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Verifiable Computation of Large Polynomials

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9473))

Abstract

Due to the proliferation of powerful cloud service, verifiable computation, which makes a computationally weak client perform intensive computations possible through outsourcing tasks to a powerful server, is attracting increasing attention. The correctness of the returned result should be verified as the server may be not trusted.

In this paper, we present a verifiable computation protocol on large polynomials, which can be publicly verified by any parties in the network. Compared with verifiable computation protocol presented by Backes et al., which is on quadratic, multi-variable polynomials, our verifiable computation protocol is on high degree, multi-variable polynomials and publicly verifiable.

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References

  1. Barbosa, M., Farshim, P.: Delegatable homomorphic encryption with applications to secure outsourcing of computation. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 296–312. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Backes, M., Fiore, D., Reischuk., R. M.: Verifiable delegation of computation on outsourced data. In: CCS 2013, pp. 863–874. ACM press (2013). A full version is avaliable at http://eprint.iacr.org/2013/469 (2013)

  3. Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable delegation of computation over large datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111–131. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Catalano, Dario, Fiore, Dario, Gennaro, Rosario, Nizzardo, Luca: Generalizing homomorphic MACs for arithmetic circuits. In: Krawczyk, Hugo (ed.) PKC 2014. LNCS, vol. 8383, pp. 538–555. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Choi, S.G., Katz, J., Kumaresan, R., Cid, C.: Multi-client non-interactive verifiable computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 499–518. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Chung, K.-M., Kalai, Y., Vadhan, S.: Improved delegation of computation using fully homomorphic encryption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 483–501. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Cormode, G., Mitzenmacher, M., Thaler, J.: Practical Verified Computation with Streaming Interactive Proofs. In: ITCS 2012, pp. 90–112. ACM press, New York (2012)

    Google Scholar 

  11. Cormode, G., Thaler, J., Yi, K.: Verifying computations with streaming interactive proofs. Proc. VLDB Endowment 5(1), 25–36 (2011)

    Article  Google Scholar 

  12. Fiore, D., Gennaro, R.: Publicly Verification delegation of large polynomials and matrix computations, with applications. In: CCS 2012, pp. 501–512. ACM press, New York (2012)

    Google Scholar 

  13. Gentry, C.: A fully homomorphic encryption scheme. In: Stanford University (2009)

    Google Scholar 

  14. Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 479–499. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In STOC 2008, pp. 113–122. ACM press, New York (2008)

    Google Scholar 

  18. Goldwasser, S., Lin, H., Rubinstein, A.: Delegation of computation without rejection problem from designated verifier cs-proofs. In: IACR Cryptology ePrint Archive, avaliable at http://eprint.iacr.org/2011/456 (2011)

  19. Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Hohenberger, S., Sahai, A., Waters, B.: Full domain hash from (leveled) multilinear maps and identity-based aggregate signatures. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 494–512. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: STOC 2012, pp. 1219–1234. ACM press (2012)

    Google Scholar 

  22. Lewko, A.B., Waters, B.: Efficient pseudorandom functions from the dicisional linear assumption and weaker variants. In: CCS 2009, pp. 112–120. ACM press, New York (2009)

    Google Scholar 

  23. Mohassel, P.: Efficient and secure delegation of linear algebra. In: IACR Cryptology ePrint Archive, avaliable at http://eprint.iacr.org/2011/605, (2011)

  24. Parno, B., Raykova, M., Vaikuntanathan, V.: How to delegate and verify in public: verifiable computation from attribute-based encryption. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 422–439. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  25. Rothblum, G.N., Vadhan, S., Wigderson, A.: Interactive proofs of proximity: delegating computation in sublinear time. In: STOC 2013, pp. 793–802. ACM press, New York (2013)

    Google Scholar 

  26. Zhang, L.F., Safavi-Naini, R.: Private outsourcing of polynomial evaluation and matrix multiplication using multilinear maps. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 329–348. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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Acknowledgment

This work is supported by the National Natural Science Foundation of China (No.61379140) and the National Basic Research Program of China (973 Program) (No. 2013CB338001). The authors wish to acknowledge the anonymous referees for helpful suggestions.

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Correspondence to Haixia Xu .

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Hong, J., Xu, H., Li, P. (2015). Verifiable Computation of Large Polynomials. In: Yung, M., Zhu, L., Yang, Y. (eds) Trusted Systems. INTRUST 2014. Lecture Notes in Computer Science(), vol 9473. Springer, Cham. https://doi.org/10.1007/978-3-319-27998-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-27998-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27997-8

  • Online ISBN: 978-3-319-27998-5

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