Abstract
We present the currently simplest, most efficient, optimally resilient, adaptively secure, and proactive threshold RSA scheme. A main technical contribution is a new rewinding strategy for analysing threshold signature schemes. This new rewinding strategy allows to prove adaptive security of a proactive threshold signature scheme which was previously assumed to be only statically secure. As a separate contribution we prove that our protocol is secure in the UC framework.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-34547-3_36
Chapter PDF
Similar content being viewed by others
References
Almansa, J.F.: A Study for Cryptologic Protocols. PhD thesis, BRICS, University of Aarhus, Department of Computer Science, IT-parken, Aabogade 34, DK-8200 Århus N, Denmark (2005)
Boyd, C. (ed.): Digital multisignatures. In: Cryptography and Coding. Oxford University Press, Oxford, pp. 241–246 (1989)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. Cryptology ePrint Archive
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science. In: FOCS 2001, p. 136 (2001)
Canetti, R.: Universally composable signature, certification, and authentication (Cryptology ePrint Archive) (August 2004). Corrected version of the paper in: Proceedings of the 17th IEEE Computer Security Foundations Workshop, pp. 219–235 (2004)
Canetti, R., Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Adaptive security for threshold cryptosystems. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 98–115. Springer, Heidelberg (1999)
Desmedt, Y.: Society and group oriented cryptography: A new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988)
Damgård, I., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)
Fujisaki, E., Damgård, I.: A statistically-hiding integer commitment scheme based on groups with hidden order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125–142. Springer, Heidelberg (2002)
Frankel, Y., Gemmell, P., Mackenzie, P., Yung, M.: Optimal resilience proactive public-key cryptosystems. In: Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, FOCS 1997, p. 384 (1997)
Frankel, Y., Gemmell, P., Mackenzie, P., Yung, M.: Proactive RSA. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 440–454. Springer, Heidelberg (1997)
Frankel, Y., Gemmell, P., Yung, M.: Witness-based cryptographic program and robust function sharing. In: 28th Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 499–508 (1996)
Frankel, Y., MacKenzie, P.D., Yung, M.: Adaptive security for the additive-sharing based proactive RSA. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 240–263. Springer, Heidelberg (2001)
Frankel, Y.: A practical protocol for large group oriented networks. In: McCurley, K.S., Ziegler, C.D. (eds.) Advances in Cryptology 1981 - 1997. LNCS, vol. 1440, pp. 56–61. Springer, Heidelberg (1999)
Gennaro, R., Jarecki, S., Krawczyk, H.: Robust and efficient sharing of RSA functions. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 157–172. Springer, Heidelberg (1996)
Jakobsson, M., Jarecki, S., Krawczyk, H., Yung, M.: proactive RSA for constant-size thresholds (unpublished manuscript, 1995)
Jarecki, S., Saxena, N.: Further simplifications in proactive RSA signature schemes. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 510–528. Springer, Heidelberg (2005)
Nielsen, J.B.: On Protocol Security in the Cryptographic Model. PhD thesis, BRICS, University of Aarhus, Department of Computer Science, IT-parken, Aabogade 34, DK-8200 Århus N, Denmark (2004)
Ostrovsky, R., Yung, M.: How to withstand mobile virus attack. In: Proceedings of the 10th ACM Symposium on Principles of Distributed Computing, PODC 1991, pp. 51–59 (1991)
Rabin, T.: A simplified approach to threshold and proactive RSA. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 89–104. Springer, Heidelberg (1998)
Santis, A.D., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: 26th Annual ACM Symposium on Theory of Computing, STOC 1994, pp. 522–533 (1994)
Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Almansa, J.F., Damgård, I., Nielsen, J.B. (2006). Simplified Threshold RSA with Adaptive and Proactive Security. In: Vaudenay, S. (eds) Advances in Cryptology - EUROCRYPT 2006. EUROCRYPT 2006. Lecture Notes in Computer Science, vol 4004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11761679_35
Download citation
DOI: https://doi.org/10.1007/11761679_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34546-6
Online ISBN: 978-3-540-34547-3
eBook Packages: Computer ScienceComputer Science (R0)