

  • Gilad Asharov
  • Yehuda Lindell
  • Thomas Schneider
  • Michael Zohner
Article

Abstract

Oblivious transfer (OT) is one of the most fundamental primitives in cryptography and is widely used in protocols for secure two-party and multi-party computation. As secure computation becomes more practical, the need for practical large-scale OT protocols is becoming more evident. OT extensions are protocols that enable a relatively small number of “base-OTs” to be utilized to compute a very large number of OTs at low cost. In the semi-honest setting, Ishai et al. (Advances in cryptology—CRYPTO’03, vol 2729 of LNCS, Springer, 2003) presented an OT extension protocol for which the cost of each OT (beyond the base-OTs) is just a few hash function operations. In the malicious setting, Nielsen et al. (Advances in cryptology—CRYPTO’12, vol 7417 of LNCS, Springer, 2012) presented an efficient OT extension protocol for the setting of malicious adversaries that is secure in a random oracle model. In this work, we improve OT extensions with respect to communication complexity, computation complexity, and scalability in the semi-honest, covert, and malicious model. Furthermore, we show how to modify our maliciously secure OT extension protocol to achieve security with respect to a version of correlation robustness instead of the random oracle. We also provide specific optimizations of OT extensions that are tailored to the use of OT in various secure computation protocols such as Yao’s garbled circuits and the protocol of Goldreich–Micali–Wigderson, which reduce the communication complexity even further. We experimentally verify the efficiency gains of our protocols and optimizations.

Keywords

Cryptographic protocols Oblivious transfer extension Implementation 

Notes

Acknowledgments

This work was partially supported by the European Union’s Seventh Framework Program (FP7/2007-2013) Grant Agreement No. 609611 (PRACTICE). The first author was supported by the Israeli Centers of Research Excellence (I-CORE) Program (Center No. 4/11). The second author is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC consolidators Grant Agreement No. 615172 (HIPS). The third and fourth authors are supported by the German Federal Ministry of Education and Research (BMBF) within CRISP, by the DFG as part of project E3 within the CRC 1119 CROSSING, and by the Hessian LOEWE excellence initiative within CASED. We would like to thank the anonymous reviewers of the Journal of Cryptology for their valuable comments on our work.

