Abstract
In this paper, we give a first example of identity based undeniable signature using pairings over elliptic curves. We extend to the identity based setting the security model for the notions of invisibility and anonymity given by Galbraith and Mao in 2003 and we prove that our scheme is existentially unforgeable under the Bilinear Diffie-Hellman assumption in the random oracle model. We also prove that it has the invisibility property under the Decisional Bilinear Diffie-Hellman assumption and we discuss about the efficiency of the scheme.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Al-Riyami, S.-S., Paterson, K.G.: Certificateless Public Key Cryptography. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 452–473. Springer, Heidelberg (2003)
Barreto, P.-S.-L.-M., Kim, H.-Y.: Fast hashing onto elliptic curves over fields of characteristic 3, eprint available at http://eprint.iacr.org/2001/098/
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Proc. of the 1st ACM Conference on Computer and Communications Security, pp. 62–73 (1993)
Boneh, D., Franklin, M.: Identity Based Encryption From the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)
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)
Boyar, J., Chaum, D., Damgård, I., Pedersen, T.: Convertible undeniable signatures. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 189–208. Springer, Heidelberg (1991)
Boyen, X.: Multipurpose Identity-Based Signcryption. A Swiss Army Knife for Identity-Based Cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 383–399. Springer, Heidelberg (2003)
Camenisch, J., Shoup, V.: Practical Verifiable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)
Cha, J.C., Cheon, J.H.: An Identity-Based Signature from Gap Diffie-Hellman Groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)
Chaum, D., van Antwerpen, H.: Undeniable signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 212–216. Springer, Heidelberg (1990)
Chaum, D.: Zero-knowledge undeniable signatures. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 458–464. Springer, Heidelberg (1991)
Chaum, D., van Heijst, E., Pfitzmann, B.: Cryptographically strong undeniable signatures, unconditionally secure for the signer. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 470–484. Springer, Heidelberg (1992)
Cheon, J.H., Lee, D.H.: Diffie-Hellman Problems and Bilinear Maps, eprint available at http://eprint.iacr.org/2002/117/
Cocks, C.: An Identity Based Encryption Scheme Based on Quadratic Residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)
Dupont, R., Enge, A.: Practical Non-Interactive Key Distribution Based on Pairings, available at http://eprint.iacr.org/2002/136
Damgård, I.B., Pedersen, T.P.: New convertible undeniable signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 372–386. Springer, Heidelberg (1996)
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)
Fujioka, A., Okamoto, T., Ohta, K.: Interactive Bi-Proof Systems and undeniable signature schemes. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 243–256. Springer, Heidelberg (1991)
Galbraith, S., Mao, W., Paterson, K.G.: RSA-based undeniable signatures for general moduli. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 200–217. Springer, Heidelberg (2002)
Galbraith, S., Mao, W.: Invisibility and Anonymity of Undeniable and Confirmer Signatures. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 80–97. Springer, Heidelberg (2003)
Gennaro, R., Krawczyk, H., Rabin, T.: RSA-based undeniable signatures. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 132–149. Springer, Heidelberg (1997)
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)
Guillou, L., Quisquater, J.-J.: A “Paradoxical” Identity-Based Signature Scheme Resulting From Zero-Knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 216–231. Springer, Heidelberg (1990)
Han, S., Yeung, K.Y., Wang, J.: Identity based confirmer signatures from pairings over elliptic curves. In: Proceedings of ACM conference on Electronic commerce, pp. 262–263 (2003)
Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)
Jakobsson, M., Sako, K., Impagliazzo, R.: Designated Verifier Proofs and Their Applications. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 143–154. Springer, Heidelberg (1996)
Katz, J., Wang, N.: Efficiency Improvements for Signature Schemes with Tight Security Reductions. To appear at ACM Conference on Computer and Communications Security (2003)
Libert, B., Quisquater, J.-J.: Identity Based Undeniable Signatures, extended version, eprint, available at http://eprint.iacr.org/2003/206
Michels, M., Stadler, M.: Efficient Convertible Undeniable Signature Schemes. In: Proc. of 4th AnnualWorkshop on Selected Areas in Cryptography, SAC 1997 (August 1997)
Okamoto, T.: Designated Confirmer Signatures and Public Key Encryption are Equivalent. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 61–74. Springer, Heidelberg (1994)
Okamoto, T., Pointcheval, D.: The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 104–118. Springer, Heidelberg (2001)
Paterson, K.G.: ID-based signatures from pairings on elliptic curves, eprint, available at http://eprint.iacr.org/2002/004/
Pointcheval, D.: Self-Scrambling Anonymizers. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 259–275. Springer, Heidelberg (2001)
Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13(3), 361–396 (2000)
Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: The 2000 Sympoium on Cryptography and Information Security (2000)
Shamir, A.: Identity Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)
Smart, N.P.: An identity based authenticated key agreement protocol based on the Weil pairing. Electronic Letters 38(13), 630–632 (2002)
Zhang, F., Kim, K.: ID-Based Blind Signature and Ring Signature from Pairings. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 533–547. Springer, Heidelberg (2002)
Zhang, F., Safavi-Naini, R., Susilo, W.: Attack on Han et al.’s ID-based Confirmer (Undeniable). Signature at ACM-EC 2003 (2003), eprint available at http://eprint.iacr.org/2003/129/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Libert, B., Quisquater, JJ. (2004). Identity Based Undeniable Signatures. In: Okamoto, T. (eds) Topics in Cryptology – CT-RSA 2004. CT-RSA 2004. Lecture Notes in Computer Science, vol 2964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24660-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-24660-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20996-6
Online ISBN: 978-3-540-24660-2
eBook Packages: Springer Book Archive