Abstract
The Fiat-Shamir paradigm was proposed as a way to remove interaction from 3-round proof of knowledge protocols and derive secure signature schemes. This generic transformation leads to very efficient schemes and has thus grown quite popular. However, this transformation is proven secure only in the random oracle model. In FOCS 2003, Goldwasser and Kalai showed that this transformation is provably insecure in the standard model by presenting a counterexample of a 3-round protocol, the Fiat-Shamir transformation of which is (although provably secure in the random oracle model) insecure in the standard model, thus showing that the random oracle is uninstantiable. In particular, for every hash function that is used to replace the random oracle, the resulting signature scheme is existentially forgeable. This result was shown by relying on the non-black-box techniques of Barak (FOCS 2001).
An alternative to the Fiat-Shamir paradigm was proposed by Fischlin in Crypto 2005. Fischlin’s transformation can be applied to any so called 3-round “Fiat-Shamir proof of knowledge’’ and can be used to derive non-interactive zero-knowledge proofs of knowledge as well as signature schemes. An attractive property of this transformation is that it provides online extractability (i.e., the extractor works without having to rewind the prover). Fischlin remarks that in comparison to the Fiat-Shamir transformation, his construction tries to “decouple the hash function from the protocol flow” and hence, the counterexample in the work of Goldwaaser and Kalai does not seem to carry over to this setting.
In this work, we show a counterexample to the Fischlin’s transformation. In particular, we construct a 3-round Fiat-Shamir proof of knowledge (on which Fischlin’s transformation is applicable), and then, present an adversary against both - the soundness of the resulting non-interactive zero-knowledge, as well as the unforegeability of the resulting signature scheme. Our attacks are successful except with negligible probability for any hash function, that is used to instantiate the random oracle, provided that there is an apriori (polynomial) bound on the running time of the hash function. By choosing the right bound, secure instantiation of Fischlin transformation with most practical cryptographic hash functions can be ruled out.
The techniques used in our work are quite unrelated to the ones used in the work of Goldwasser and Kalai. Our primary technique is to bind the protocol flow with the hash function if the code of the hash function is available. We believe that our ideas are of independent interest and maybe applicable in other related settings.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Abdalla, M., An, J.H., Bellare, M., Namprempre, C.: From Identification to Signatures via the Fiat-Shamir Transform: Minimizing Assumptions for Security and Forward-Security. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 418–433. Springer, Heidelberg (2002)
Barak, B.: How to go beyond the black-box simulation barrier. In: FOCS, pp. 106–115 (2001)
Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably-sound zero-knowledge and its applications. In: FOCS, pp. 116–125 (2001)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (Im)possibility of Obfuscating Programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51, 557–594 (2004)
Deng, Y., Goyal, V., Sahai, A.: Resolving the simultaneous resettability conjecture and a new non-black-box simulation strategy. In: FOCS, pp. 251–260 (2009)
Fischlin, M.: Communication-Efficient Non-interactive Proofs of Knowledge with Online Extractors. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 152–168. Springer, Heidelberg (2005)
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., Kalai, Y.T.: On the (in)security of the fiat-shamir paradigm. In: FOCS, pp. 102–113 (2003)
Goldwasser, S., Kalai, Y.T.: Yael Tauman Kalai. On the impossibility of obfuscation with auxiliary input. In: 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005, pp. 553–562 (October 2005)
Guillou, L.C., 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)
Micali, S., Reyzin, L.: Improving the exact security of digital signature schemes. J. Cryptology 15(1), 1–18 (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)
Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority, pp. 232–241 (2004)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptology 13(3), 361–396 (2000)
Schnorr, C.-P.: Efficient signature generation by smart cards. J. Cryptology 4(3), 161–174 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Ananth, P., Bhaskar, R., Goyal, V., Rao, V. (2013). On the (In)security of Fischlin’s Paradigm. In: Sahai, A. (eds) Theory of Cryptography. TCC 2013. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36594-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-36594-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36593-5
Online ISBN: 978-3-642-36594-2
eBook Packages: Computer ScienceComputer Science (R0)