References

  1. 1.
    Y. Aumann, Y. Lindell. Security against covert adversaries: Efficient protocols for realistic adversaries, in Journal of Cryptology, vol. 23(2), (Springer, 2010) pp. 281–343Google Scholar
  2. 2.
    G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More efficient oblivious transfer and extensions for faster secure computation, in ACM Computer and Communications Security (CCS’13), pp. 535–548. ACM, 2013. Code: http://encrypto.de/code/OTExtension
  3. 3.
    G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More efficient oblivious transfer extensions with security for malicious adversaries, in Advances in Cryptology—EUROCRYPT’15, vol. 9056 of LNCS, (Springer, 2015) pp. 673–701. Full version: http://eprint.iacr.org/2015/061
  4. 4.
    J. Bringer, H. Chabanne, A. Patey. SHADE: secure hamming distance computation from oblivious transfer, in Financial Cryptography and Data Security (FC’13), vol. 7862 of LNCS, (Springer, 2013), pp. 164–176Google Scholar
  5. 5.
    D. Beaver. Efficient multiparty protocols using circuit randomization, in Advances in cryptology—-CRYPTO’91, vol. 576 of LNCS, (Springer, 1991), pp. 420–432Google Scholar
  6. 6.
    D. Beaver. Correlated pseudorandomness and the complexity of private computations, in Symposium on the theory of computing (STOC’96), (ACM, 1996), pp. 479–488Google Scholar
  7. 7.
    M. Bellare, V. Hoang, S. Keelveedhi, P. Rogaway. Efficient garbling from a fixed-key blockcipher, on IEEE Symposium on Security and Privacy (S&P’13), (IEEE, 2013), pp. 478–492Google Scholar
  8. 8.
    S. S. Burra, E. Larraia, J. B. Nielsen, P. S. Nordholt, C. Orlandi, E. Orsini, P. Scholl, and N. P. Smart. High performance multi-party computation for binary circuits based on oblivious transfer. Cryptology ePrint Archive, Report 2015/472, 2015. Online: http://eprint.iacr.org/2015/472.
  9. 9.
    A. Ben-David, N. Nisan, B. Pinkas. FairplayMP: a system for secure multi-party computation, in ACM Computer and Communications Security (CCS’08), (ACM, 2008) pp. 257–266Google Scholar
  10. 10.
    R. Canetti. Security and composition of multiparty cryptographic protocols. J. Cryptology, 13(1):143–202, 2000.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    S.G. Choi, K.-W. Hwang, J. Katz, T. Malkin, D. Rubenstein. Secure multi-party computation of Boolean circuits with applications to privacy in on-line marketplaces, in Cryptographers’ Track at the RSA Conference (CT-RSA’12), vol. 7178 of LNCS, (Springer, 2012) pp. 416–432Google Scholar
  12. 12.
    T. Chou, C. Orlandi. The simplest protocol for oblivious transfer, in Progress in Cryptology—LATINCRYPT’15, vol. 9230 of LNCS, (Springer, 2015), pp. 40–58Google Scholar
  13. 13.
    C. Dong, L. Chen, Z. Wen. When private set intersection meets big data: an efficient and scalable protocol, in ACM Computer and Communications Security (CCS’13), (ACM, 2013), pp. 789–800Google Scholar
  14. 14.
    I. Damgård, R. Lauritsen, T. Toft. An empirical study and some improvements of the MiniMac protocol for secure computation, in Security and Cryptography for Networks (SCN’14), vol. 8642 of LNCS, (Springer, 2014), pp. 398–415Google Scholar
  15. 15.
    D. Demmler, T. Schneider, M. Zohner. ABY—a framework for efficient mixed-protocol secure two-party computation, in Network and Distributed System Security (NDSS’15). The Internet Society, 2015Google Scholar
  16. 16.
    I. Damgård, S. Zakarias. Constant-overhead secure computation of Boolean circuits using preprocessing, in Theory of cryptography conference (TCC’13), vol. 7785 of LNCS, (Springer, 2013), pp. 621–641Google Scholar
  17. 17.
    Z. Erkin, M. Franz, J. Guajardo, S. Katzenbeisser, I. Lagendijk, T. Toft. Privacy-preserving face recognition, in Privacy Enhancing Technologies Symposium (PETS’09), vol. 5672 of LNCS, (Springer, 2009), pp. 235–253Google Scholar
  18. 18.
    Y. Ejgenberg, M. Farbstein, M. Levy, Y. Lindell. SCAPI: the secure computation application programming interface. Cryptology ePrint Archive, Report 2012/629, 2012. Online: http://eprint.iacr.org/2012/629
  19. 19.
    S. Even, O. Goldreich, A. Lempel. A randomized protocol for signing contracts, in Communications of the ACM, vol. 28(6), (ACM, 1985), pp. 637–647Google Scholar
  20. 20.
    J.O. Eklundh. A fast computer method for matrix transposing, in IEEE Transactions on Computers, vol. C-21(7), (IEEE, 1972), pp. 801–803Google Scholar
  21. 21.
    K. Frikken, M. Atallah, C. Zhang. Privacy-preserving credit checking, in Electronic Commerce (EC’05), (ACM, 2005), pp. 147–154Google Scholar
  22. 22.
