Abstract
An aggregate signature (ASIG) scheme allows any user to compress multiple signatures into a short signature called an aggregate signature. While a conventional ASIG scheme cannot detect any invalid messages from an aggregate signature, an ASIG scheme with detecting functionality (D-ASIG) has an additional property which can identify invalid messages from aggregate signatures. Hence, D-ASIG is useful to reduce the total amount of signature-sizes on a channel. On the other hand, development of quantum computers has been advanced recently. However, all existing D-ASIG schemes are insecure against attacks using quantum algorithms, which we call quantum attacks. In this paper, we propose a D-ASIG scheme with quantum-security which means security in a quantum setting. Hence, we first introduce quantum-security notions of ASIGs and D-ASIGs because there is no research on such security notions for (D-)ASIGs. Second, we propose a lattice-based aggregate one-time signature scheme with detecting functionality, and prove that this scheme satisfies our quantum-security in the quantum random oracle model and the certified key model. Hence, this scheme is the first quantum-secure D-ASIG.
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
Similar content being viewed by others
References
Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_26
Boneh, D., Kim, S.: One-time and interactive aggregate signatures from lattices (2020). https://crypto.stanford.edu/~skim13/agg_ots.pdf
Boneh, D., Zhandry, M.: Secure signatures and chosen ciphertext security in a quantum computing world. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 361–379. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_21
Du, D.Z., Hwang, F.K.: Combinatorial Group Testing and Its Applications, 2nd edn. Series on Applied Mathematics, vol. 12. World Scientific (2000)
Hartung, G., Kaidel, B., Koch, A., Koch, J., Rupp, A.: Fault-tolerant aggregate signatures. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 331–356. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_13
Hohenberger, S., Sahai, A., Waters, B.: Full domain hash from (leveled) multilinear maps and identity-based aggregate signatures. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 494–512. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_27
Ishii, R., et al.: Aggregate signature with traceability of devices dynamically generating invalid signatures. In: Zhou, J., et al. (eds.) ACNS 2021. LNCS, vol. 12809, pp. 378–396. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81645-2_22
Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential aggregate signatures, multisignatures, and verifiably encrypted signatures without random oracles. J. Cryptol. 26(2), 340–373 (2013)
Lyubashevsky, V., Micciancio, D.: Asymptotically efficient lattice-based digital signatures. J. Cryptol. 31(3), 774–797 (2018)
Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: ACM Conference on Computer and Communications Security, pp. 2111–2128. ACM (2019)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)
Rückert, M., Schröder, D.: Aggregate and verifiably encrypted signatures from multilinear maps without random oracles. In: Park, J.H., Chen, H.-H., Atiquzzaman, M., Lee, C., Kim, T., Yeo, S.-S. (eds.) ISA 2009. LNCS, vol. 5576, pp. 750–759. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02617-1_76
Sato, S., Shikata, J., Matsumoto, T.: Aggregate signature with detecting functionality from group testing. IACR Cryptol. ePrint Arch., 1219 (2020)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Acknowledgement
This research was conducted under a contract of “Research and development on new generation cryptography for secure wireless communication services” among “Research and Development for Expansion of Radio Wave Resources (JPJ000254)”, which was supported by the Ministry of Internal Affairs and Communications, Japan.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Sato, S., Shikata, J. (2022). Quantum-Secure Aggregate One-time Signatures with Detecting Functionality. In: Barolli, L., Hussain, F., Enokido, T. (eds) Advanced Information Networking and Applications. AINA 2022. Lecture Notes in Networks and Systems, vol 450. Springer, Cham. https://doi.org/10.1007/978-3-030-99587-4_49
Download citation
DOI: https://doi.org/10.1007/978-3-030-99587-4_49
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-99586-7
Online ISBN: 978-3-030-99587-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)