Abstract
One of the earliest identification schemes was proposed by Beth in [6]. Since its introduction, variations and generalizations of this scheme have been considered, and, recently, the property of security against passive impersonation was shown, under a weak unforgeability assumption on the hashed El Gamal signature scheme, for two such variants: one in the standard (i.e., not identity-based) and one in the identity-based model. However, the security of both protocols under active and concurrent impersonation attacks was left open.
In this paper we prove that very minor modifications to these schemes result in schemes that satisfy security under active and concurrent impersonation attacks, assuming a one-more-dlog assumption. The resulting protocols are just as efficient as the original variants, which are, in turn, somewhat more efficient (but less general) of the original one proposed by Beth.
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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., Miner, S.: A forward-secure digital signature scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 431. Springer, Heidelberg (1999)
Bellare, M., Palacio, A.: GQ and schnorr identification schemes: Proofs of security against impersonation under active and concurrent attacks. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 162. Springer, Heidelberg (2002)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory 31, 469–472 (1985)
Beth, T.: Efficient zero-knowledged identification scheme for smart cards. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 77–84. Springer, Heidelberg (1988)
Burmester, M., Desmedt, Y., Beth, T.: Efficient Zero-Knowledge Identification Schemes for Smart Cards. The Computer Journal 35(1), 21–29 (1992)
Burmester, M., Desmedt, Y., Piper, F., Walker, M.: A General Zero-Knowledge Schemes. Designs, Codes and Cryptography 12(1) (1997)
Chaum, D.: Blind Signatures for Untraceable Payments. In: Proc. of CRYPTO 1982, Plemum, NY (1983)
De Santis, A., Di Crescenzo, G., Persiano, G.: Communication-Efficient Anonymous Group Identification. In: Proc. of 1998 ACM Conference on Computer and Communications Security. ACM Press, New York (1998)
Dodis, Y., Katz, J., Xu, S., Yung, M.: Strong key-insulated signature schemes. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 130–144. Springer, Heidelberg (2002)
Feige, U., Shamir, A.: Witness Indistinguishable and Witness Hiding Protocols. In: Proc. of the 22nd Annual ACM Symposium on the Theory of Computing (STOC 1990) (1990)
Feige, U., Fiat, A., Shamir, A.: Zero Knowledge Proofs of Identity. Journal of Cryptology 1(2), 77–94 (1988)
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)
Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof-Systems. SIAM J. on Computing 18(1) (1989)
Goldwasser, S., Micali, S., Rivest, R.: A Digital Signature Scheme Secure against Adaptive Chosen-Message Attacks. SIAM Journal of Computing 17(2) (1988)
Guillou, L.C., Quisquater, 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)
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)
Pointcheval, D., Stern, J.: Security Arguments for Digital Signatures and Blind Signatures. Journal of Cryptology 13(3), 361–396 (2000)
Schnorr, C.: Efficient Signature Generation by Smart Cards. Journal of Cryptology 4(3), 161–174 (1991)
Schnorr, C.: Security of 2t-root identification and signatures. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 143–157. Springer, Heidelberg (1996)
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)
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Di Crescenzo, G. (2008). On the Security of Beth’s Identification Schemes against Active and Concurrent Adversaries . In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_1
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DOI: https://doi.org/10.1007/978-3-540-89994-5_1
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