Abstract
It is a challenging task to construct a signature that it can be tightly reduced to a weak security assumption in the standard model. In this paper, we introduce a simple chameleon-hash-based transformation and show that it can tighten a security reduction of a signature scheme that suffers from a loose security reduction. Taking the Waters’ signature from Eurocrypt 2005 as an example, we demonstrate an improvement of the security reduction that the probability of success in the security reduction can be made as a constant and independent of the signature queries from an adversary. Our reduction methodology has never been considered in the literature and is applicable to many signature schemes such as identity-based signature schemes, online/offline signatures, and signatures with strong unforeability.
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Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Boneh, D., Shen, E., Waters, B.: Strongly unforgeable signatures based on computational diffie-hellman. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 229–240. Springer, Heidelberg (2006)
Cheon, J.H.: Security analysis of the strong diffie-hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006)
Camenisch, J.L., Hohenberger, S., Pedersen, M.: Batch verification of short signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007)
Camenisch, J.L., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)
Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Trans. on Information and System Security 3(3), 161–185 (2000)
Chen, X., Zhang, F., Susilo, W., Mu, Y.: Efficient generic online/offline signatures without key exposure. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 18–30. Springer, Heidelberg (2007)
Even, S., Goldreich, O., Micali, S.: Online/offline digital signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 263–275. Springer, Heidelberg (1990)
Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)
Gennaro, R., Halevi, S., Rabin, T.: Secure hash-and-sign signatures without the random oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)
Goh, E.J., Jarecki, S.: A signature scheme as secure as the Diffie- Hellman problem. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 401–415. Springer, Heidelberg (2003)
Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)
Horwitz, J., Lynn, B.: Toward hierarchical identity-based encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466–481. Springer, Heidelberg (2002)
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)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: Symposium on Network and Distributed Systems Security (NDSS 2000), February 2000, pp. 143–154. Internet Society (2000)
Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: 10th ACM Conf. on Computer and Communications Security, pp. 155–164 (2003)
Paterson, K., Schuldt, J.: Efficient identity-based signatures secure in the standard model. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 207–222. Springer, Heidelberg (2006)
Shamir, A., Tauman, Y.: Improved online/offline signature schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001)
Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
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Guo, F., Mu, Y., Susilo, W. (2009). How to Prove Security of a Signature with a Tighter Security Reduction. In: Pieprzyk, J., Zhang, F. (eds) Provable Security. ProvSec 2009. Lecture Notes in Computer Science, vol 5848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04642-1_9
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DOI: https://doi.org/10.1007/978-3-642-04642-1_9
Publisher Name: Springer, Berlin, Heidelberg
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