Advertisement

Two-Round Multiparty Secure Computation from Minimal Assumptions

  • Sanjam Garg
  • Akshayaram Srinivasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10821)

Abstract

We provide new two-round multiparty secure computation (MPC) protocols assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions. Finally, we provide several extensions.

References

  1. [AIK04]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC\(^0\). In: 45th FOCS, Rome, Italy, 17–19 October 2004, pp. 166–175. IEEE Computer Society Press (2004)Google Scholar
  2. [AIK05]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. In: 20th Annual IEEE Conference on Computational Complexity (CCC 2005), San Jose, CA, USA, 11–15 June 2005, pp. 260–274 (2005)Google Scholar
  3. [AIR01]
    Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44987-6_8CrossRefGoogle Scholar
  4. [AJL+12]
    Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483–501. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_29CrossRefGoogle Scholar
  5. [BF01]
    Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_13CrossRefGoogle Scholar
  6. [BFM88]
    Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: 20th ACM STOC, Chicago, IL, USA, 2–4 May 1988, pp. 103–112. ACM Press (1988)Google Scholar
  7. [BGI+01]
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_1CrossRefGoogle Scholar
  8. [BGI16]
    Boyle, E., Gilboa, N., Ishai, Y.: Breaking the circuit size barrier for secure computation under DDH. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 509–539. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53018-4_19CrossRefGoogle Scholar
  9. [BGI17]
    Boyle, E., Gilboa, N., Ishai, Y.: Group-based secure computation: optimizing rounds, communication, and computation. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 163–193. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56614-6_6CrossRefGoogle Scholar
  10. [BH15]
    Bellare, M., Hoang, V.T.: Adaptive witness encryption and asymmetric password-based cryptography. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 308–331. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46447-2_14Google Scholar
  11. [BHR12]
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 12, Raleigh, NC, USA, 16–18 October 2012, pp. 784–796. ACM Press (2012)Google Scholar
  12. [BL18]
    Benhamouda, F., Lin, H.: k-round multiparty computation from k-round oblivious transfer via garbled interactive circuits. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 500–532. Springer, Cham (2018). https://eprint.iacr.org/2017/1125Google Scholar
  13. [BMR90]
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd ACM STOC, Baltimore, MD, USA, 14–16 May 1990, pp. 503–513. ACM Press (1990)Google Scholar
  14. [BP16]
    Brakerski, Z., Perlman, R.: Lattice-based fully dynamic multi-key FHE with short ciphertexts. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 190–213. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53018-4_8CrossRefGoogle Scholar
  15. [Can00a]
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol. 13(1), 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  16. [Can00b]
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. Cryptology ePrint Archive, Report 2000/067 (2000). http://eprint.iacr.org/2000/067
  17. [Can01]
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, Las Vegas, NV, USA, 14–17 October 2001, pp. 136–145. IEEE Computer Society Press (2001)Google Scholar
  18. [Can05]
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols, Version of December 2005 (2005). http://eccc.uni-trier.de/eccc-reports/2001/TR01-016
  19. [CCM98]
    Cachin, C., Crépeau, C., Marcil, J.: Oblivious transfer with a memory-bounded receiver. In: 39th FOCS, Palo Alto, CA, USA, 8–11 November 1998, pp. 493–502. IEEE Computer Society Press (1998)Google Scholar
  20. [CDG+17]
    Cho, C., Döttling, N., Garg, S., Gupta, D., Miao, P., Polychroniadou, A.: Laconic oblivious transfer and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 33–65. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_2CrossRefGoogle Scholar
  21. [CLOS02]
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th ACM STOC, Montréal, Québec, Canada, 19–21 May 2002, pp. 494–503. ACM Press (2002)Google Scholar
  22. [CM15]
    Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 630–656. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_31CrossRefGoogle Scholar
  23. [DG17]
    Döttling, N., Garg, S.: Identity-based encryption from the Diffie-Hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_18CrossRefGoogle Scholar
  24. [DHRS04]
    Ding, Y.Z., Harnik, D., Rosen, A., Shaltiel, R.: Constant-round oblivious transfer in the bounded storage model. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 446–472. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24638-1_25CrossRefGoogle Scholar
  25. [FLS90]
    Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: 31st FOCS, St. Louis, Missouri, 22–24 October 1990, pp. 308–317. IEEE Computer Society Press (1990)Google Scholar
  26. [Gen09]
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, Bethesda, MD, USA, 31 May–2 June 2009, pp. 169–178. ACM Press (2009)Google Scholar
  27. [GGH+13]
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, Berkeley, CA, USA, 26–29 October 2013, pp. 40–49. IEEE Computer Society Press (2013)Google Scholar
