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Efficient Rational Proofs with Strong Utility-Gap Guarantees

  • Jing Chen
  • Samuel McCauley
  • Shikha SinghEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11059)

Abstract

As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for verifiable computation delegation.

Rational proofs are payment-based interactive proofs. The payments are designed to incentivize the provers to give correct answers. If the provers misreport the answer then they incur a payment loss of at least 1 / u, where u is the utility gap of the protocol.

In this work, we tightly characterize the power of rational proofs that are super efficient, that is, require only logarithmic time and communication for verification. We also characterize the power of single-round rational protocols that require only logarithmic space and randomness for verification. Our protocols have strong (that is, polynomial, logarithmic, and even constant) utility gap. Finally, we show when and how rational protocols can be converted to give the completeness and soundness guarantees of classical interactive proofs.

References

  1. 1.
    Allender, E., Hertrampf, U.: On the power of uniform families of constant depth threshold circuits. In: Symposium on Mathematical Foundations of Computer Science, pp. 158–164 (1990)Google Scholar
  2. 2.
    Azar, P.D., Micali, S.: Rational proofs. In: Proceedings of 44th Symposium on Theory of Computing, pp. 1017–1028 (2012)Google Scholar
  3. 3.
    Azar, P.D., Micali, S.: Super-efficient rational proofs. In: Proceedings of 14th Conference on Electronic Commerce, pp. 29–30 (2013)Google Scholar
  4. 4.
    Bellare, M., Goldreich, O., Goldwasser, S.: Randomness in interactive proofs. Comput. Complex. 3(4), 319–354 (1993)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.: Short PCPs verifiable in polylogarithmic time. In: Proceedings of Conference on Computational Complexity, pp. 120–134 (2005)Google Scholar
  6. 6.
    Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.: Robust PCPs of proximity, shorter PCPs, and applications to coding. SIAM J. Comput. 36(4), 889–974 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bitansky, N., Chiesa, A.: Succinct arguments from multi-prover interactive proofs and their efficiency benefits. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 255–272. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_16CrossRefGoogle Scholar
  8. 8.
    Buhrman, H., Kadin, J., Thierauf, T.: On functions computable with nonadaptive queries to NP. In: Proceedings of 9th Structure in Complexity Theory Conference, pp. 43–52 (1994)Google Scholar
  9. 9.
    Campanelli, M., Gennaro, R.: Sequentially composable rational proofs. In: Proceedings of Decision and Game Theory for Security, pp. 270–288 (2015)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.
    Chakrabarti, A., Cormode, G., McGregor, A., Thaler, J., Venkatasubramanian, S.: Verifiable stream computation and Arthur-Merlin communication. In: Proceedings of Conference on Computational Complexity, pp. 217–243 (2015)Google Scholar
  12. 12.
    Chandra, A.K., Stockmeyer, L.J.: Alternation. In: Proceedings of 17th Symposium on Foundations of Computer Science, pp. 98–108 (1976)Google Scholar
  13. 13.
    Chen, J., McCauley, S., Singh, S.: Rational proofs with multiple provers. In: Proceedings of 7th Innovations in Theoretical Computer Science Conference, pp. 237–248 (2016)Google Scholar
  14. 14.
    Chen, J., McCauley, S., Singh, S.: Rational proofs with non-cooperative provers. arXiv preprint arXiv:1708.00521 (2017)
  15. 15.
    Chen, J., McCauley, S., Singh, S.: Efficient Rational Proofs with Strong Utility-Gap Guarantees http://arxiv.org/abs/1807.01389 (2018)
  16. 16.
    Condon, A., Ladner, R.: Interactive proof systems with polynomially bounded strategies. J. Comput. Syst. Sci. 50(3), 506–518 (1995)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Cormode, G., Thaler, J., Yi, K.: Verifying computations with streaming interactive proofs. Proc. VLDB Endow. 5(1), 25–36 (2011)CrossRefGoogle Scholar
  18. 18.
    Daruki, S., Thaler, J., Venkatasubramanian, S.: Streaming verification in data analysis. In: Elbassioni, K., Makino, K. (eds.) ISAAC 2015. LNCS, vol. 9472, pp. 715–726. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48971-0_60CrossRefGoogle Scholar
  19. 19.
    Feige, U., Kilian, J.: Two prover protocols: low error at affordable rates. In: Proceedings of 26th Symposium on Theory of Computing, pp. 172–183 (1994)Google Scholar
  20. 20.
    Feige, U., Kilian, J.: Making games short. In: Proceedings of 29th Symposium On Theory of Computing, pp. 506–516 (1997)Google Scholar
  21. 21.
    Feigenbaum, J., Koller, D., Shor, P.: A game-theoretic classification of interactive complexity classes. In: Proceedings of 10th Structure in Complexity Theory Conference, pp. 227–237 (1995)Google Scholar
  22. 22.
    Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Proceedings of 40th Symposium on Theory of Computing, pp. 113–122 (2008)Google Scholar
  23. 23.
    Guo, S., Hubáček, P., Rosen, A., Vald, M.: Rational arguments: single round delegation with sublinear verification. In: Proceedings of 5th Innovations in Theoretical Computer Science, pp. 523–540 (2014)Google Scholar
  24. 24.
    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
  25. 25.
    Hesse, W., Allender, E., Barrington, D.A.M.: Uniform constant-depth threshold circuits for division and iterated multiplication. J. Comput. Syst. Sci. 65(4), 695–716 (2002)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Hubáček, P.: Rationality in the Cryptographic Model. Ph.D thesis, Department Office Computer Science, Aarhus University (2014)Google Scholar
  27. 27.
    Inasawa, K., Yasunaga, K.: Rational proofs against rational verifiers. Fundam. Electron. Commun. Comput. Sci. 100(11), 2392–2397 (2017)Google Scholar
  28. 28.
    Kalai, Y.T., Rothblum, R.D.: Arguments of proximity. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 422–442. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_21CrossRefGoogle Scholar
  29. 29.
    Koller, D., Megiddo, N.: The complexity of two-person zero-sum games in extensive form. Games Econ. Behav. 4(4), 528–552 (1992)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Krentel, M.W.: The complexity of optimization problems. J. Comput. Syst. Sci. 36(3), 490–509 (1988)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Raz, R.: A parallel repetition theorem. SIAM J. Comput. 27(3), 763–803 (1998)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Reif, J.H.: The complexity of two-player games of incomplete information. J. Comput. Syst. Sci. 29(2), 274–301 (1984)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Rothblum, G.N., Vadhan, S., Wigderson, A.: Interactive proofs of proximity: delegating computation in sublinear time. In: Proceedings of 45th Symposium on Theory of Computing, pp. 793–802 (2013)Google Scholar
  34. 34.
    Wagner, K.W.: Bounded query classes. SIAM J. Comput. 19(5), 833–846 (1990)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Zhang, Y., Blanton, M.: Efficient secure and verifiable outsourcing of matrix multiplications. In: Chow, S.S.M., Camenisch, J., Hui, L.C.K., Yiu, S.M. (eds.) ISC 2014. LNCS, vol. 8783, pp. 158–178. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-13257-0_10CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Stony Brook UniversityStony BrookUSA
  2. 2.Wellesley CollegeWellesleyUSA

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