Advertisement

Founding Secure Computation on Blockchains

  • Arka Rai ChoudhuriEmail author
  • Vipul Goyal
  • Abhishek Jain
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11477)

Abstract

We study the foundations of secure computation in the blockchain-hybrid model, where a blockchain – modeled as a global functionality – is available as an Oracle to all the participants of a cryptographic protocol. We demonstrate both destructive and constructive applications of blockchains:
  • We show that classical rewinding-based simulation techniques used in many security proofs fail against blockchain-active adversaries that have read and post access to a global blockchain. In particular, we show that zero-knowledge (ZK) proofs with black-box simulation are impossible against blockchain-active adversaries.

  • Nevertheless, we show that achieving security against blockchain-active adversaries is possible if the honest parties are also blockchain active. We construct an \(\omega (1)\)-round ZK protocol with black-box simulation. We show that this result is tight by proving the impossibility of constant-round ZK with black-box simulation.

  • Finally, we demonstrate a novel application of blockchains to overcome the known impossibility results for concurrent secure computation in the plain model. We construct a concurrent self-composable secure computation protocol for general functionalities in the blockchain-hybrid model based on standard cryptographic assumptions.

We develop a suite of techniques for constructing secure protocols in the blockchain-hybrid model that we hope will find applications to future research in this area.

Notes

Acknowledgments

The second author’s research was supported in part by a grant from Northrop Grumman, a gift from DOS Networks, and, a Cylab seed funding award. The first and third authors’ research was supported in part by a DARPA/ARL Safeware Grant W911NF-15-C-0213, and a subaward from NSF CNS-1414023.

