Abstract
In this paper, we construct the first tightly secure signature scheme against adaptive chosen message attacks (CMA) from the Decisional Composite Residuosity (DCR) Assumption. Moreover, the verification key in our scheme is of constant size. Based on the DCR assumption, we design a one-time secure signature scheme first, then we employ a flat tree structure to obtain a signature scheme that is secure against non-adaptive chosen message attacks (NCMA). By combining the one-time scheme and NCMA-secure scheme, we obtain the final CMA-secure signature scheme with a tight security reduction to the DCR assumption.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Since the q leaves are the leftmost ones, \(N_{i+1}^{(j)\text {left}}\) has already been determined.
References
Blazy, O., Kakvi, S.A., Kiltz, E., Pan, J.: Tightly-secure signatures from chameleon hash functions. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 256–279. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46447-2_12
Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) Identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 408–425. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44371-2_23
Boneh, D., Mironov, I., Shoup, V.: A secure signature scheme from bilinear maps. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 98–110. Springer, Heidelberg (2003). doi:10.1007/3-540-36563-X_7
Cramer, R., Damgård, I.: New generation of secure and practical RSA-based signatures. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 173–185. Springer, Heidelberg (1996). doi:10.1007/3-540-68697-5_14
Catalano, D., Gennaro, R.: Cramer-Damgård signatures revisited: efficient flat-tree signatures based on factoring. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 313–327. Springer, Heidelberg (2005). doi:10.1007/978-3-540-30580-4_22
Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 435–460. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40084-1_25
Damgård, I., Jurik, M.: A generalisation, a simplication and some applications of Paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001). doi:10.1007/3-540-44586-2_9
Even, S., Goldreich, O., Micali, S.: On-Line/Off-Line digital signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 263–275. Springer, New York (1990). doi:10.1007/0-387-34805-0_24
Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)
Goldreich, O.: Two remarks concerning the Goldwasser-Micali-Rivest signature scheme. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 104–110. Springer, Heidelberg (1987). doi:10.1007/3-540-47721-7_8
Hofheinz, D., Jager, T.: Tightly secure signatures and public-key encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 590–607. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32009-5_35
Hofheinz, D., Jager, T., Kiltz, E.: Short signatures from weaker assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 647–666. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25385-0_35
Hofheinz, D.: Adaptive partitioning. IACR Cryptology ePrint Archive 2016, 373 (2016)
Hofheinz, D.: Algebraic partitioning: fully compact and (almost) tightly secure cryptography. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 251–281. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49096-9_11
Hohenberger, S., Waters, B.: Realizing hash-and-sign signatures under standard assumptions. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 333–350. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01001-9_19
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). doi:10.1007/978-3-642-29011-4_41
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). doi:10.1007/3-540-48910-X_16
Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 387–394. ACM (1990)
Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). doi:10.1007/11426639_7
Acknowledgments
The authors are supported by the National Natural Science Foundation of China Grant (Nos. 61672346, 61373153, 61472250). We thank the anonymous reviewers for their comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Zhang, X., Liu, S., Gu, D. (2017). Tightly-Secure Signatures from the Decisional Composite Residuosity Assumption. In: Pieprzyk, J., Suriadi, S. (eds) Information Security and Privacy. ACISP 2017. Lecture Notes in Computer Science(), vol 10342. Springer, Cham. https://doi.org/10.1007/978-3-319-60055-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-60055-0_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60054-3
Online ISBN: 978-3-319-60055-0
eBook Packages: Computer ScienceComputer Science (R0)