    T.K. Frederiksen, M. Keller, E. Orsini, P. Scholl. A unified approach to MPC with preprocessing using OT, in Advances in Cryptology—ASIACRYPT’15, vol. 9452 of LNCS, (Springer, 2015), pp. 711–735Google Scholar
  23. 23.
    T. K. Frederiksen, J. B. Nielsen. Fast and maliciously secure two-party computation using the GPU, in Applied Cryptography and Network Security (ACNS’13), vol. 7954 of LNCS, (Springer, 2013), pp. 339–356Google Scholar
  24. 24.
    S.D. Gordon, J. Katz, V. Kolesnikov, F. Krell, T. Malkin, M. Raykova, Y. Vahlis. Secure two-party computation in sublinear (amortized) time, in ACM Computer and Communications Security (CCS’12), (ACM, 2012), pp. 513–524Google Scholar
  25. 25.
    O. Goldreich, S. Micali, A. Wigderson. How to play any mental game or a completeness theorem for protocols with honest majority, in Symposium on Theory of Computing (STOC’87), (ACM, 1987), pp. 218–229Google Scholar
  26. 26.
    O. Goldreich. Foundations of Cryptography, vol. 2: Basic Applications. Cambridge University Press, 2004Google Scholar
  27. 27.
    Y. Huang, P. Chapman, D. Evans. Privacy-preserving applications on smartphones, in Hot topics in security (HotSec’11). USENIX, 2011Google Scholar
  28. 28.
    Y. Huang, D. Evans, J. Katz. Private set intersection: Are garbled circuits better than custom protocols? in Network and Distributed System Security (NDSS’12). The Internet Society, 2012Google Scholar
  29. 29.
    Y. Huang, D. Evans, J. Katz, L. Malka. Faster secure two-party computation using garbled circuits, in USENIX Security’11, (USENIX, 2011), pp. 539–554Google Scholar
  30. 30.
    A. Holzer, M. Franz, S. Katzenbeisser, H. Veith. Secure two-party computations in ANSI C, in ACM Computer and Communications Security (CCS’12), (ACM, 2012) pp. 772–783Google Scholar
  31. 31.
    D. Harnik, Y. Ishai, E. Kushilevitz, J. Buus Nielsen. OT-combiners via secure computation, in Theory of Cryptography Conference (TCC’08), vol. 4948 of LNCS, (Springer, 2008), pp. 393–411Google Scholar
  32. 32.
    W. Henecka, S. Kögl, A.-R. Sadeghi, T. Schneider, I. Wehrenberg. TASTY: Tool for Automating Secure Two-partY computations, in ACM Computer and Communications Security (CCS’10), (ACM, 2010), pp. 451–462Google Scholar
  33. 33.
    Y. Huang, L. Malka, D. Evans, J. Katz. Efficient privacy-preserving biometric identification, in Network and Distributed Security Symposium (NDSS’11). The Internet Society, 2011Google Scholar
  34. 34.
    W. Henecka, T. Schneider. Faster secure two-party computation with less memory, in ACM Symposium on Information, Computer and Communications Security (ASIACCS’13), (ACM, 2013), pp. 437–446Google Scholar
  35. 35.
    Y. Ishai, J. Kilian, K. Nissim, E. Petrank. Extending oblivious transfers efficiently, in Advances in Cryptology—CRYPTO’03, vol. 2729 of LNCS, (Springer, 2003), pp. 145–161Google Scholar
  36. 36.
    Y. Ishai, E. Kushilevitz, R. Ostrovsky, A. Sahai. Cryptography with constant computational overhead, in ACM Symposium on Theory of Computing (STOC’08), (ACM, 2008), pp. 433–442Google Scholar
  37. 37.
    Y. Ishai, M. Prabhakaran, and A. Sahai. Founding cryptography on oblivious transfer - efficiently, in Advances in Cryptology—CRYPTO’08, vol. 5157 of LNCS, (Springer, 2008), pp. 572–591Google Scholar
  38. 38.
    R. Impagliazzo, S. Rudich. Limits on the provable consequences of one-way permutations, in Advances in Cryptology—CRYPTO’88, vol. 403 of LNCS, (Springer, 1988), pp. 8–26Google Scholar
  39. 39.
    F. Kerschbaum. Automatically optimizing secure computation, in ACM Computer and Communications Security (CCS’11), (ACM, 2011), pp. 703–714Google Scholar
  40. 40.
    V. Kolesnikov, R. Kumaresan. Improved OT extension for transferring short secrets, in Advances in Cryptology—CRYPTO’13, vol. 8043 of LNCS, (Springer, 2013) pp. 54–70Google Scholar
  41. 41.
    M. Keller, E. Orsini, P. Scholl. Actively secure OT extension with optimal overhead, in Advances in Cryptology—CRYPTO’15, vol. 9215 of LNCS, (Springer, 2015), pp. 724–741Google Scholar
  42. 42.
    V. Kolesnikov, T. Schneider. Improved garbled circuit: free XOR gates and applications, in International Colloquium on Automata, Languages and Programming (ICALP’08), vol. 5126 of LNCS, (Springer, 2008), pp. 486–498Google Scholar
  43. 43.
    B. Kreuter, A. Shelat, C. Shen. Billion-gate secure computation with malicious adversaries, in USENIX Security’12, (USENIX, 2012), pp. 285–300Google Scholar
  44. 44.
    M. Keller, P. Scholl, N.P. Smart. An architecture for practical actively secure MPC with dishonest majority, in ACM Computer and Communications Security (CCS’13), (ACM, 2013), pp. 549–560Google Scholar
