Advertisement

Outsourcing Computation: The Minimal Refereed Mechanism

  • Yuqing Kong
  • Chris Peikert
  • Grant Schoenebeck
  • Biaoshuai TaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11920)

Abstract

We consider a setting where a verifier with limited computation power delegates a resource intensive computation task—which requires a \(T\times S\) computation tableau—to two provers where the provers are rational in that each prover maximizes their own payoff—taking into account losses incurred by the cost of computation. We design a mechanism called the Minimal Refereed Mechanism (MRM) such that if the verifier has \(O(\log S + \log T)\) time and \(O(\log S + \log T)\) space computation power, then both provers will provide a honest result without the verifier putting any effort to verify the results. The amount of computation required for the provers (and thus the cost) is a multiplicative \(\log \) S-factor more than the computation itself, making this schema efficient especially for low-space computations.

Keywords

Outsourcing Minimal refereed mechanism Merkle hash tree Prisoner’s dilemma 

References

  1. 1.
    Azar, P.D., Micali, S.: Rational proofs. In: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, pp. 1017–1028. ACM (2012)Google Scholar
  2. 2.
    Azar, P.D., Micali, S.: Super-efficient rational proofs. In: Proceedings of the Fourteenth ACM Conference on Electronic Commerce, pp. 29–30. ACM (2013)Google Scholar
  3. 3.
    Babai, L., Moran, S.: Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity classes. J. Comput. Syst. Sci. 36(2), 254–276 (1988)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Badrinarayanan, S., Kalai, Y.T., Khurana, D., Sahai, A., Wichs, D.: Succinct delegation for low-space non-deterministic computation. In: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, pp. 709–721. ACM, New York (2018).  https://doi.org/10.1145/3188745.3188924
  5. 5.
    Belenkiy, M., Chase, M., Erway, C.C., Jannotti, J., Küpçü, A., Lysyanskaya, A.: Incentivizing outsourced computation. In: Proceedings of the 3rd International Workshop on Economics of Networked Systems, pp. 85–90. ACM (2008)Google Scholar
  6. 6.
    Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM (1993)Google Scholar
  7. 7.
    Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 326–349. ACM (2012)Google Scholar
  8. 8.
    Brier, G.W.: Verification of forecasts expressed in terms of probability. Mon. Weather Rev. 78(1), 1–3 (1950)CrossRefGoogle Scholar
  9. 9.
    Canetti, R., Riva, B., Rothblum, G.N.: Practical delegation of computation using multiple servers. In: Proceedings of the 18th ACM Conference on Computer and Communications Security, pp. 445–454. ACM (2011)Google Scholar
  10. 10.
    Canetti, R., Riva, B., Rothblum, G.N.: Refereed delegation of computation. Inf. Comput. 226, 16–36 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Dong, C., Wang, Y., Aldweesh, A., McCorry, P., van Moorsel, A.: Betrayal, distrust, and rationality: smart counter-collusion contracts for verifiable cloud computing. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pp. 211–227. ACM (2017)Google Scholar
  12. 12.
    Feige, U., Kilian, J.: Making games short. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 506–516. ACM (1997)Google Scholar
  13. 13.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14623-7_25CrossRefGoogle Scholar
  14. 14.
    Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102(477), 359–378 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 113–122. ACM (2008)Google Scholar
  16. 16.
    Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. J. ACM 62(4), 27 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Guo, S., Hubáček, P., Rosen, A., Vald, M.: Rational arguments: single round delegation with sublinear verification. In: Proceedings of the 5th Conference on Innovations in Theoretical Computer Science, pp. 523–540. ACM (2014)Google Scholar
  19. 19.
    Guo, S., Hubáček, P., Rosen, A., Vald, M.: Rational sumchecks. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 319–351. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49099-0_12CrossRefGoogle Scholar
  20. 20.
    Halpern, J.Y., Pass, R.: Algorithmic rationality: game theory with costly computation. J. Econ. Theor. 156, 246–268 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Halpern, J.Y., Pass, R., Seeman, L.: Computational extensive-form games. In: Proceedings of the 2016 ACM Conference on Economics and Computation, pp. 681–698. ACM (2016)Google Scholar
  22. 22.
    Kalai, Y.T., P.O., Yang, L.: How to delegate computations publicly. In: STOC 2019: Proceedings of the 51th Annual ACM SIGACT Symposium on Theory of Computing. ACM (2019)Google Scholar
  23. 23.
    Lindell, Y., Katz, J.: Introduction to Modern Cryptography. Chapman and Hall/CRC, Boca Raton (2014)zbMATHGoogle Scholar
  24. 24.
    Lund, C., Fortnow, L., Karloff, H., Nisan, N.: Algebraic methods for interactive proof systems. J. ACM (JACM) 39(4), 859–868 (1992)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Reingold, O., Rothblum, G.N., Rothblum, R.D.: Constant-round interactive proofs for delegating computation. In: Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, pp. 49–62. ACM (2016)Google Scholar
  26. 26.
    Shamir, A.: IP = PSPACE. J. ACM (JACM) 39(4), 869–877 (1992)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Teutsch, J., Reitwießner, C.: A scalable verification solution for blockchains. https://people.cs.uchicago.edu/teutsch/papers/truebit pdf (2017)

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Peking UniversityHaidianChina
  2. 2.University of MichiganAnn ArborUSA

Personalised recommendations