Abstract
Blind signatures constitute basic cryptographic ingredients for privacy-preserving applications such as anonymous credentials, e-voting, and Bitcoin. Despite the great variety of cryptographic applications blind signatures also found their way in real-world scenarios. Due to the expected progress in cryptanalysis using quantum computers, it remains an important research question to find practical and secure alternatives to current systems based on the hardness of classical security assumptions such as factoring and computing discrete logarithms. In this work we present BLAZE: a new practical blind signature scheme from lattice assumptions. With respect to all relevant efficiency metrics BLAZE is more efficient than all previous blind signature schemes based on assumptions conjectured to withstand quantum computer attacks. For instance, at approximately 128 bits of security signatures are as small as 6.6 KB, which represents an improvement factor of 2.7 compared to all previous candidates, and an expansion factor of 2.5 compared to the NIST PQC submission \(\textsf {Dilithium}\). Our software implementation demonstrates the efficiency of BLAZE to be deployed in practical applications. In particular, generating a blind signature takes just 18 ms. The running time of both key generation and verification is in the same order as state-of-the-art ordinary signature schemes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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). https://doi.org/10.1007/11605805_17
Albrecht, M., Player, R., Scott, S.: On the concrete hardness of learning with errors. J. Math. Cryptol. 9(3), 169–203 (2015). https://bitbucket.org/malb/lwe-estimator/src
Alkeilani Alkadri, N., Buchmann, J., El Bansarkhani, R., Krämer, J.: A framework to select parameters for lattice-based cryptography. Cryptology ePrint Archive, Report 2017/615 (2017). http://eprint.iacr.org/2017/615
Alkeilani Alkadri, N., El Bansarkhani, R., Buchmann, J.: BLAZE: Practical lattice-based blind signatures for privacy-preserving applications. Cryptology ePrint Archive, Report 2019/1167 (2019). http://eprint.iacr.org/2019/1167, Full version of this paper
Bai, S., Galbraith, S.D.: An improved compression technique for signatures based on learning with errors. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 28–47. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04852-9_2
Baldimtsi, F., Lysyanskaya, A.: Anonymous credentials light. In: ACM Conference on Computer and Communications Security - CCS 13, pp. 1087–1098. ACM (2013)
Becker, A., Ducas, L., Gama, N., Laarhoven, T.: New directions in nearest neighbor searching with applications to lattice sieving. In: ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, pp. 10–24. SIAM (2016)
Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: ACM Conference on Computer and Communications Security, pp. 390–399. ACM (2006)
Blazy, O., Gaborit, P., Schrek, J., Sendrier, N.: A code-based blind signature. In: IEEE International Symposium on Information Theory, ISIT 2017, pp. 2718–2722. IEEE (2017)
Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_1
Camenisch, J., Neven, G., Shelat, A.: 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. Adv. Cryptol.-CRYPTO 82, 199–203 (1982)
Chen, L., Cui, Y., Tang, X., Hu, D., Wan, X.: Hierarchical id-based blind signature from lattices. In: International Conference on Computational Intelligence and Security, CIS 2011, pp. 803–807. IEEE Computer Society (2011)
Chen, Y.: Réduction de réseau et sécurité concrete du chiffrement completement homomorphe. Ph.D. thesis, ENS-Lyon, France (2013)
Chen, Y., Nguyen, P.Q.: BKZ 2.0: Better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_1
HASNC Coordinator: National strategy for trusted identities in cyberspace. Cyberwar Resources Guide, Item #163 (2010), http://www.projectcyw-d.org/resources/items/show/163, Accessed 11 Sep 2019
Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schwabe, P., Seiler, G., Stehlé, D.: CRYSTALS-Dilithium: a lattice-based digital signature scheme. Trans. Crypt. Hardw. Embed. Syst. - TCHES 2018(1), 238–268 (2018)
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
