Non-Interactive Zero-Knowledge Proofs in the Quantum Random Oracle Model

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9057)

Abstract

We present a construction for non-interactive zero-knowledge proofs of knowledge in the random oracle model from general sigma-protocols. Our construction is secure against quantum adversaries. Prior constructions (by Fiat-Shamir and by Fischlin) are only known to be secure against classical adversaries, and Ambainis, Rosmanis, Unruh (FOCS 2014) gave evidence that those constructions might not be secure against quantum adversaries in general.

To prove security of our constructions, we additionally develop new techniques for adaptively programming the quantum random oracle.

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References

  1. 1.
    Adida, B.: Helios: web-based open-audit voting. In: van Oorschot, P.C. (ed.) USENIX Security Symposium 2008, pp. 335–348. USENIX (2008). http://www.usenix.org/events/sec08/tech/full_papers/adida/adida.pdf
  2. 2.
    Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems (the hardness of quantum rewinding). In: FOCS 2014, pp. 474–483. IEEE, October 2014Google Scholar
  3. 3.
    Ben-Or, M.: Probabilistic algorithms in finite fields. In: FOCS 1981, pp. 394–398. IEEE (1981)Google Scholar
  4. 4.
    Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 103–112. ACM, New York (1988)Google Scholar
  5. 5.
    Brickell, E., Camenisch, J., Chen, L.: Direct anonymous attestation. In: ACM CCS 2004, pp. 132–145. ACM, New York (2004)Google Scholar
  6. 6.
    Cramer, R., Damgård, I.B., Schoenmakers, B.: Proof of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994) Google Scholar
  7. 7.
    Dagdelen, Ö., Fischlin, M., Gagliardoni, T.: The fiat–shamir transformation in a quantum world. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 62–81. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  8. 8.
    Damgård, I.: On \(\sigma \)-protocols. Course notes for “Cryptologic Protocol Theory" (2010). http://www.cs.au.dk/~ivan/Sigma.pdf, http://www.webcitation.org/6O9USFecZ (Retrieved March 17, 2014)
  9. 9.
    Faust, S., Kohlweiss, M., Marson, G.A., Venturi, D.: On the non-malleability of the fiat-shamir transform. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 60–79. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  10. 10.
    Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987) CrossRefGoogle Scholar
  11. 11.
    Fischlin, M.: Communication-efficient non-interactive proofs of knowledge with online extractors. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 152–168. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  12. 12.
    Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J ACM 38(3), 690–728 (1991)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  14. 14.
    Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  15. 15.
    Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996) CrossRefGoogle Scholar
  16. 16.
    A. Sahai. Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS 1999, pp. 543–553. IEEE (1999)Google Scholar
  17. 17.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: FOCS 1994, pp. 124–134. IEEE (1994)Google Scholar
  18. 18.
    Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135–152. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  19. 19.
    Unruh, D.: Non-interactive zero-knowledge proofs in the quantum random oracle model. IACR ePrint 2014/587 (2014). Full version of this paperGoogle Scholar
  20. 20.
    Unruh, D.: Quantum position verification in the random oracle model. In: Crypto 2014, LNCS. Springer, February 2014. To appear, preprint on IACR ePrint 2014/118Google Scholar
  21. 21.
    Unruh, D.: Revocable quantum timed-release encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 129–146. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  22. 22.
    Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Zhandry, M.: Secure identity-based encryption in the quantum random oracle model. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 758–775. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  24. 24.
    Zhandry, M.: A note on the quantum collision and set equality problems, Dec. 2013. arXiv:1312.1027v3 [cs.CC]

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.University of TartuTartuEstonia

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