Abstract
An OR-proof is a protocol that enables a user to prove the possession of a witness for one of two (or more) statements, without revealing which one. Abe and Okamoto (CRYPTO 2000) used this technique to build a partially blind signature scheme whose security is based on the hardness of the discrete logarithm problem. Inspired by their approach, we present 
, an efficient blind signature scheme from OR-proofs based on lattices over modules. Using OR-proofs allows us to reduce the security of our scheme from the \(\mathsf {MLWE}\) and \(\mathsf {MSIS}\) problems, yielding a much more efficient solution compared to previous works.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abe, M., Okamoto, T.: Provably secure partially blind signatures. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 271–286. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_17
Agrawal, S., Yadav, A.L.: Towards practical and round-optimal lattice-based threshold and blind signatures. Cryptology ePrint Archive, Report 2021/381
Alkeilani Alkadri, N., El Bansarkhani, R., Buchmann, J.: BLAZE: practical lattice-based blind signatures for privacy-preserving applications. In: Bonneau, J., Heninger, N. (eds.) FC 2020. LNCS, vol. 12059, pp. 484–502. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51280-4_26
Alkeilani Alkadri, N., El Bansarkhani, R., Buchmann, J.: On lattice-based interactive protocols: an approach with less or no aborts. In: Liu, J.K., Cui, H. (eds.) ACISP 2020. LNCS, vol. 12248, pp. 41–61. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55304-3_3
Alkeilani Alkadri, N., Harasser, P., Janson, C.: BlindOR: an efficient lattice-based blind signature scheme from or-proofs. Cryptology ePrint Archive, Report 2021/1385
Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: ACM CCS 2006
Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: ACM CCS 93
Camenisch, J., Neven, G., Shelat: Simulatable adaptive oblivious transfer. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 573–590. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_33
Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology. LNCS, pp. 199–203. Springer, Boston, MA (1983). https://doi.org/10.1007/978-1-4757-0602-4_18
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_19
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). https://doi.org/10.1007/11818175_4
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). https://doi.org/10.1007/978-3-642-00468-1_17
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). https://doi.org/10.1007/978-3-642-22792-9_36
Hauck, E., Kiltz, E., Loss, J.: A modular treatment of blind signatures from identification schemes. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 345–375. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_12
Rückert, M.: Lattice-based blind signatures. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 413–430. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_24
Juels, A., Luby, M., Ostrovsky, R.: Security of blind digital signatures (extended abstract). In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052233
Lyubashevsky, V.: Fiat-shamir with aborts: applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598–616. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_35
Lyubashevsky, V.: Lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_43
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptology 13(3), 361–396 (2000)
Rückert, M.: Lattice-based blind signatures. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 413–430. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_24
Schröder, D., Unruh, D.: Security of blind signatures revisited. J. Cryptology, 30(2), 470–494 (2017)
Acknowledgments
We thank Marc Fischlin for helpful discussions. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1119 – 236615297.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Alkeilani Alkadri, N., Harasser, P., Janson, C. (2021). BlindOR: an Efficient Lattice-Based Blind Signature Scheme from OR-Proofs. In: Conti, M., Stevens, M., Krenn, S. (eds) Cryptology and Network Security. CANS 2021. Lecture Notes in Computer Science(), vol 13099. Springer, Cham. https://doi.org/10.1007/978-3-030-92548-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-92548-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-92547-5
Online ISBN: 978-3-030-92548-2
eBook Packages: Computer ScienceComputer Science (R0)