Gao, W., Hu, Y., Wang, B., Xie, J.: Identity-based blind signature from lattices in standard model. In: Chen, K., Lin, D., Yung, M. (eds.) Inscrypt 2016. LNCS, vol. 10143, pp. 205–218. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54705-3_13
Gao, W., Hu, Y., Wang, B., Xie, J., Liu, M.: Identity-based blind signature from lattices. Wuhan Univ. J. Nat. Sci. 22(4), 355–360 (2017). https://doi.org/10.1007/s11859-017-1258-x
Gemalto: Integration of gemalto’s smart card security with microsoft u-prove (2011). https://www.securetechalliance.org/gemalto-integrates-smart-card-security-with-microsoft-u-prove. Accessed 11 Sep 2019
Heilman, E., Baldimtsi, F., Goldberg, S.: Blindly signed contracts: anonymous on-blockchain and off-blockchain bitcoin transactions. In: Clark, J., Meiklejohn, S., Ryan, P.Y.A., Wallach, D., Brenner, M., Rohloff, K. (eds.) FC 2016. LNCS, vol. 9604, pp. 43–60. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53357-4_4
Juels, A., Luby, M., Ostrovsky, R.: Security of blind digital signatures. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052233
Kiltz, E., Lyubashevsky, V., Schaffner, C.: A concrete treatment of Fiat-Shamir signatures in the quantum random-oracle model. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 552–586. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_18
Kumar, M., Katti, C.P., Saxena, P.C.: A secure anonymous e-voting system using identity-based blind signature scheme. In: Shyamasundar, R.K., Singh, V., Vaidya, J. (eds.) ICISS 2017. LNCS, vol. 10717, pp. 29–49. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72598-7_3
Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. Des. Codes Crypt. 75(3), 565–599 (2014). https://doi.org/10.1007/s10623-014-9938-4
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
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1
Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41
Microsoft: Microsoft’s open specification promise (2007). https://docs.microsoft.com/en-us/openspecs/dev_center/ms-devcentlp/1c24c7c8-28b0-4ce1-a47d-95fe1ff504bc. Accessed 11 Sept 2019
Paquin, C.: U-Prove technology overview v1.1 (revision 2) (2013). https://www.microsoft.com/en-us/research/publication/u-prove-technology-overview-v1-1-revision-2/
European Parliament Council of the European Union: Regulation (ec) no 45/2001. Official Journal of the European Union (2001)
European Parliament of the Council European Union: Directive 2009/136/ec. Official Journal of the European Union (2009)
Petzoldt, A., Szepieniec, A., Mohamed, M.S.E.: A practical multivariate blind signature scheme. In: Kiayias, A. (ed.) FC 2017. LNCS, vol. 10322, pp. 437–454. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70972-7_25
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 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. Cryptol. 30(2), 470–494 (2017)
Zhang, L., Ma, Y.: A lattice-based identity-based proxy blind signature scheme in the standard model. Math. Probl. Eng. 2014 (2014)
Zhang, Y., Hu, Y.: Forward-secure identity-based shorter blind signature from lattices. Am. J. Netw. Commun. 5(2), 17–26 (2016)
Zhu, H., Tan, Y., Zhang, X., Zhu, L., Zhang, C., Zheng, J.: A round-optimal lattice-based blind signature scheme for cloud services. Future Gener. Comput. Syst. 73, 106–114 (2017)
Acknowledgements
The authors are grateful to the anonymous reviewers of FC20 for their comments and suggestions. This work has been partially supported by the German Research Foundation (DFG) as part of project P1 within the CRC 1119 CROSSING.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 International Financial Cryptography Association
About this paper
Cite this paper
Alkeilani Alkadri, N., El Bansarkhani, R., Buchmann, J. (2020). BLAZE: Practical Lattice-Based Blind Signatures for Privacy-Preserving Applications. In: Bonneau, J., Heninger, N. (eds) Financial Cryptography and Data Security. FC 2020. Lecture Notes in Computer Science(), vol 12059. Springer, Cham. https://doi.org/10.1007/978-3-030-51280-4_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-51280-4_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-51279-8
Online ISBN: 978-3-030-51280-4
eBook Packages: Computer ScienceComputer Science (R0)