  28. [GGHR14]
    Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure MPC from indistinguishability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74–94. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54242-8_4CrossRefGoogle Scholar
  29. [GGMP16]
    Garg, S., Gupta, D., Miao, P., Pandey, O.: Secure multiparty RAM computation in constant rounds. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 491–520. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_19CrossRefGoogle Scholar
  30. [GGSW13]
    Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, Palo Alto, CA, USA, 1–4 June 2013, pp. 467–476. ACM Press (2013)Google Scholar
  31. [GHL+14]
    Gentry, C., Halevi, S., Lu, S., Ostrovsky, R., Raykova, M., Wichs, D.: Garbled RAM revisited. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 405–422. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-55220-5_23CrossRefGoogle Scholar
  32. [GKK+12]
    Dov Gordon, S., Katz, J., Kolesnikov, V., Krell, F., Malkin, T., Raykova, M., Vahlis, Y.: Secure two-party computation in sublinear (amortized) time. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, Raleigh, NC, USA, 16–18 October 2012, pp. 513–524. ACM Press (2012)Google Scholar
  33. [GLO15]
    Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. In: Guruswami, V. (ed.) 56th FOCS, Berkeley, CA, USA, 17–20 October 2015, pp. 210–229. IEEE Computer Society Press (2015)Google Scholar
  34. [GLOS15]
    Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled RAM from one-way functions. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, Portland, OR, USA, 14–17 June 2015, pp. 449–458. ACM Press (2015)Google Scholar
  35. [GLS15]
    Dov Gordon, S., Liu, F.-H., Shi, E.: Constant-round MPC with fairness and guarantee of output delivery. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 63–82. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_4CrossRefGoogle Scholar
  36. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, New York City, NY, USA, 25–27 May 1987, pp. 218–229. ACM Press (1987)Google Scholar
  37. [GOS06]
    Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006).  https://doi.org/10.1007/11761679_21CrossRefGoogle Scholar
  38. [GOVW12]
    Garg, S., Ostrovsky, R., Visconti, I., Wadia, A.: Resettable statistical zero knowledge. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 494–511. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-28914-9_28CrossRefGoogle Scholar
  39. [GS17]
    Garg, S., Srinivasan, A.: Garbled protocols and two-round MPC from bilinear maps. In: 58th FOCS, pp. 588–599. IEEE Computer Society Press (2017)Google Scholar
  40. [GS18]
    Garg, S., Srinivasan, A.: Two-round multiparty secure computation from minimal assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 468–499. Springer, Cham (2018). https://eprint.iacr.org/2017/1156Google Scholar
  41. [HK12]
    Halevi, S., Kalai, Y.T.: Smooth projective hashing and two message oblivious transfer. J. Cryptol. 25(1), 158–193 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  42. [HY16]
    Hazay, C., Yanai, A.: Constant-round maliciously secure two-party computation in the RAM model. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 521–553. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_20CrossRefGoogle Scholar
  43. [IPS08]
    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).  https://doi.org/10.1007/978-3-540-85174-5_32CrossRefGoogle Scholar
  44. [Jou04]
    Joux, A.: A one round protocol for tripartite Diffie-Hellman. J. Cryptol. 17(4), 263–276 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  45. [Kil88]
    Kilian, J.: Founding cryptography on oblivious transfer. In: 20th ACM STOC, Chicago, IL, USA, 2–4 May 1988, pp. 20–31. ACM Press (1988)Google Scholar
  46. [LO13]
    Lu, S., Ostrovsky, R.: How to garble RAM programs? In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 719–734. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_42CrossRefGoogle Scholar
  47. [LP09]
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  48. [MW16]
    Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49896-5_26CrossRefGoogle Scholar
  49. [NP01]
    Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Rao Kosaraju, S. (ed.) 12th SODA, Washington, DC, USA, 7–9 January 2001, pp. 448–457. ACM-SIAM (2001)Google Scholar
  50. [OS97]
    Ostrovsky, R., Shoup, V.: Private information storage (extended abstract). In: 29th ACM STOC, El Paso, TX, USA, 4–6 May 1997, pp. 294–303. ACM Press (1997)Google Scholar
  51. [PS16]
    Peikert, C., Shiehian, S.: Multi-key FHE from LWE, revisited. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 217–238. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_9CrossRefGoogle Scholar
  52. [PVW08]
    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).  https://doi.org/10.1007/978-3-540-85174-5_31CrossRefGoogle Scholar
  53. [PW00]
    Pfitzmann, B., Waidner, M.: Composition and integrity preservation of secure reactive systems. In: Jajodia, S., Samarati, P. (eds.) ACM CCS 2000, Athens, Greece, 1–4 November 2000, pp. 245–254. ACM Press (2000)Google Scholar
  54. [Yao86]
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, Toronto, Ontario, Canada, 27–29 October 1986, pp. 162–167. IEEE Computer Society Press (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations