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Lower Bounds on Structure-Preserving Signatures for Bilateral Messages

  • Masayuki AbeEmail author
  • Miguel Ambrona
  • Miyako Ohkubo
  • Mehdi Tibouchi
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11035)

Abstract

Lower bounds for structure-preserving signature (SPS) schemes based on non-interactive assumptions have only been established in the case of unilateral messages, i.e. schemes signing tuples of group elements all from the same source group. In this paper, we consider the case of bilateral messages, consisting of elements from both source groups. We show that, for Type-III bilinear groups, SPS’s must consist of at least 6 group elements: many more than the 4 elements needed in the unilateral case, and optimal, as it matches a known upper bound from the literature. We also obtain the first non-trivial lower bounds for SPS’s in Type-II groups: a minimum of 4 group elements, whereas constructions with 3 group elements are known from interactive assumptions.

Keywords

Structure-preserving signatures Bilateral messages Crucial relation 
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References

  1. 1.
    Abe, M., Ambrona, M., Ohkubo, M., Tibouchi, M.: Lower bounds on structurepreserving signatures for bilateral messages. IACR Cryptology ePrint Archive 2018/640 (2018). https://eprint.iacr.org/2018/640
  2. 2.
    Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: generic constructions and simple assumptions. J. Cryptol. 29(4), 833–878 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. J. Cryptol. 29(2), 363–421 (2016)MathSciNetCrossRefGoogle 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).  https://doi.org/10.1007/978-3-642-22792-9_37CrossRefzbMATHGoogle 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).  https://doi.org/10.1007/978-3-642-25385-0_34CrossRefGoogle Scholar
  6. 6.
    Abe, M., Groth, J., Ohkubo, M., Tibouchi, M.: Structure-preserving signatures from type II pairings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 390–407. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_22. Full version: IACR Cryptology ePrint Archive 2014/312CrossRefGoogle Scholar
  7. 7.
    Abe, M., Groth, J., Ohkubo, M., Tibouchi, M.: Structure-preserving signatures from type II pairings. IACR Cryptology ePrint Archive, 2014/312 (2014)Google Scholar
  8. 8.
    Abe, M., Groth, J., Ohkubo, M., Tibouchi, M.: Unified, minimal and selectively randomizable structure-preserving signatures. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 688–712. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54242-8_29CrossRefGoogle Scholar
  9. 9.
    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_3CrossRefGoogle Scholar
  10. 10.
    Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 59–71. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0054117CrossRefGoogle Scholar
  11. 11.
    Chatterjee, S., Menezes, A.: Type 2 structure-preserving signature schemes revisited. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 286–310. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48797-6_13CrossRefGoogle Scholar
  12. 12.
    Coron, J.-S.: Optimal security proofs for PSS and other signature schemes. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 272–287. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-46035-7_18CrossRefGoogle Scholar
  13. 13.
    Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_8CrossRefGoogle Scholar
  14. 14.
    Fuchsbauer, G., Kiltz, E., Loss, J.: The algebraic group model and its applications. Cryptology ePrint Archive, Report 2017/620 (2017). https://eprint.iacr.org/2017/620
  15. 15.
    Fuchsbauer, G., Hanser, C., Slamanig, D.: Practical round-optimal blind signatures in the standard model. IACR Cryptology ePrint Archive 2015/626 (2015). https://eprint.iacr.org/2015/626
  16. 16.
    Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008). Applications of Algebra to CryptographyMathSciNetCrossRefGoogle Scholar
  17. 17.
    Garg, S., Bhaskar, R., Lokam, S.V.: Improved bounds on security reductions for discrete log based signatures. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 93–107. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85174-5_6CrossRefGoogle Scholar
  18. 18.
    Ghadafi, E.: Short structure-preserving signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 305–321. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-29485-8_18CrossRefGoogle Scholar
  19. 19.
    Ghadafi, E.: How low can you go? Short structure-preserving signatures for Diffie-Hellman vectors. In: O’Neill, M. (ed.) IMACC 2017. LNCS, vol. 10655, pp. 185–204. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-71045-7_10CrossRefGoogle Scholar
  20. 20.
    Ghadafi, E.: More efficient structure-preserving signatures - or: bypassing the type-III lower bounds. In: Foley, S.N., Gollmann, D., Snekkenes, E. (eds.) ESORICS 2017. LNCS, vol. 10493, pp. 43–61. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66399-9_3CrossRefGoogle Scholar
  21. 21.
    Ghadafi, E., Smart, N.P., Warinschi, B.: Groth–sahai proofs revisited. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 177–192. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13013-7_11CrossRefGoogle Scholar
  22. 22.
    Jutla, C.S., Roy, A.: Improved structure preserving signatures under standard bilinear assumptions. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10175, pp. 183–209. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-662-54388-7_7CrossRefGoogle Scholar
  23. 23.
    Kiltz, E., Pan, J., Wee, H.: Structure-preserving signatures from standard assumptions, revisited. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 275–295. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_14CrossRefGoogle Scholar
  24. 24.
    Libert, B., Peters, T., Yung, M.: Short group signatures via structure-preserving signatures: standard model security from simple assumptions. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 296–316. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_15CrossRefGoogle Scholar
  25. 25.
    Paillier, P., Vergnaud, D.: Discrete-log-based signatures may not be equivalent to discrete log. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 1–20. Springer, Heidelberg (2005).  https://doi.org/10.1007/11593447_1CrossRefGoogle Scholar
  26. 26.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_7CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Masayuki Abe
    • 1
    Email author
  • Miguel Ambrona
    • 2
  • Miyako Ohkubo
    • 3
  • Mehdi Tibouchi
    • 1
  1. 1.Secure Platform LaboratoriesNTT CorporationTokyoJapan
  2. 2.IMDEA Software Institute & Universidad Politécnica de MadridMadridSpain
  3. 3.Security Fundamentals LabCSRI, NICTTokyoJapan

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