Unified, Minimal and Selectively Randomizable Structure-Preserving Signatures

  • Masayuki Abe
  • Jens Groth
  • Miyako Ohkubo
  • Mehdi Tibouchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)

Abstract

We construct a structure-preserving signature scheme that is selectively randomizable and works in all types of bilinear groups. We give matching lower bounds showing that our structure-preserving signature scheme is optimal with respect to both signature size and public verification key size.

State of the art structure-preserving signatures in the asymmetric setting consist of 3 group elements, which is known to be optimal. Our construction preserves the signature size of 3 group elements and also at the same time minimizes the verification key size to 1 group element.

Depending on the application, it is sometimes desirable to have strong unforgeability and in other situations desirable to have randomizable signatures. To get the best of both worlds, we introduce the notion of selective randomizability where the signer may for specific signatures provide randomization tokens that enable randomization.

Our structure-preserving signature scheme unifies the different pairing-based settings since it can be instantiated in both symmetric and asymmetric groups. Since previously optimal structure-preserving signatures had only been constructed in asymmetric bilinear groups this closes an important gap in our knowledge. Having a unified signature scheme that works in all types of bilinear groups is not just conceptually nice but also gives a hedge against future cryptanalytic attacks. An instantiation of our signature scheme in an asymmetric bilinear group may remain secure even if cryptanalysts later discover an efficiently computable homomorphism between the source groups.

Keywords

Structure-preserving signatures automorphic signatures selective randomizability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: Generic constructions and simple assumptions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 4–24. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Abe, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Tagged one-time signatures: Tight security and optimal tag size. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 312–331. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Abe, M., Groth, J., Haralambiev, K., Ohkubo, M.: Optimal structure-preserving signatures in asymmetric bilinear groups. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 649–666. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Abe, M., Groth, J., Ohkubo, M.: Separating short structure-preserving signatures from non-interactive assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 628–646. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Abe, M., Haralambiev, K., Ohkubo, M.: Signing on group elements for modular protocol designs. IACR ePrint Archive, Report 2010/133 (2010), http://eprint.iacr.org
  7. 7.
    Abe, M., Haralambiev, K., Ohkubo, M.: Efficient message space extension for automorphic signatures. In: Burmester, M., Tsudik, G., Magliveras, S., Ilić, I. (eds.) ISC 2010. LNCS, vol. 6531, pp. 319–330. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Barbulescu, R., Gaudry, P., Joux, A., Thomé, E.: A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. IACR ePrint Archive, Report 2013/400 (2013), http://eprint.iacr.org/
  11. 11.
    Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Cryptology 21(2), 149–177 (2008)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Camenisch, J., Dubovitskaya, M., Enderlein, R.R., Neven, G.: Oblivious transfer with hidden access control from attribute-based encryption. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 559–579. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Cathalo, J., Libert, B., Yung, M.: Group encryption: Non-interactive realization in the standard model. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 179–196. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Malleable proof systems and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 281–300. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Fuchsbauer, G.: Automorphic signatures in bilinear groups. IACR ePrint Archive, Report 2009/320 (2009), http://eprint.iacr.org
  16. 16.
    Fuchsbauer, G.: Commuting signatures and verifiable encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 224–245. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Fuchsbauer, G., Vergnaud, D.: Fair blind signatures without random oracles. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 16–33. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Applied Mathematics 156(16), 3113–3121 (2008)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Green, M., Hohenberger, S.: Universally composable adaptive oblivious transfer. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 179–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    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
  21. 21.
    Groth, J., Sahai, A.: Efficient noninteractive proof systems for bilinear groups. SIAM J. Comput. 41(5), 1193–1232 (2012)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Hofheinz, D., Jager, T.: Tightly secure signatures and public-key encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 590–607. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Hofheinz, D., Jager, T., Knapp, E.: Waters signatures with optimal security reduction. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 66–83. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Libert, B., Peters, T., Joye, M., Yung, M.: Linearly homomorphic structure-preserving signatures and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 289–307. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  25. 25.
    Libert, B., Peters, T., Yung, M.: Group signatures with almost-for-free revocation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 571–589. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  26. 26.
    Zhang, J., Li, Z., Guo, H.: Anonymous transferable conditional e-cash. In: Keromytis, A.D., Di Pietro, R. (eds.) SecureComm 2012. LNICST, vol. 106, pp. 45–60. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  27. 27.
    Zhou, S., Lin, D.: Unlinkable randomizable signature and its application in group signature. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 328–342. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Masayuki Abe
    • 1
  • Jens Groth
    • 2
  • Miyako Ohkubo
    • 3
  • Mehdi Tibouchi
    • 1
  1. 1.Secure Platform Laboratories, NTT CorporationJapan
  2. 2.University College LondonUK
  3. 3.Security Architecture Lab, NSRI, NICTJapan

Personalised recommendations