Abstract
The well-known forking lemma by Pointcheval and Stern has been used to prove the security of the so-called generic signature schemes. These signature schemes are obtained via the Fiat-Shamir transform from three-pass identification schemes. A number of five-pass identification protocols have been proposed in the last few years. Extending the forking lemma and the Fiat-Shamir transform would allow to obtain new signature schemes since, unfortunately, these newly proposed schemes fall outside the original framework. In this paper, we provide an extension of the forking lemma in order to assess the security of what we call n-generic signature schemes. These include signature schemes that are derived from certain (2n + 1)-pass identification schemes. We thus obtain a generic methodology for proving the security of a number of signature schemes derived from recently published five-pass identification protocols, and potentially for (2n + 1)-pass identification schemes to come.
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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)
Aguilar Melchor, C., Gaborit, P., Schrek, J.: A new zero-knowledge code based identification scheme with reduced communication. CoRR, abs/1111.1644 (2011)
Cayrel, P.-L., Lindner, R., Rückert, M., Silva, R.: Improved Zero-Knowledge Identification with Lattices. In: Heng, S.-H., Kurosawa, K. (eds.) ProvSec 2010. LNCS, vol. 6402, pp. 1–17. Springer, Heidelberg (2010)
Cayrel, P.-L., Véron, P., El Yousfi Alaoui, S.M.: A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 171–186. Springer, Heidelberg (2011)
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)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: STOC 1985, pp. 291–304. ACM (1985)
Lampe, R., Patarin, J.: Analysis of some natural variants of the PKP algorithm. Cryptology ePrint Archive, Report 2011/686 (2011), http://eprint.iacr.org/
Ohta, K., Okamoto, T.: On Concrete Security Treatment of Signatures Derived from Identification. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 354–369. Springer, Heidelberg (1998)
Pointcheval, D.: A New Identification Scheme Based on the Perceptrons Problem. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 319–328. Springer, Heidelberg (1995)
Pointcheval, D., Poupard, G.: A new NP-complete problem and public-key identification. Des. Codes Cryptography 28, 5–31 (2003)
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. J. Cryptology 13(3), 361–396 (2000)
Sakumoto, K., Shirai, T., Hiwatari, H.: Public-Key Identification Schemes Based on Multivariate Quadratic Polynomials. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 706–723. Springer, Heidelberg (2011)
Shamir, A.: An Efficient Identification Scheme Based on Permuted Kernels (Extended Abstract). In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 606–609. Springer, Heidelberg (1990)
Silva, R., Cayrel, P.-L., Lindner, R.: Zero-knowledge identification based on lattices with low communication costs. XI Simpósio Brasileiro de Segurança da Informação e de Sistemas Computacionais 8, 95–107 (2011)
Stern, J.: A New Identification Scheme Based on Syndrome Decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)
Stern, J.: Designing Identification Schemes with Keys of Short Size. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 164–173. Springer, Heidelberg (1994)
Yao, A.C., Zhao, Y.: Digital signatures from challenge-divided sigma-protocols. Cryptology ePrint Archive, Report 2012/001 (2012), http://eprint.iacr.org/
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El Yousfi Alaoui, S.M., Dagdelen, Ö., Véron, P., Galindo, D., Cayrel, PL. (2012). Extended Security Arguments for Signature Schemes. In: Mitrokotsa, A., Vaudenay, S. (eds) Progress in Cryptology - AFRICACRYPT 2012. AFRICACRYPT 2012. Lecture Notes in Computer Science, vol 7374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31410-0_2
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DOI: https://doi.org/10.1007/978-3-642-31410-0_2
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