Abstract
The identity-based signature, initially introduced by Shamir [26], plays a fundamental role in the domain of identity-based cryptography. It offers the capability to generate a signature on a message, allowing any user to verify the authenticity of the signature using the signer’s identifier information (e.g., an email address), instead of relying on a public key stored in a digital certificate. Another significant concept in practical applications is the threshold signature, which serves as a valuable tool for distributing the signing authority. The notion of an identity-based threshold signature scheme pertains to the distribution of a secret key associated with a specific identity among multiple entities, rather than depending on a master secret key generated by a public key generator. This approach enables a qualified group of participants to jointly engage in the signing process. In this paper, we present two identity-based threshold signature schemes based on isogenies, each of which addresses a different aspect of security. The first scheme prioritizes efficiency but offers security with abort, while the second scheme focuses on robustness. Both schemes ensure active security in the quantum random oracle model. To build these identity-based threshold signatures, we begin by modifying the identity-based signature scheme proposed by Shaw and Dutta [27], to accommodate the CSI-SharK signature scheme. Subsequently, we leverage the resulting identity-based signature and build two threshold schemes within the CSIDH (Commutative Supersingular Isogeny Diffie-Hellman) framework. Our proposed identity-based threshold signatures are designed based on CSI-SharK and can be easily adapted with minimal adjustments to function with CSI-FiSh.
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
Atapoor, S.: Identity-based threshold signatures from isogenies. Cryptology ePrint Archive, Paper 2023/1459 (2023). https://eprint.iacr.org/2023/1459
Atapoor, S., Baghery, K., Cozzo, D., Pedersen, R.: CSI-SharK: CSI-FiSh with Sharing-friendly Keys. In: Simpson, L., Rezazadeh Baee, M.A. (eds.) Information Security and Privacy - 28th Australasian Conference, ACISP 2023, Brisbane, QLD, Australia, 5–7 July 2023, Proceedings. LNCS, vol. 13915, pp. 471–502. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-35486-1_21
Atapoor, S., Baghery, K., Cozzo, D., Pedersen, R.: VSS from distributed ZK proofs and applications. In: Guo, J., Steinfeld, R. (eds.) Advances in Cryptology - ASIACRYPT 2023–29th International Conference on the Theory and Application of Cryptology and Information Security, Guangzhou, China, 4–8 December 2023, Proceedings. LNCS. Springer, Cham (2023)
Baek, J., Zheng, Y.: Identity-based threshold signature scheme from the bilinear pairings. In: International Conference on Information Technology: Coding and Computing (ITCC 2004), Las Vegas, Nevada, USA, 5–7 April 2004, vol. 1, pp. 124–128. IEEE Computer Society (2004)
Baghery, K., Cozzo, D., Pedersen, R.: An isogeny-based ID protocol using structured public keys. In: Paterson, M.B. (ed.) IMACC 2021. LNCS, vol. 13129, pp. 179–197. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92641-0_9
Bellare, M., Namprempre, C., Neven, G.: Security proofs for identity-based identification and signature schemes. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 268–286. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_17
Bernstein, D., De Feo, L., Leroux, A., Smith, B.: Faster computation of isogenies of large prime degree. arXiv preprint arXiv:2003.10118 (2020)
Beullens, W., Disson, L., Pedersen, R., Vercauteren, F.: CSI-RAShi: distributed key generation for CSIDH. In: Cheon, J.H., Tillich, J.-P. (eds.) PQCrypto 2021 2021. LNCS, vol. 12841, pp. 257–276. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81293-5_14
Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 227–247. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_9
Bonnetain, X., Schrottenloher, A.: Quantum security analysis of CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 493–522. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_17
Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11274, pp. 395–427. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03332-3_15
Couveignes, J.M.: Hard homogeneous spaces. IACR Cryptology ePrint Archive 2006:291 (2006)
Cozzo, D., Smart, N.P.: Sashimi: cutting up CSI-FiSh secret keys to produce an actively secure distributed signing protocol. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 169–186. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_10
Crites, E.C., Komlo, C., Maller, M.: Fully adaptive Schnorr threshold signatures. In: Handschuh, H., Lysyanskaya, A. (eds.) Advances in Cryptology - CRYPTO 2023–43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, 20–24 August 2023, Proceedings, Part I. LNCS, vol. 14081, pp. 678–709. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-38557-5_22
De Feo, L.: Mathematics of isogeny based cryptography. arXiv preprint arXiv:1711.04062 (2017)
De Feo, L., Galbraith, S.D.: SeaSign: compact isogeny signatures from class group actions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 759–789. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_26
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
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust threshold DSS signatures. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 354–371. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_31
Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_20
Kiltz, E., Neven, G.: Identity-based signatures. In: Joye, M., Neven, G. (eds.) Identity-Based Cryptography. Cryptology and Information Security Series, vol. 2, pp. 31–44. IOS Press (2009)
Kitaev, A.Y.: Quantum measurements and the abelian stabilizer problem. Electronic Colloquium on Computational Complexity, TR96-003 (1996)
Kurosawa, K., Heng, S.-H.: From digital signature to ID-based identification/signature. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 248–261. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24632-9_18
Peikert, C.: He gives C-sieves on the CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 463–492. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_16
Peng, C., Chen, J., Zhou, L., Choo, K.-K.R., He, D.: CsiiBS: a post-quantum identity-based signature scheme based on isogenies. J. Inf. Secur. Appl. 54, 102504 (2020)
Rostovtsev, A., Stolbunov, A.: Public-key cryptosystem based on isogenies. IACR Cryptology ePrint Archive, 2006:145 (2006)
Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5
Shaw, S., Dutta, R.: Identification scheme and forward-secure signature in identity-based setting from isogenies. In: Huang, Q., Yu, Yu. (eds.) ProvSec 2021. LNCS, vol. 13059, pp. 309–326. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90402-9_17
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)
Silverman, J.H.: The Arithmetic of Elliptic Curves. GTM, vol. 106. Springer, New York (2009). https://doi.org/10.1007/978-0-387-09494-6
Stolbunov, A.: Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Adv. Math. Commun. 4(2), 215 (2010)
Vélu, J.: Isogénies entre courbes elliptiques. CR Acad. Sci. Paris, Séries A 273, 305–347 (1971)
Acknowledgments
We thank the anonymous reviewers for their valuable comments and suggestions. We would also like to extend our special thanks to Elizabeth Crites for shepherding the final version of the paper and her insightful and valuable comments. Additionally, we would like to acknowledge Karim Baghery for his helpful discussions during the initial phases of the paper.
This work has been supported in part by the FWO under an Odysseus project GOH9718N and by CyberSecurity Research Flanders with reference number VR20192203. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Cyber Security Research Flanders or the FWO.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Atapoor, S. (2024). Identity-Based Threshold Signatures from Isogenies. In: Quaglia, E.A. (eds) Cryptography and Coding. IMACC 2023. Lecture Notes in Computer Science, vol 14421. Springer, Cham. https://doi.org/10.1007/978-3-031-47818-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-47818-5_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-47817-8
Online ISBN: 978-3-031-47818-5
eBook Packages: Computer ScienceComputer Science (R0)