References

  1. 1.
    Agrawal, S., Goyal, V., Jain, A., Prabhakaran, M., Sahai, A.: New impossibility results for concurrent composition and a non-interactive completeness theorem for secure computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 443–460. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_26CrossRefGoogle Scholar
  2. 2.
    Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, L.: Secure multiparty computations on bitcoin. In: 2014 IEEE Symposium on Security and Privacy, SP 2014, Berkeley, CA, USA, 18–21 May, pp. 443–458 (2014)Google Scholar
  3. 3.
    Badertscher, C., Gaži, P., Kiayias, A., Russell, A., Zikas, V.: Ouroboros genesis: composable proof-of-stake blockchains with dynamic availability. Cryptology ePrint Archive, Report 2018/378 (2018). https://eprint.iacr.org/2018/378
  4. 4.
    Badertscher, C., Maurer, U., Tschudi, D., Zikas, V.: Bitcoin as a transaction ledger: a composable treatment. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 324–356. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_11CrossRefGoogle Scholar
  5. 5.
    Badrinarayanan, S., Khurana, D., Ostrovsky, R., Visconti, I.: Unconditional UC-secure computation with (stronger-malicious) PUFs. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part I. LNCS, vol. 10210, pp. 382–411. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56620-7_14CrossRefGoogle Scholar
  6. 6.
    Barak, B., Canetti, R., Nielsen, J.B., Pass, R.: Universally composable protocols with relaxed set-up assumptions. In: 45th FOCS, 17–19 October, pp. 186–195. IEEE Computer Society Press, Rome (2004)Google Scholar
  7. 7.
    Barak, B., Lindell, Y.: Strict polynomial-time in simulation and extraction. In: 34th ACM STOC, 19–21 May, pp. 484–493. ACM Press, Montréal (2002)Google Scholar
  8. 8.
    Barak, B., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero knowledge. In: 47th FOCS, 21–24 October, pp. 345–354. IEEE Computer Society Press, Berkeley (2006)Google Scholar
  9. 9.
    Bellare, M., Jakobsson, M., Yung, M.: Round-optimal zero-knowledge arguments based on any one-way function. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 280–305. Springer, Heidelberg (1997).  https://doi.org/10.1007/3-540-69053-0_20CrossRefGoogle Scholar
  10. 10.
    Bentov, I., Kumaresan, R.: How to use bitcoin to design fair protocols. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 421–439. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44381-1_24CrossRefGoogle Scholar
  11. 11.
    Blum, M.: How to prove a theorem so no one else can claim it. In: International Congress of Mathematicians, pp. 1444–1451 (1987)Google Scholar
  12. 12.
    Brzuska, C., Fischlin, M., Schröder, H., Katzenbeisser, S.: Physically uncloneable functions in the universal composition framework. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 51–70. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22792-9_4CrossRefzbMATHGoogle Scholar
  13. 13.
    Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. J. Cryptol. 19(2), 135–167 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, 14–17 October, pp. 136–145. IEEE Computer Society Press, Las Vegas (2001)Google Scholar
  15. 15.
    Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally composable security with global setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-70936-7_4CrossRefGoogle Scholar
  16. 16.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_2CrossRefGoogle Scholar
  17. 17.
    Canetti, R., Goyal, V., Jain, A.: Concurrent secure computation with optimal query complexity. In: Gennaro, R., Robshaw, M.J.B. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 43–62. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_3CrossRefGoogle Scholar
  18. 18.
    Canetti, R., Jain, A., Scafuro, A.: Practical UC security with a global random oracle. In: Ahn, G.J., Yung, M., Li, N. (eds.) ACM CCS 14, 3–7 November, pp. 597–608. ACM Press, Scottsdale (2014)Google Scholar
  19. 19.
    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
  20. 20.
    Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: 51st FOCS, 23–26 October, pp. 541–550. IEEE Computer Society Press, Las Vegas (2010)Google Scholar
  21. 21.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th ACM STOC, 19–21 May, pp. 494–503. ACM Press, Montréal (2002)Google Scholar
  22. 22.
    Chandran, N., Goyal, V., Sahai, A.: New constructions for UC secure computation using tamper-proof hardware. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 545–562. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78967-3_31CrossRefGoogle Scholar
  23. 23.
    Choudhuri, A.R., Goyal, V., Jain, A.: Founding secure computation on blockchains. Cryptology ePrint Archive, Report 2019/253 (2019). https://eprint.iacr.org/2019/253
  24. 24.
    Choudhuri, A.R., Green, M., Jain, A., Kaptchuk, G., Miers, I.: Fairness in an unfair world: fair multiparty computation from public bulletin boards. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 17, October 31–2 November, pp. 719–728. ACM Press, Dallas (2017)Google Scholar
  25. 25.
    Dachman-Soled, D., Fleischhacker, N., Katz, J., Lysyanskaya, A., Schröder, D.: Feasibility and infeasibility of secure computation with malicious PUFs. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 405–420. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44381-1_23CrossRefGoogle Scholar
  26. 26.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: 23rd ACM STOC, 6–8 May, pp. 542–552. ACM Press, New Orleans (1991)Google Scholar
  27. 27.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. In: 30th ACM STOC, 23–26 May, pp. 409–418. ACM Press, Dallas (1998)Google Scholar
  28. 28.
    Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: 22nd ACM STOC, 14–16 May, pp. 416–426. ACM Press, Baltimore (1990)Google Scholar
  29. 29.
    Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987).  https://doi.org/10.1007/3-540-47721-7_12CrossRefGoogle Scholar
  30. 30.
