Compact Round-Optimal Partially-Blind Signatures

  • Olivier Blazy
  • David Pointcheval
  • Damien Vergnaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7485)


Partially-blind signatures find many applications in the area of anonymity, such as in e-cash or e-voting systems. They extend classical blind signatures, with a signed message composed of two parts: a public one (common to the user and the signer) and a private one (chosen by the user, and blindly signed). The signer cannot link later the message-signature to the initial interaction with the user, among other signatures on messages with the same public part.

This paper presents a one-round partially-blind signature which achieves perfect blindness in the standard model using a Common Reference String, under classical assumptions: CDH and DLin assumptions in symmetric groups, and similar ones in asymmetric groups. This scheme is more efficient than the previous ones: reduced round complexity and communication complexity, but still weaker complexity assumptions. A great advantage is also to end up with a standard Waters signature, which is quite short.

In addition, in all the previous schemes, the public part required a prior agreement between the parties on the public part of the message before running the blind signature protocol. Our protocol does not require such pre-processing: the public part can be chosen by the signer only.

Our scheme even allows multiple messages provided from independent sources to be blindly signed. These messages can either be concatenated or aggregated by the signer, without learning any information about them, before returning the blind signature to the recipient. For the aggregation (addition of the messages), we provide a new result, of independent interest, about the Waters hash function over non binary-alphabets.


Signature Scheme Blind Signature Blind Signature Scheme Prior Agreement Common Reference String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-Preserving Signatures and Commitments to Group Elements. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 209–236. Springer, Heidelberg (2010)Google Scholar
  2. 2.
    Abe, M., Fujisaki, E.: How to Date Blind Signatures. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 244–251. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  3. 3.
    Abe, M., Okamoto, T.: Provably Secure Partially Blind Signatures. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 271–286. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Blazy, O., Fuchsbauer, G., Pointcheval, D., Vergnaud, D.: Signatures on Randomizable Ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 403–422. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Blazy, O., Pointcheval, D., Vergnaud, D.: Round-Optimal Privacy-Preserving Protocols with Smooth Projective Hash Functions. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 94–111. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Blazy, O., Pointcheval, D., Vergnaud, D.: Compact Round-Optimal Partially-Blind Signatures. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 95–112. Springer, Heidelberg (2012)Google Scholar
  7. 7.
    Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Chaum, D.: Blind signatures for untraceable payments. In: CRYPTO 1982, pp. 199–203. Plenum Press, New York (1983)Google Scholar
  10. 10.
    Davis, B., McDonald, D.: An elementary proof of the local central limit theorem. Journal of Theoretical Probability 8(3) (July 1995)Google Scholar
  11. 11.
    Fischlin, M.: Round-Optimal Composable Blind Signatures in the Common Reference String Model. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 60–77. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Fuchsbauer, G.: Commuting signatures and verifiable encryption and an application to non-interactively delegatable credentials. Cryptology ePrint Archive, Report 2010/233 (2010)Google Scholar
  13. 13.
    Garg, S., Rao, V., Sahai, A., Schröder, D., Unruh, D.: Round Optimal Blind Signatures. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 630–648. Springer, Heidelberg (2011)Google 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.
    Hofheinz, D., Kiltz, E.: Programmable Hash Functions and Their Applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008)Google Scholar
  16. 16.
    Naccache, D.: Secure and practical identity-based encryption. Cryptology ePrint Archive, Report 2005/369 (2005)Google Scholar
  17. 17.
    Okamoto, T.: Efficient Blind and Partially Blind Signatures Without Random Oracles. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 80–99. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13(3), 361–396 (2000)zbMATHCrossRefGoogle Scholar
  19. 19.
    Seo, J.H., Cheon, J.H.: Beyond the Limitation of Prime-Order Bilinear Groups, and Round Optimal Blind Signatures. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 133–150. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  20. 20.
    Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Olivier Blazy
    • 1
  • David Pointcheval
    • 1
  • Damien Vergnaud
    • 1
  1. 1.ENSParisFrance

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