  45. 45.
    E. Larraia. Extending oblivious transfer efficiently, or - how to get active security with constant cryptographic overhead, in Progress in Cryptology– LATINCRYPT’14, vol. 8895 of LNCS, (Springer, 2014), pp. 368–386Google Scholar
  46. 46.
    E. Larraia, E. Orsini, N.P. Smart. Dishonest majority multi-party computation for binary circuits, in Advances in Cryptology—CRYPTO’14, vol. 8617 of LNCS, (Springer, 2014), pp. 495–512Google Scholar
  47. 47.
    L. Lovász, M.D. Plummer. Matching Theory. Akadémiai Kiadó, Budapest, 1986. Also published as vol. 121 of the North-Holland Mathematics Studies, North-Holland Publishing, AmsterdamGoogle Scholar
  48. 48.
    Y. Lindell, B. Pinkas. Secure two-party computation via cut-and-choose oblivious transfer, in Theory of Cryptography Conference (TCC’11), vol. 6597 of LNCS, (Springer, 2011), pp. 329–346Google Scholar
  49. 49.
    Y. Lindell, B. Riva. Blazing fast 2pc in the offline/online setting with security for malicious adversaries, in ACM Computer and Communications Security (CCS’15), (ACM, 2015), pp. 579–590Google Scholar
  50. 50.
    Y. Lindell, H. Zarosim. On the feasibility of extending oblivious transfer, in Theory of Cryptography Conference (TCC’13), vol. 7785 of LNCS, (Springer, 2013), pp. 519–538Google Scholar
  51. 51.
    L. Malka. VMCrypt—modular software architecture for scalable secure computation, in ACM Computer and Communications Security (CCS’11), (ACM, 2011), pp. 715–724Google Scholar
  52. 52.
    D. Malkhi, N. Nisan, B. Pinkas, Y. Sella. Fairplay—a secure two-party computation system, in USENIX Security’04, (USENIX, 2004), pp. 287–302Google Scholar
  53. 53.
    P. MacKenzie, A. Oprea, M.K. Reiter. Automatic generation of two-party computations, in ACM Computer and Communications Security (CCS’03), (ACM, 2003), pp. 210–219Google Scholar
  54. 54.
    J.B. Nielsen. Extending oblivious transfers efficiently—how to get robustness almost for free. Cryptology ePrint Archive, Report 2007/215, 2007. Online: http://eprint.iacr.org/2007/215
  55. 55.
    NIST. NIST Special Publication 800-57, Recommendation for Key Management Part 1: General (Rev. 3). Technical report, NIST, 2012Google Scholar
  56. 56.
    J. B. Nielsen, P.S. Nordholt, C. Orlandi, S.S. Burra. A new approach to practical active-secure two-party computation. In Advances in Cryptology – CRYPTO’12, vol. 7417 of LNCS, (Springer, 2012), pp. 681–700Google Scholar
  57. 57.
    M. Naor, B. Pinkas. Efficient oblivious transfer protocols, in Symposium on Discrete Algorithms (SODA’01), (ACM/SIAM, 2001), pp. 448–457Google Scholar
  58. 58.
    V. Nikolaenko, U. Weinsberg, S. Ioannidis, M. Joye, D. Boneh, N. Taft. Privacy-preserving ridge regression on hundreds of millions of records, in IEEE Symposium on Security and Privacy (S&P’13), (IEEE, 2013), pp. 334–348Google Scholar
  59. 59.
    B. Pinkas, T. Schneider, G. Segev, M. Zohner. Phasing: Private set intersection using permutation-based hashing, in USENIX Security’15, (USENIX, 2015), pp. 515–530Google Scholar
  60. 60.
    B. Pinkas, T. Schneider, M. Zohner. Faster private set intersection based on ot extension, in USENIX Security’14, (USENIX, 2014), pp. 797–812Google Scholar
  61. 61.
    C. Peikert, V. Vaikuntanathan, B. Waters. A framework for efficient and composable oblivious transfer, in Advances in Cryptology—CRYPTO’08, vol. 5157 of LNCS, (Springer, 2008) pp. 554–571Google Scholar
  62. 62.
    M.O. Rabin. How to exchange secrets with oblivious transfer, TR-81 edition, 1981. Aiken Computation Lab, Harvard University.Google Scholar
  63. 63.
    A. Schröpfer, F. Kerschbaum. Demo: secure computation in JavaScript, in ACM Computer and Communications Security (CCS’11), (ACM, 2011), pp. 849–852Google Scholar
  64. 64.
    T. Schneider, M. Zohner. GMW vs. Yao? Efficient secure two-party computation with low depth circuits, in Financial Cryptography and Data Security (FC’13), vol. 7859 of LNCS, (Springer, 2013), pp. 275–292Google Scholar
  65. 65.
    A.C. Yao. How to generate and exchange secrets, in Foundations of Computer Science (FOCS’86), (IEEE, 1986), pp. 162–167Google Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Gilad Asharov
    • 1
  • Yehuda Lindell
    • 2
  • Thomas Schneider
    • 3
  • Michael Zohner
    • 3
  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA
  2. 2.The Department of Computer ScienceBar-Ilan UniversityRamat GanIsrael
  3. 3.Department of Computer ScienceTU DarmstadtGermany

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