    Garay, J., Kiayias, A., Leonardos, N.: The bitcoin backbone protocol: analysis and applications. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 281–310. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46803-6_10CrossRefGoogle Scholar
  31. 31.
    Garay, J., Kiayias, A., Leonardos, N.: The bitcoin backbone protocol with chains of variable difficulty. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 291–323. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_10CrossRefGoogle Scholar
  32. 32.
    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
  33. 33.
    Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)MathSciNetCrossRefGoogle Scholar
  34. 34.
    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, 25–27 May, pp. 218–229. ACM Press, New York City (1987)Google Scholar
  35. 35.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 6–8 May 1985, Providence, Rhode Island, USA, pp. 291–304 (1985)Google Scholar
  36. 36.
    Goyal, R., Goyal, V.: Overcoming cryptographic impossibility results using blockchains. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017, Part I. LNCS, vol. 10677, pp. 529–561. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70500-2_18CrossRefGoogle Scholar
  37. 37.
    Goyal, V.: Positive results for concurrently secure computation in the plain model. In: 53rd FOCS, 20–23 October, pp. 41–50. IEEE Computer Society Press, New Brunswick (2012)Google Scholar
  38. 38.
    Goyal, V., Gupta, D., Jain, A.: What information is leaked under concurrent composition? In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 220–238. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_13CrossRefGoogle Scholar
  39. 39.
    Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-11799-2_19CrossRefzbMATHGoogle Scholar
  40. 40.
    Goyal, V., Jain, A., Ostrovsky, R.: Password-authenticated session-key generation on the internet in the plain model. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 277–294. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14623-7_15CrossRefGoogle Scholar
  41. 41.
    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, Part I. LNCS, vol. 9014, pp. 260–289. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46494-6_12CrossRefGoogle Scholar
  42. 42.
    Haitner, I., Horvitz, O., Katz, J., Koo, C.-Y., Morselli, R., Shaltiel, R.: Reducing complexity assumptions for statistically-hiding commitment. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 58–77. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_4CrossRefGoogle Scholar
  43. 43.
    Hazay, C., Polychroniadou, A., Venkitasubramaniam, M.: Composable security in the tamper-proof hardware model under minimal complexity. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part I. LNCS, vol. 9985, pp. 367–399. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_15CrossRefGoogle Scholar
  44. 44.
    Kalai, Y.T., Lindell, Y., Prabhakaran, M.: Concurrent general composition of secure protocols in the timing model. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, 22–24 May, pp. 644–653. ACM Press, Baltimore (2005)Google Scholar
  45. 45.
    Katz, J.: Universally composable multi-party computation using tamper-proof hardware. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 115–128. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-72540-4_7CrossRefGoogle Scholar
  46. 46.
    Kiayias, A., Russell, A., David, B., Oliynykov, R.: Ouroboros: a provably secure proof-of-stake blockchain protocol. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 357–388. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_12CrossRefGoogle Scholar
  47. 47.
    Kiayias, A., Zhou, H.-S., Zikas, V.: Fair and robust multi-party computation using a global transaction ledger. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 705–734. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49896-5_25CrossRefGoogle Scholar
  48. 48.
    Kilian, J.: Founding cryptography on oblivious transfer. In: 20th ACM STOC, 2–4 May, pp. 20–31. ACM Press, Chicago (1988)Google Scholar
  49. 49.
    Kilian, J., Petrank, E.: Concurrent and resettable zero-knowledge in poly-loalgorithm rounds. In: STOC, pp. 560–569 (2001)Google Scholar
  50. 50.
    Lindell, Y.: General composition and universal composability in secure multi-party computation. In: FOCS, pp. 394–403 (2003)Google Scholar
  51. 51.
    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
  52. 52.
    Lindell, Y.: Lower bounds and impossibility results for concurrent self composition. J. Cryptol. 21(2), 200–249 (2008)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Micali, S., Pass, R.: Local zero knowledge. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, USA, 21–23 May 2006, pp. 306–315 (2006).  https://doi.org/10.1145/1132516.1132561
  54. 54.
    Naor, M.: Bit commitment using pseudorandomness. J. Cryptol. 4(2), 151–158 (1991)CrossRefGoogle Scholar
  55. 55.
    Naor, M., Ostrovsky, R., Venkatesan, R., Yung, M.: Perfect zero-knowledge arguments for NP using any one-way permutation. J. Cryptol. 11(2), 87–108 (1998)MathSciNetCrossRefGoogle Scholar
  56. 56.
    Pass, R., Seeman, L., Shelat, A.: Analysis of the blockchain protocol in asynchronous networks. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part II. LNCS, vol. 10211, pp. 643–673. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56614-6_22CrossRefzbMATHGoogle Scholar
  57. 57.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: 43rd FOCS, 16–19 November, pp. 366–375. IEEE Computer Society Press, Vancouver (2002)Google Scholar
  58. 58.
    Richardson, R., Kilian, J.: On the concurrent composition of zero-knowledge proofs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 415–431. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48910-X_29CrossRefGoogle Scholar
  59. 59.
    Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, 27–29 October, pp. 162–167, IEEE Computer Society Press, Toronto (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Johns Hopkins UniversityBaltimoreUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations