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CHQS: Publicly Verifiable Homomorphic Signatures Beyond the Linear Case

  • Lucas Schabhüser
  • Denis Butin
  • Johannes Buchmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11125)

Abstract

Sensitive data is often outsourced to cloud servers, with the server performing computation on the data. Computational correctness must be efficiently verifiable by a third party while the input data remains confidential. We introduce CHQS, a homomorphic signature scheme from bilinear groups fulfilling these requirements. CHQS is the first such scheme to be both context hiding and publicly verifiable for arithmetic circuits of degree 2. It also achieves amortized efficiency: after a precomputation, verification can be faster than the circuit evaluation itself.

Notes

Acknowledgment

This work has received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No 644962.

References

  1. 1.
    Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: new privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 367–385. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_23CrossRefGoogle Scholar
  2. 2.
    Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 386–404. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36362-7_24CrossRefGoogle Scholar
  3. 3.
    Backes, M., Fiore, D., Reischuk, R.M.: Verifiable delegation of computation on outsourced data. In: ACM CCS 2013, pp. 863–874. ACM (2013)Google Scholar
  4. 4.
    Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19379-8_1CrossRefGoogle Scholar
  5. 5.
    Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-00468-1_5CrossRefGoogle Scholar
  6. 6.
    Catalano, D., Fiore, D.: Using linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data. In: ACM CCS 2015, pp. 1518–1529. ACM (2015)Google Scholar
  7. 7.
    Catalano, D., Fiore, D., Gennaro, R., Nizzardo, L.: Generalizing homomorphic MACs for arithmetic circuits. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 538–555. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54631-0_31CrossRefGoogle Scholar
  8. 8.
    Catalano, D., Fiore, D., Nizzardo, L.: Programmable hash functions go private: constructions and applications to (homomorphic) signatures with shorter public keys. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 254–274. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_13CrossRefGoogle Scholar
  9. 9.
    Catalano, D., Fiore, D., Warinschi, B.: Efficient network coding signatures in the standard model. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 680–696. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-30057-8_40CrossRefGoogle Scholar
  10. 10.
    Catalano, D., Fiore, D., Warinschi, B.: Homomorphic signatures with efficient verification for polynomial functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 371–389. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_21CrossRefGoogle Scholar
  11. 11.
    Coron, J.-S., Lee, M.S., Lepoint, T., Tibouchi, M.: Cryptanalysis of GGH15 multilinear maps. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 607–628. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53008-5_21CrossRefGoogle Scholar
  12. 12.
    Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40041-4_26CrossRefGoogle Scholar
  13. 13.
    Demirel, D., Schabhüser, L., Buchmann, J.A.: Privately and Publicly Verifiable Computing Techniques – A Survey. Springer Briefs in Computer Science. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-319-53798-6CrossRefGoogle Scholar
  14. 14.
    Desmedt, Y.: Computer security by redefining what a computer is. In: NSPW, pp. 160–166. ACM (1993)Google Scholar
  15. 15.
    Fiore, D., Mitrokotsa, A., Nizzardo, L., Pagnin, E.: Multi-key homomorphic authenticators. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 499–530. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_17CrossRefGoogle Scholar
  16. 16.
    Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-30057-8_41CrossRefGoogle Scholar
  17. 17.
    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).  https://doi.org/10.1007/978-3-642-38348-9_1CrossRefGoogle Scholar
  18. 18.
    Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure network coding over the integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 142–160. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13013-7_9CrossRefGoogle Scholar
  19. 19.
    Geovandro, C.C.F.P., Simplício Jr., M.A., Naehrig, M., Barreto, P.S.L.M.: A family of implementation-friendly BN elliptic curves. J. Syst. Softw. 84(8), 1319–1326 (2011)CrossRefGoogle Scholar
  20. 20.
    Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: STOC 2015, pp. 469–477. ACM (2015)Google Scholar
  21. 21.
    Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45760-7_17CrossRefGoogle Scholar
  22. 22.
    Lee, H.T., Seo, J.H.: Security analysis of multilinear maps over the integers. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 224–240. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_13CrossRefGoogle Scholar
  23. 23.
    Menezes, A., Sarkar, P., Singh, S.: Challenges with assessing the impact of NFS advances on the security of pairing-based cryptography. In: Phan, R.C.-W., Yung, M. (eds.) Mycrypt 2016. LNCS, vol. 10311, pp. 83–108. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-61273-7_5CrossRefGoogle Scholar
  24. 24.
    Miles, E., Sahai, A., Zhandry, M.: Annihilation attacks for multilinear maps: cryptanalysis of indistinguishability obfuscation over GGH13. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 629–658. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53008-5_22CrossRefGoogle Scholar
  25. 25.
    Schabhüser, L., Buchmann, J., Struck, P.: A linearly homomorphic signature scheme from weaker assumptions. In: O’Neill, M. (ed.) IMACC 2017. LNCS, vol. 10655, pp. 261–279. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-71045-7_14CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lucas Schabhüser
    • 1
  • Denis Butin
    • 1
  • Johannes Buchmann
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

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