Advertisement

A New Approach to Black-Box Concurrent Secure Computation

  • Sanjam Garg
  • Susumu Kiyoshima
  • Omkant Pandey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10821)

Abstract

We consider the task of constructing concurrently composable protocols for general secure computation by making only black-box use of underlying cryptographic primitives. Existing approaches for this task first construct a black-box version of CCA-secure commitments which provide a strong form of concurrent security to the committed value(s). This strong form of security is then crucially used to construct higher level protocols such as concurrently secure OT/coin-tossing (and eventually all functionalities).

This work explores a fresh approach. We first aim to construct a concurrently-secure OT protocol whose concurrent security is proven directly using concurrent simulation techniques; in particular, it does not rely on the usual “non-polynomial oracles” of CCA-secure commitments. The notion of concurrent security we target is super-polynomial simulation (SPS). We show that such an OT protocol can be constructed from polynomial hardness assumptions in a black-box manner, and within a constant number of rounds. In fact, we only require the existence of (constant round) semi-honest OT and standard collision-resistant hash functions.

Next, we show that such an OT protocol is sufficient to obtain SPS-secure (concurrent) multiparty computation (MPC) for general functionalities. This transformation does not require any additional assumptions; it also maintains the black-box nature as well as the constant round feature of the original OT protocol. Prior to our work, the only known black-box construction of constant-round concurrently composable MPC required stronger assumptions; namely, verifiable perfectly binding homomorphic commitment schemes and PKE with oblivious public-key generation.

