Abstract
Blind signatures have proved an essential building block for applications that protect privacy while ensuring unforgeability, i.e., electronic cash and electronic voting. One of the oldest, and most efficient blind signature schemes is the one due to Schnorr that is based on his famous identification scheme. Although it was proposed over twenty years ago, its unforgeability remains an open problem, even in the random-oracle model. In this paper, we show that current techniques for proving security in the random oracle model do not work for the Schnorr blind signature by providing a meta-reduction which we call “personal nemesis adversary”. Our meta-reduction is the first one that does not need to reset the adversary and can also rule out reductions to interactive assumptions. Our results generalize to other important blind signatures, such as the one due to Brands. Brands’ blind signature is at the heart of Microsoft’s newly implemented UProve system, which makes this work relevant to cryptographic practice as well.
Chapter PDF
Similar content being viewed by others
References
Abe, M.: A secure three-move blind signature scheme for polynomially many signatures. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 136–151. Springer, Heidelberg (2001)
Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 209–236. Springer, Heidelberg (2010)
Abe, M., Okamoto, T.: Provably Secure Partially Blind Signatures. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 271–286. Springer, Heidelberg (2000)
Baldimtsi, F., Lysyanskaya, A.: On the security of one-witness blind signature schemes. Cryptology ePrint Archive, Report 2012/197 (2012)
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, 185–215 (2003)
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, pp. 162–177. Springer, Heidelberg (2002)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM-CCS 1993, pp. 62–73. ACM (1993)
Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-diffie-hellman-group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)
Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 59–71. Springer, Heidelberg (1998)
Brands, S.: An efficient off-line electronic cash system based on the representation problem. In CWI Technical Report CS-R9323
Brands, S.: Untraceable off-line cash in wallets with observers. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 302–318. Springer, Heidelberg (1994)
Camenisch, J., Hohenberger, S., Lysyanskaya, A.: Compact E-Cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005)
Camenisch, J., Lysyanskaya, A.: An efficient system for non-transferable anonymous credentials with optional anonymity revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93–118. Springer, Heidelberg (2001)
Chaum, D., Fiat, A., Naor, M.: Untraceable electronic cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)
Chaum, D.: Blind signatures for untraceable payment. In: CRYPTO 1982, pp. 199–203 (1982)
Coron, J.-S.: On the exact security of full domain hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000)
Schnorr, C.P., Jakobsson, M.: Security of discrete log cryptosystems in the random oracle + generic model. In: The Mathematics of Public-Key Cryptography, The Fields Institute (1999)
Fischlin, M.: Black-box reductions and separations in cryptography. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 413–422. Springer, Heidelberg (2012)
Fischlin, M., Fleischhacker, N.: Limitations of the meta-reduction technique: The case of schnorr signatures. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 444–460. Springer, Heidelberg (2013)
Fischlin, M., Lehmann, A., Ristenpart, T., Shrimpton, T., Stam, M., Tessaro, S.: Random oracles with(out) programmability. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 303–320. Springer, Heidelberg (2010)
Fischlin, M., Schröder, D.: On the impossibility of three-move blind signature schemes. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 197–215. Springer, Heidelberg (2010)
Guillou, L.C., Quisquater, J.-J.: A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988)
Hazay, C., Katz, J., Koo, C.-Y., Lindell, Y.: Concurrently-secure blind signatures without random oracles or setup assumptions. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 323–341. Springer, Heidelberg (2007)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: The non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
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., Ohta, K.: Universal electronic cash. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 324–337. Springer, Heidelberg (1992)
Paillier, P., Vergnaud, D.: Discrete-log-based signatures may not be equivalent to discrete log. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 1–20. Springer, Heidelberg (2005)
Paquin, C.: U-prove cryptographic specification v1.1. In Microsoft Technical Report (February 2011), http://connect.microsoft.com/site1188
Paquin, C.: U-prove technology overview v1.1. In Microsoft Technical Report (February 2011), http://connect.microsoft.com/site1188
European Parliament and Council of the European Union. Directive 2009/136/ec. In Official Journal of the European Union (2009)
Pass, R.: Limits of provable security from standard assumptions. In: STOC, pp. 109–118 (2011)
Pointcheval, D., Stern Provably, J.: secure blind signature schemes. In: Kim, K.-C., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 252–265. Springer, Heidelberg (1996)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13, 361–396 (2000)
Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
IBM Security Team. Specification of the identity mixer cryptographic library, version 2.3.0. In IBM Research Report (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baldimtsi, F., Lysyanskaya, A. (2013). On the Security of One-Witness Blind Signature Schemes. In: Sako, K., Sarkar, P. (eds) Advances in Cryptology - ASIACRYPT 2013. ASIACRYPT 2013. Lecture Notes in Computer Science, vol 8270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42045-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-42045-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-42044-3
Online ISBN: 978-3-642-42045-0
eBook Packages: Computer ScienceComputer Science (R0)