Abstract
In this paper, we revisit Paillier’s trapdoor one-way function [15], focusing on the computational problem underlying its one-wayness. We formulate a new computational problem that we call one-more Paillier inversion problem. It is a natural extension of Paillier inversion problem to the setting where adversaries have access to an inversion oracle and a challenge oracle. We study the relation between the proposed problem and the one-more RSA inversion problem introduced by Bellare et al. in [2]; we prove that the one-more Paillier inversion problem is hard if and only if the one-more RSA inversion problem is hard. Then we propose a new identification scheme; we show the assumed hardness of the one-more Paillier inversion problem leads to a proof that the proposed identification scheme achieves security against concurrent impersonation attack. Compared with the known RSA-related identification schemes, the proposed identification scheme is only slightly inefficient than the best known GQ scheme, but is more efficient than Okamoto’s.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The one-more-RSA inversion problems and the security of Chaum’s blind signature scheme. Journal of Cryptology 16(3), 185–215 (2003)
Bellare, M., Palacio, A.: GQ and Schnorr identification Schemes: proofs of security against impersonation under active and concurrent attack. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 162–177. Springer, Heidelberg (2002)
Catalano, D., Gennaro, R., Howgrave-Graham, N., Nguyen, P.Q.: Paillier’s cryptosystem revisited. In: Proceedings of the 8th ACM conference on Computer and Communications Security, pp. 206–214. ACM Press, New York (2001)
Cohen, J.D., Fischer, M.: A robust and verifiable cryptographically secure election scheme. In: Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science 1985, pp. 372–382 (1985)
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)
Damgård, I., Jurik, M.: A generalisation, a simplification 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)
Feige, U., Fiat, A., Shamir, A.: Zero knowledge proofs of identity. Journal of Cryptology 1(2), 77–94 (1988)
Galbraith, S.D.: Elliptic curve Paillier schemes. Journal of Cryptology 15(2), 129–138 (2002)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)
Guillou, L., Quisquater, J.: A practical zero-knowledge protocol fitted to security microprocesors minimizing both transmission and memory. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988)
Naccache, D., Stern, J.: A new public key cryptosystem based on higher residues. In: Proceedings of 5th Symposium on Computer and Communications Security, pp. 59–66. ACM Press, New York (1998)
Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993)
Okamoto, T., Uchiyama, S.: A new public-key cryptosystem as secure as factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Song, Y. (2007). One-More Extension of Paillier Inversion Problem and Concurrent Secure Identification. In: Lopez, J., Samarati, P., Ferrer, J.L. (eds) Public Key Infrastructure. EuroPKI 2007. Lecture Notes in Computer Science, vol 4582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73408-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-73408-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73407-9
Online ISBN: 978-3-540-73408-6
eBook Packages: Computer ScienceComputer Science (R0)