Abstract
At Crypto 2015 Fuchsbauer, Hanser and Slamanig (FHS) presented the first standard-model construction of efficient round-optimal blind signatures that does not require complexity leveraging. It is conceptually simple and builds on the primitive of structure-preserving signatures on equivalence classes (SPS-EQ). FHS prove the unforgeability of their scheme assuming EUF-CMA security of the SPS-EQ scheme and hardness of a version of the DH inversion problem. Blindness under adversarially chosen keys is proven under an interactive variant of the DDH assumption.
We propose a variant of their scheme whose blindness can be proven under a non-interactive assumption, namely a variant of the bilinear DDH assumption. We moreover prove its unforgeability assuming only unforgeability of the underlying SPS-EQ but no additional assumptions as needed for the FHS scheme.
C. Hanser—Supported by EU FP7 through project MATTHEW (GA No. 610436).
C. Kamath—Research supported by the European Research Council, ERC starting grant (259668-PSPC) and ERC consolidator grant (682815 - TOCNeT).
C. Hanser and D. Slamanig—Supported by EU Horizon 2020 through project Prismacloud (GA No. 644962).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
For BN-curves [9], the most common choice for Type-3 pairings, group generation is deterministic.
References
Abdalla, M., Namprempre, C., Neven, G.: On the (im)possibility of blind message authentication codes. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 262–279. Springer, Heidelberg (2006)
Abe, M.: A secure three-move blind signature scheme for polynomially many signatures. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 136–151. Springer, Heidelberg (2001)
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)
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)
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)
Abe, M., Groth, J., Ohkubo, M., Tibouchi, M.: Structure-preserving signatures from Type II pairings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 390–407. Springer, Heidelberg (2014)
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)
Abe, M., Haralambiev, K., Ohkubo, M.: Signing on elements in bilinear groups for modular protocol design. Cryptology ePrint Archive, Report 2010/133 (2010). http://eprint.iacr.org/2010/133
Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006)
Barthe, G., Fagerholm, E., Fiore, D., Scedrov, A., Schmidt, B., Tibouchi, M.: Strongly-optimal structure preserving signatures from Type II pairings: synthesis and lower bounds. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 355–376. Springer, Heidelberg (2015)
Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The one-more-RSA-inversion problems and the security of Chaum’s blind signature scheme. J. Cryptol. 16(3), 185–215 (2003)
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)
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)
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)
Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-Diffie-Hellman-group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)
Camenisch, J.L., Koprowski, M., Warinschi, B.: Efficient blind signatures without random oracles. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 134–148. Springer, Heidelberg (2005)
Chatterjee, S., Menezes, A.: On cryptographic protocols employing asymmetric pairings - the role of \(\psi \) revisited. Discret. Appl. Math. 159(13), 1311–1322 (2011)
Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) CRYPTO 1982, pp. 199–203. Plenum Press, New York (1982)
Chaum, D.: Blind signature system. In: Chaum, D. (ed.) CRYPTO 1983, p. 153. Plenum Press, New York (1984)
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)
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)
Fischlin, M., Schröder, D.: Security of blind signatures under aborts. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 297–316. Springer, Heidelberg (2009)
Fischlin, M., Schröder, D.: On the impossibility of three-move blind signature schemes. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 197–215. Springer, Heidelberg (2010)
Fuchsbauer, G.: Automorphic signatures in bilinear groups and an application to round-optimal blind signatures. Cryptology ePrint Archive, Report 2009/320 (2009). http://eprint.iacr.org/2009/320
Fuchsbauer, G., Hanser, C., Slamanig, D.: Structure-preserving signatures on equivalence classes and constant-size anonymous credentials. Cryptology ePrint Archive, Report 2014/944 (2014). http://eprint.iacr.org/2014/944
Fuchsbauer, G., Hanser, C., Slamanig, D.: Practical round-optimal blind signatures in the standard model. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 233–253. Springer, Heidelberg (2015)
Garg, S., Gupta, D.: Efficient round optimal blind signatures. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 477–495. Springer, Heidelberg (2014)
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)
Ghadafi, E.: Short structure-preserving signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 305–321. Springer, Heidelberg (2016)
Ghadafi, E., Smart, N.P.: Efficient two-move blind signatures in the common reference string model. In: Gollmann, D., Freiling, F.C. (eds.) ISC 2012. LNCS, vol. 7483, pp. 274–289. Springer, Heidelberg (2012)
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)
Hanser, C., Slamanig, D.: Structure-preserving signatures on equivalence classes and their application to anonymous credentials. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 491–511. Springer, Heidelberg (2014)
Hanzlik, L., Kluczniak, K.: A short paper on blind signatures from knowledge assumptions. FC 2016. LNCS. Springer, Heidelberg (2016)
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)
Joux, A.: A one round protocol for tripartite Diffie-hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000). http://dx.doi.org/10.1007/10722028_23
Juels, A., Luby, M., Ostrovsky, R.: Security of blind digital signatures. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997)
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)
Lindell, Y.: Bounded-concurrent secure two-party computation without setup assumptions. In: 35th ACM STOC, pp. 683–692. ACM Press, San Diego, 9–11 June 2003
Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993)
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)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 13(3), 361–396 (2000)
Schröder, D., Unruh, D.: Security of blind signatures revisited. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 662–679. Springer, Heidelberg (2012)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Fuchsbauer, G., Hanser, C., Kamath, C., Slamanig, D. (2016). Practical Round-Optimal Blind Signatures in the Standard Model from Weaker Assumptions. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-44618-9_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44617-2
Online ISBN: 978-3-319-44618-9
eBook Packages: Computer ScienceComputer Science (R0)