References

  1. 1.
    Badrinarayanan, S., Goyal, V., Jain, A., Khurana, D., Sahai, A.: Round optimal concurrent MPC via strong simulation. Cryptology ePrint Archive, Report 2017/597 (2017), http://eprint.iacr.org/2017/597
  2. 2.
    Barak, B., Sahai, A.: How to play almost any mental game over the net - concurrent composition via super-polynomial simulation. In: 46th FOCS, pp. 543–552. IEEE Computer Society Press, October 2005Google Scholar
  3. 3.
    Broadnax, B., Döttling, N., Hartung, G., Müller-Quade, J., Nagel, M.: Concurrently composable security with shielded super-polynomial simulators. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 351–381. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56620-7_13CrossRefGoogle Scholar
  4. 4.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001Google Scholar
  5. 5.
    Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 68–86. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-39200-9_5CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: 51st FOCS, pp. 541–550. IEEE Computer Society Press, October 2010Google Scholar
  7. 7.
    Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. SIAM J. Comput. 45(5), 1793–1834 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th ACM STOC, pp. 494–503. ACM Press, May 2002Google Scholar
  9. 9.
    Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: A black-box construction of non-malleable encryption from semantically secure encryption. J. Cryptol. (2017)Google Scholar
  10. 10.
    Cramer, R., Hanaoka, G., Hofheinz, D., Imai, H., Kiltz, E., Pass, R., Shelat, A., Vaikuntanathan, V.: Bounded CCA2-secure encryption. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 502–518. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-76900-2_31CrossRefGoogle Scholar
  11. 11.
    Dachman-Soled, D., Malkin, T., Raykova, M., Venkitasubramaniam, M.: Adaptive and concurrent secure computation from new adaptive, non-malleable commitments. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8269, pp. 316–336. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-42033-7_17CrossRefGoogle Scholar
  12. 12.
    Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: 22nd ACM STOC, pp. 416–426. ACM Press, May 1990Google Scholar
  13. 13.
    Garay, J.A., MacKenzie, P.D.: Concurrent oblivious transfer. In: 41st FOCS, pp. 314–324. IEEE Computer Society Press, November 2000Google Scholar
  14. 14.
    Garg, S., Goyal, V., Jain, A., Sahai, A.: Concurrently secure computation in constant rounds. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 99–116. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_8CrossRefGoogle Scholar
  15. 15.
    Garg, S., Kumarasubramanian, A., Ostrovsky, R., Visconti, I.: Impossibility results for static input secure computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 424–442. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_25CrossRefGoogle Scholar
  16. 16.
    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, pp. 218–229. ACM Press, May 1987Google Scholar
  17. 17.
    Goyal, V.: Constant round non-malleable protocols using one way functions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 695–704. ACM Press, June 2011Google Scholar
  18. 18.
    Goyal, V., Jain, A.: On concurrently secure computation in the multiple ideal query model. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 684–701. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38348-9_40CrossRefGoogle Scholar
  19. 19.
    Goyal, V., Lee, C.K., Ostrovsky, R., Visconti, I.: Constructing non-malleable commitments: a black-box approach. In: 53rd FOCS, pp. 51–60. IEEE Computer Society Press, October 2012Google Scholar
  20. 20.
    Goyal, V., Lin, H., Pandey, O., Pass, R., Sahai, A.: Round-efficient concurrently composable secure computation via a robust extraction lemma. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 260–289. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46494-6_12Google Scholar
  21. 21.
    Goyal, V., Ostrovsky, R., Scafuro, A., Visconti, I.: Black-box non-black-box zero knowledge. In: Shmoys, D.B. (ed.) 46th ACM STOC, pp. 515–524. ACM Press, May/June 2014Google Scholar
  22. 22.
    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).  https://doi.org/10.1007/978-3-540-78524-8_23CrossRefGoogle Scholar
  23. 23.
    Haitner, I., Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-box constructions of protocols for secure computation. SIAM J. Comput. 40(2), 225–266 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Hazay, C., Venkitasubramaniam, M.: Composable adaptive secure protocols without setup under polytime assumptions. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 400–432. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_16CrossRefGoogle Scholar
  26. 26.
    Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-box constructions for secure computation. In: Kleinberg, J.M. (ed.) 38th ACM STOC, pp. 99–108. ACM Press, May 2006Google Scholar
  27. 27.
    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
  28. 28.
    Kiyoshima, S.: Round-efficient black-box construction of composable multi-party computation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 351–368. Springer, Heidelberg (2014).  https://doi.org/10.1007/s00145-018-9276-1CrossRefGoogle Scholar
  29. 29.
    Kiyoshima, S., Manabe, Y., Okamoto, T.: Constant-round black-box construction of composable multi-party computation protocol. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 343–367. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54242-8_15CrossRefGoogle Scholar
  30. 30.
    Lin, H., Pass, R.: Non-malleability amplification. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 189–198. ACM Press, May/June 2009Google Scholar
  31. 31.
    Lin, H., Pass, R.: Black-box constructions of composable protocols without set-up. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 461–478. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_27CrossRefGoogle Scholar
  32. 32.
    Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78524-8_31CrossRefGoogle Scholar
  33. 33.
    Lin, H., Pass, R., Venkitasubramaniam, M.: A unified framework for concurrent security: universal composability from stand-alone non-malleability. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 179–188. ACM Press, May/June 2009Google Scholar
  34. 34.
    Lindell, Y.: Bounded-concurrent secure two-party computation without setup assumptions. In: 35th ACM STOC, pp. 683–692. ACM Press, June 2003Google Scholar
  35. 35.
    Lindell, Y.: Lower bounds for concurrent self composition. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 203–222. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24638-1_12CrossRefGoogle Scholar
  36. 36.
    Malkin, T., Moriarty, R., Yakovenko, N.: Generalized environmental security from number theoretic assumptions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 343–359. Springer, Heidelberg (2006).  https://doi.org/10.1007/11681878_18CrossRefGoogle Scholar
  37. 37.
    Micali, S., Pass, R., Rosen, A.: Input-indistinguishable computation. In: 47th FOCS, pp. 367–378. IEEE Computer Society Press, October 2006Google Scholar
  38. 38.
    Naor, M.: Bit commitment using pseudorandomness. J. Cryptol. 4(2), 151–158 (1991)CrossRefzbMATHGoogle Scholar
  39. 39.
    Ostrovsky, R., Richelson, S., Scafuro, A.: Round-optimal black-box two-party computation. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 339–358. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_17CrossRefGoogle Scholar
  40. 40.
    Ostrovsky, R., Scafuro, A., Venkitasubramanian, M.: Resettably sound zero-knowledge arguments from OWFs - the (semi) black-box way. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 345–374. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46494-6_15Google Scholar
  41. 41.
    Pass, R.: Simulation in quasi-polynomial time, and its application to protocol composition. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 160–176. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-39200-9_10CrossRefGoogle Scholar
  42. 42.
    Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Babai, L. (ed.) 36th ACM STOC, pp. 232–241. ACM Press, June 2004Google Scholar
  43. 43.
    Pass, R., Lin, H., Venkitasubramaniam, M.: A unified framework for UC from only OT. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 699–717. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_42CrossRefGoogle Scholar
  44. 44.
    Pass, R., Wee, H.: Black-box constructions of two-party protocols from one-way functions. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 403–418. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-00457-5_24CrossRefGoogle Scholar
  45. 45.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. SIAM J. Comput. 40(6), 1803–1844 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Prabhakaran, M., Sahai, A.: New notions of security: achieving universal composability without trusted setup. In: Babai, L. (ed.) 36th ACM STOC, pp. 242–251. ACM Press, June 2004Google Scholar
  47. 47.
    Venkitasubramaniam, M.: On adaptively secure protocols. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 455–475. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10879-7_26Google Scholar
  48. 48.
    Wee, H.: Black-box, round-efficient secure computation via non-malleability amplification. In: 51st FOCS, pp. 531–540. IEEE Computer Society Press, October 2010Google Scholar
  49. 49.
    Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986Google Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.NTT Secure Platform LaboratoriesTokyoJapan
  3. 3.Stony Brook UniversityStony BrookUSA

Personalised recommendations