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Group Signature Without Random Oracles from Randomizable Signatures

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Provable and Practical Security (ProvSec 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12505))

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Abstract

Group signature is a central tool for privacy-preserving protocols, ensuring authentication, anonymity and accountability. It has been massively used in cryptography, either directly or through variants such as direct anonymous attestations. However, it remains a complex tool, especially if one wants to avoid proving security in the random oracle model.

In this work, we propose a new group signature scheme proven secure without random oracles which significantly decreases the complexity in comparison with the state-of-the-art. More specifically, we halve both the size and the computational cost compared to the most efficient alternative in the same model. Moreover, our construction is also competitive against the most efficient ones in the random oracle model.

Our construction is based on a tailored combination of two popular signatures, which avoids the explicit use of encryption schemes or zero-knowledge proofs while signing. It is flexible enough to achieve security in different models and is thus suitable for most contexts.

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Notes

  1. 1.

    We nevertheless note that the hardness of the corresponding problem depends on the function h. For example, if h is constant then no adversary can succeed as soon as it makes (at least) one query to \(\mathcal {O}\).

  2. 2.

    Any EUF-CMA signature scheme can be selected here, without any impact on the complexity of the group signatures.

References

  1. Abdalla, M., Warinschi, B.: On the minimal assumptions of group signature schemes. In: Lopez, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 1–13. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30191-2_1

    Chapter  Google Scholar 

  2. Ateniese, G., Camenisch, J., Joye, M., Tsudik, G.: A practical and provably secure coalition-resistant group signature scheme. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 255–270. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_16

    Chapter  Google Scholar 

  3. Backes, M., Hanzlik, L., Kluczniak, K., Schneider, J.: Signatures with flexible public key: introducing equivalence classes for public keys. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part II. LNCS, vol. 11273, pp. 405–434. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_14

    Chapter  Google Scholar 

  4. Barbulescu, R., Duquesne, S.: Updating key size estimations for pairings. J. Cryptology 32(4), 1298–1336 (2019). https://doi.org/10.1007/s00145-018-9280-5

    Article  MathSciNet  MATH  Google Scholar 

  5. Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_38

    Chapter  Google Scholar 

  6. Bellare, M., Shi, H., Zhang, C.: Foundations of group signatures: the case of dynamic groups. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 136–153. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30574-3_11

    Chapter  Google Scholar 

  7. Bichsel, P., Camenisch, J., Neven, G., Smart, N.P., Warinschi, B.: Get shorty via group signatures without encryption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 381–398. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15317-4_24

    Chapter  Google Scholar 

  8. Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_3

    Chapter  Google Scholar 

  9. Boneh, D., Shacham, H.: Group signatures with verifier-local revocation. In: ACM CCS (2004)

    Google Scholar 

  10. Bos, J.W., Costello, C., Naehrig, M.: Exponentiating in pairing groups. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 438–455. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43414-7_22

    Chapter  MATH  Google Scholar 

  11. Bowe, S.: BLS12-381: New zk-SNARK Elliptic Curve Construction (2017). https://electriccoin.co/blog/new-snark-curve/

  12. Bowe, S., Chiesa, A., Green, M., Miers, I., Mishra, P., Wu, H.: Zexe: enabling decentralized private computation. IACR Cryptology ePrint Archive (2018)

    Google Scholar 

  13. Boyen, X., Waters, B.: Compact group signatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 427–444. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_26

    Chapter  Google Scholar 

  14. Camenisch, J., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_4

    Chapter  Google Scholar 

  15. Canard, S., Pointcheval, D., Sanders, O., Traoré, J.: Divisible E-cash made practical. In: PKC (2015)

    Google Scholar 

  16. Canetti, R., Goldreich, O., Halevi, S.: On the random-oracle methodology as applied to length-restricted signature schemes. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 40–57. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_3

    Chapter  Google Scholar 

  17. Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_22

    Chapter  Google Scholar 

  18. Clarisse, R., Sanders, O.: Group Signature without Random Oracles from Randomizable Signatures (full version of this work). IACR Cryptol. ePrint Arch., 2018–1115 (2020)

    Google Scholar 

  19. Derler, D., Slamanig, D.: Highly-efficient fully-anonymous dynamic group signatures. In: ASIACCS (2018)

    Google Scholar 

  20. 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). https://doi.org/10.1007/3-540-47721-7_12

    Chapter  Google Scholar 

  21. Fuchsbauer, G., Hanser, C., Slamanig, D.: Structure-preserving signatures on equivalence classes and constant-size anonymous credentials. J. Cryptol. 32(2), 498–546 (2019)

    Article  MathSciNet  Google Scholar 

  22. Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)

    Article  MathSciNet  Google Scholar 

  23. Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_10

    Chapter  Google Scholar 

  24. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24

    Chapter  Google Scholar 

  25. Guillevic, A.: Comparing the pairing efficiency over composite-order and prime-order elliptic curves. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 357–372. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38980-1_22

    Chapter  Google Scholar 

  26. Kim, T., Barbulescu, R.: Extended tower number field sieve: a new complexity for the medium prime case. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part I. LNCS, vol. 9814, pp. 543–571. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_20

    Chapter  Google Scholar 

  27. Libert, B., Peters, T., Joye, M., Yung, M.: Non-malleability from malleability: simulation-sound quasi-adaptive NIZK proofs and CCA2-secure encryption from homomorphic signatures. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 514–532. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_29

    Chapter  Google Scholar 

  28. Pointcheval, D., Sanders, O.: Short randomizable signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 111–126. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29485-8_7

    Chapter  Google Scholar 

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Acknowledgements

The authors are grateful for the support of the ANR through project ANR-16-CE39-0014 PERSOCLOUD and project ANR-18-CE-39-0019-02 MobiS5.

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Authors and Affiliations

  1. Orange Labs, Applied Crypto Group, Cesson-Sévigné, France

    Rémi Clarisse & Olivier Sanders

  2. Univ Rennes, CNRS, IRMAR - UMR 6625, 35000, Rennes, France

    Rémi Clarisse

Authors
  1. Rémi Clarisse
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  2. Olivier Sanders
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Correspondence to Olivier Sanders .

Editor information

Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Khoa Nguyen

  2. Chinese Academy of Sciences, Beijing, China

    Wenling Wu

  3. Nanyang Technological University, Singapore, Singapore

    Kwok Yan Lam

  4. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Clarisse, R., Sanders, O. (2020). Group Signature Without Random Oracles from Randomizable Signatures. In: Nguyen, K., Wu, W., Lam, K.Y., Wang, H. (eds) Provable and Practical Security. ProvSec 2020. Lecture Notes in Computer Science(), vol 12505. Springer, Cham. https://doi.org/10.1007/978-3-030-62576-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-62576-4_1

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  • Online ISBN: 978-3-030-62576-4

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