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Network Oblivious Transfer

  • Ranjit Kumaresan
  • Srinivasan Raghuraman
  • Adam SealfonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9815)

Abstract

Motivated by the goal of improving the concrete efficiency of secure multiparty computation (MPC), we study the possibility of implementing an infrastructure for MPC. We propose an infrastructure based on oblivious transfer (OT), which would consist of OT channels between some pairs of parties in the network. We devise information-theoretically secure protocols that allow additional pairs of parties to establish secure OT correlations using the help of other parties in the network in the presence of a dishonest majority. Our main technical contribution is an upper bound that matches a lower bound of Harnik, Ishai, and Kushilevitz (Crypto 2007), who studied the number of OT channels necessary and sufficient for MPC. In particular, we characterize which n-party OT graphs G allow t-secure computation of OT correlations between all pairs of parties, showing that this is possible if and only if the complement of G does not contain the complete bipartite graph \(K_{n-t,n-t}\) as a subgraph.

Keywords

Secure Computation Oblivious Transfer Honest Party Computational Security Secure Multiparty Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Applebaum, B., Ishai, Y., Kushilevitz, E., Waters, B.: Encoding functions with constant online rate or how to compress garbled circuits keys. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 166–184. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Beaver, D.: Correlated pseudorandomness and the complexity of private computations. In: STOC, pp. 479–488 (1996)Google Scholar
  3. 3.
    Beaver, D.: Precomputing oblivious transfer. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 97–109. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Beimel, A., Malkin, T., Micali, S.: The all-or-nothing nature of two-party secure computation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 80–97. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Beimel, A., Omri, E., Orlov, I.: Protocols for multiparty coin toss with dishonest majority. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 538–557. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Bellare, M., Hoang, V.T., Keelveedhi, S., Rogaway, P.: Efficient garbling from a fixed-key blockcipher. In: IEEE Security and Privacy, pp. 478–492 (2013)Google Scholar
  8. 8.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for noncryptographic fault-tolerant distributed computations. In: STOC, pp. 1–10 (1988)Google Scholar
  9. 9.
    Ben-Sasson, E., Fehr, S., Ostrovsky, R.: Near-linear unconditionally-secure multiparty computation with a dishonest minority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 663–680. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Boyle, E., Chung, K.-M., Pass, R.: Large-scale secure computation: multi-party computation for (parallel) RAM programs. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 742–762. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  14. 14.
    Boyle, E., Goldwasser, S., Tessaro, S.: Communication locality in secure multi-party computation - how to run sublinear algorithms in a distributed setting. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 356–376. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Canetti, R., Damgård, I., Dziembowski, S., Ishai, Y., Malkin, T.: On adaptive vs. non-adaptive security of multiparty protocols. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 262–279. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC, pp. 11–19 (1988)Google Scholar
  17. 17.
    Chor, B., Kushilevitz, E.: A zero-one law for boolean privacy (extended abstract). In: STOC, pp. 62–72 (1989)Google Scholar
  18. 18.
    Chou, T., Orlandi, C.: The simplest protocol for oblivious transfer. In: Lauter, K., Rodríguez-Henríquez, F. (eds.) LatinCrypt 2015. LNCS, vol. 9230, pp. 40–58. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  19. 19.
    Damgård, I., Ishai, Y.: Scalable secure multiparty computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 501–520. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly secure multiparty computation and the computational overhead of cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445–465. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Damgård, I., Ishai, Y., Krøigaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241–261. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Damgård, I., Kilian, J., Salvail, L.: On the (im)possibility of basing oblivious transfer and bit commitment on weakened security assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999)Google Scholar
  23. 23.
    Damgård, I., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572–590. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  25. 25.
    Dani, V., King, V., Movahedi, M., Saia, J.: Brief announcement: breaking the o(nm) bit barrier, secure multiparty computation with a static adversary. In: PODC, pp. 227–228 (2012)Google Scholar
  26. 26.
    Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. In: FOCS, pp. 36–45 (1990)Google Scholar
  27. 27.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology, pp. 205–210. Springer, New York (1983)CrossRefGoogle Scholar
  28. 28.
    Fitzi, M., Franklin, M.K., Garay, J.A., Vardhan, S.H.: Towards optimal and efficient perfectly secure message transmission. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 311–322. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  29. 29.
    Garay, J.A., Katz, J., Koo, C.-Y., Ostrovsky, R.: Round complexity of authenticated broadcast with a dishonest majority. In: FOCS, pp. 658–668 (2007)Google Scholar
  30. 30.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  31. 31.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game, or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)Google Scholar
  32. 32.
    Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity for all languages in NP have zero-knowledge proof systems. J. ACM 38(3), 691–729 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Goldreich, O., Vainish, R.: How to solve any protocol problem - an efficiency improvement. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 73–86. Springer, Heidelberg (1988)Google Scholar
  34. 34.
    Goldwasser, S., Kalai, Y., Popa, R., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: STOC, pp. 555–564 (2013)Google Scholar
  35. 35.
    Haitner, I.: Semi-honest to malicious oblivious transfer—the black-box way. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 412–426. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  36. 36.
    Harnik, D., Ishai, Y., Kushilevitz, E.: How many oblivious transfers are needed for secure multiparty computation? In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 284–302. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  37. 37.
    Harnik, D., Ishai, Y., Kushilevitz, E., Nielsen, J.B.: OT-combiners via secure computation. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 393–411. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  38. 38.
    Harnik, D., Kilian, J., Naor, M., Reingold, O., Rosen, A.: On robust combiners for oblivious transfer and other primitives. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 96–113. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  39. 39.
    Hirt, M., Lucas, C., Maurer, U.: A dynamic tradeoff between active and passive corruptions in secure multi-party computation. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 203–219. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  40. 40.
    Huang, Y., Katz, J., Evans, D.: Efficient secure two-party computation using symmetric cut-and-choose. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 18–35. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  41. 41.
    Huang, Y., Katz, J., Kolesnikov, V., Kumaresan, R., Malozemoff, A.J.: Amortizing garbled circuits. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 458–475. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  42. 42.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: STOC, pp. 44–61 (1989)Google Scholar
  43. 43.
    Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  44. 44.
    Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: On combining privacy with guaranteed output delivery in secure multiparty computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 483–500. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  45. 45.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  46. 46.
    Kilian, J.: Founding cryptography on oblivious transfer. In: STOC, pp. 20–31 (1988)Google Scholar
  47. 47.
    Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  48. 48.
    Kovári, T., Sós, V., Turán, P.: On a problem of K. Zarankiewicz. Colloquium Math. 3(1), 50–57 (1954)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Kushilevitz, E.: Privacy and communication complexity. In: FOCS, pp. 416–421 (1989)Google Scholar
  50. 50.
    Larraia, E., Orsini, E., Smart, N.P.: Dishonest majority multi-party computation for binary circuits. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 495–512. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  51. 51.
    Lindell, Y., Pinkas, B., Smart, N.P., Yanai, A.: Efficient constant round multi-party computation combining BMR and SPDZ. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 319–338. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  52. 52.
    Lindell, Y., Riva, B.: Cut-and-choose yao-based secure computation in the online/offline and batch settings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 476–494. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  53. 53.
    Lindell, Y.: Fast cut-and-choose based protocols for malicious and covert adversaries. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 1–17. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  54. 54.
    Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  55. 55.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: A zero-one law for cryptographic complexity with respect to computational UC security. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 595–612. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  56. 56.
    Meier, R., Przydatek, B., Wullschleger, J.: Robuster combiners for oblivious transfer. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 404–418. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  57. 57.
    Mohassel, P., Riva, B.: Garbled circuits checking garbled circuits: more efficient and secure two-party computation. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 36–53. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  58. 58.
    Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA, pp. 448–457 (2001)Google Scholar
  59. 59.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  60. 60.
    Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  61. 61.
    Prabhakaran, M., Prabhakaran, V.: On secure multiparty sampling for more than two parties. In: Information Theory Workshop (ITW) (2012)Google Scholar
  62. 62.
    Rabin, M.: How to exchange secrets by oblivious transfer (1981)Google Scholar
  63. 63.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC, pp. 73–85 (1989)Google Scholar
  64. 64.
    Wolf, S., Wullschleger, J.: Oblivious transfer is symmetric. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 222–232. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  65. 65.
    Wullschleger, J.: Oblivious-transfer amplification. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 555–572. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  66. 66.
    Yao, A.C.-C.: How to generate and exchange secrets. In: FOCS, pp. 162–167 (1986)Google Scholar
  67. 67.
    Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015)Google Scholar
  68. 68.
    Zamani, M., Movahedi, M., Saia, J.: Millions of millionaires: Multiparty computation in large networks. In: ePrint 2014/149Google Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Ranjit Kumaresan
    • 1
  • Srinivasan Raghuraman
    • 1
  • Adam Sealfon
    • 1
    Email author
  1. 1.MITCambridgeUSA

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