Abstract
A blind ring signature scheme is a combination of a ring signature and a blind signature, which allows not only any member of a group of signers to sign on a message on behalf of the group without revealing its identity but also the user who possesses the message to blind it before sending to the group to be signed. Blind ring signature schemes are essential components in e-commercial, e-voting etc. In this paper, we propose the first blind ring signature scheme based on lattices. More precisely, our proposed scheme is proven to be secure in random oracle model under the hardness of the short integer solution (SIS) problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguilar-Melchor, C., Bettaieb, S., Boyen, X., Fousse, L., Gaborit, P.: Adapting Lyubashevsky’s Signature Schemes to the Ring Signature Setting. Cryptology ePrint Archive, Report 2013/281 (2013). https://eprint.iacr.org/2013/281
Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 99–108. ACM, New York (1996). http://doi.acm.org/10.1145/237814.237838
Bellare, M., Neven, G.: New Multi-Signature Schemes and a General Forking Lemma. http://soc1024.ece.illinois.edu/teaching/ece498ac/fall2018/forkinglemma.pdf
Buchmann, J., Ding, J. (eds.): PQCrypto 2008. LNCS, vol. 5299, 1st edn. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88403-3
Bresson, E., Stern, J., Szydlo, M.: Threshold ring signatures and applications to ad-hoc groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 465–480. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_30
Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology, pp. 199–203. Springer, Boston, MA (1983). https://doi.org/10.1007/978-1-4757-0602-4_18
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, STOC 2008, pp. 197–206. ACM, New York (2008). http://doi.acm.org/10.1145/1374376.1374407
Ghadafi, E.M.: Sub-linear blind ring signatures without random oracles. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 304–323. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-45239-0_18
Guo, F., Susilo, W., Mu, Y.: Foundations of security reduction. Introduction to Security Reduction, pp. 29–146. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93049-7_4
Halevi, S., Micali, S.: Practical and provably-secure commitment schemes from collision-free hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68697-5_16
Herranz, J., Laguillaumie, F.: Blind ring signatures secure under the chosen-target-CDH assumption. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds.) ISC 2006. LNCS, vol. 4176, pp. 117–130. Springer, Heidelberg (2006). https://doi.org/10.1007/11836810_9
Kawachi, A., Tanaka, K., Xagawa, K.: Concurrently secure identification schemes based on the worst-case hardness of lattice problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 372–389. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_23
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. Cryptology ePrint Archive, Report 2011/537, Full version of paper appearing at Eurocrypt 2012 (2012). https://eprint.iacr.org/2011/537. Accessed 18 Oct 2017
Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: A Cryptographic Perspective. The Kluwer International Series in Engineering and Computer Science, vol. 671. Kluwer Academic Publishers, Boston (2002)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007). https://doi.org/10.1137/S0097539705447360
Peikert, C.: A decade of lattice cryptography. Found. Trends Theor. Comput. Sci. 10(4), 283–424 (2016). https://doi.org/10.1561/0400000074
Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_32
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
van Saberhagen, N.: Cryptonote v 2.0 (2013). https://cryptonote.org/whitepaper.pdf
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134, November 1994. https://doi.org/10.1109/SFCS.1994.365700
Susilo, W., Mu, Y.: Non-interactive deniable ring authentication. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 386–401. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24691-6_29
Susilo, W., Mu, Y., Zhang, F.: Perfect concurrent signature schemes. In: Lopez, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 14–26. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30191-2_2
Wang, S., Zhao, R., Zhang, Y.: Lattice-based ring signature scheme under the random oracle model. Int. J. High Perform. Comput. Netw. 11(4), 332–341 (2018). https://doi.org/10.1504/IJHPCN.2018.093236
Wu, Q., Zhang, F., Susilo, W., Mu, Y.: An efficient static blind ring signature scheme. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 410–423. Springer, Heidelberg (2006). https://doi.org/10.1007/11734727_32
Zhang, P., Jiang, H., Zheng, Z., Hu, P., Xu, Q.: A new post-quantum blind signature from lattice assumptions. IEEE Access 6, 27251–27258 (2018). https://doi.org/10.1109/ACCESS.2018.2833103
Acknowledgment
The first author would like to thank Prof. Masaya Yasuda for his financial support. The authors would like to thank anonymous reviewers for their helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Le, H.Q., Duong, D.H., Susilo, W. (2020). A Blind Ring Signature Based on the Short Integer Solution Problem. In: You, I. (eds) Information Security Applications. WISA 2019. Lecture Notes in Computer Science(), vol 11897. Springer, Cham. https://doi.org/10.1007/978-3-030-39303-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-39303-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39302-1
Online ISBN: 978-3-030-39303-8
eBook Packages: Computer ScienceComputer Science (R0)