Skip to main content

Outsourcing Computation: The Minimal Refereed Mechanism

Part of the Lecture Notes in Computer Science book series (LNISA,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

The first and third authors gratefully acknowledge the support of the National Science Foundation under CCF #1618187. The last two authors gratefully acknowledge the support of NSF under Career Award #1452915.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-35389-6_19
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-35389-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)

References

  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. 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. 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)

    MathSciNet  CrossRef  Google Scholar 

  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. 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. 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. 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. Brier, G.W.: Verification of forecasts expressed in terms of probability. Mon. Weather Rev. 78(1), 1–3 (1950)

    CrossRef  Google Scholar 

  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. Canetti, R., Riva, B., Rothblum, G.N.: Refereed delegation of computation. Inf. Comput. 226, 16–36 (2013)

    MathSciNet  CrossRef  Google Scholar 

  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. 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. 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_25

    CrossRef  Google Scholar 

  14. Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102(477), 359–378 (2007)

    MathSciNet  CrossRef  Google Scholar 

  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. Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. J. ACM 62(4), 27 (2015)

    MathSciNet  CrossRef  Google Scholar 

  17. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)

    MathSciNet  CrossRef  Google Scholar 

  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. 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_12

    CrossRef  Google Scholar 

  20. Halpern, J.Y., Pass, R.: Algorithmic rationality: game theory with costly computation. J. Econ. Theor. 156, 246–268 (2015)

    MathSciNet  CrossRef  Google Scholar 

  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. 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. Lindell, Y., Katz, J.: Introduction to Modern Cryptography. Chapman and Hall/CRC, Boca Raton (2014)

    MATH  Google Scholar 

  24. Lund, C., Fortnow, L., Karloff, H., Nisan, N.: Algebraic methods for interactive proof systems. J. ACM (JACM) 39(4), 859–868 (1992)

    MathSciNet  CrossRef  Google Scholar 

  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. Shamir, A.: IP = PSPACE. J. ACM (JACM) 39(4), 869–877 (1992)

    MathSciNet  CrossRef  Google Scholar 

  27. Teutsch, J., Reitwießner, C.: A scalable verification solution for blockchains. https://people.cs.uchicago.edu/teutsch/papers/truebit pdf (2017)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Biaoshuai Tao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Kong, Y., Peikert, C., Schoenebeck, G., Tao, B. (2019). Outsourcing Computation: The Minimal Refereed Mechanism. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-35389-6_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35388-9

  • Online ISBN: 978-3-030-35389-6

  • eBook Packages: Computer ScienceComputer Science (R0)