Abstract
Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the DDH assumption, excluding any recent pairing-based cryptosystems. In this paper, we extend their techniques to support, and exploit, pairing-based properties: we take advantage of pairing-friendly groups to obtain efficient (simulation-sound) zero-knowledge proofs, whose security relies on the Decisional Linear assumption. As a consequence, we provide efficient protocols, secure in the standard model, for ElGamal decryption as in [1], but also for Linear decryption, as well as extraction of several identity-based cryptosystems [6,4]. Furthermore, we strenghten their security model by suppressing the useless testPwd queries in the functionality.
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References
Abdalla, M., Boyen, X., Chevalier, C., Pointcheval, D.: Distributed public-key cryptography from weak secrets. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 139–159. Springer, Heidelberg (2009)
Barak, B., Canetti, R., Lindell, Y., Pass, R., Rabin, T.: Secure computation without authentication. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 361–377. Springer, Heidelberg (2005)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM CCS 1993: 1st Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)
Boneh, D., Boyen, X.: Efficient selective-ID secure identity based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)
Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boneh, D., Franklin, M.K.: 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)
Boyen, X., Chevalier, C., Fuchsbauer, G., Pointcheval, D.: Strong cryptography from weak secrets: Building efficient PKE and IBE from distributed passwords. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 305–322. Springer, Heidelberg (2010); Full version available from the web page of the authors
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science, pp. 136–145. IEEE Computer Society Press, Los Alamitos (2001)
Canetti, R., Halevi, S., Katz, J., Lindell, Y., MacKenzie, P.D.: Universally composable password-based key exchange. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 404–421. Springer, Heidelberg (2005)
ElGamal, 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)
Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006)
Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006)
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)
Katz, J., Shin, J.S.: Modeling insider attacks on group key-exchange protocols. In: ACM CCS 2005: 12th Conference on Computer and Communications Security, pp. 180–189. ACM Press, New York (2005)
Waters, B.R.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
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Boyen, X., Chevalier, C., Fuchsbauer, G., Pointcheval, D. (2010). Strong Cryptography from Weak Secrets. In: Bernstein, D.J., Lange, T. (eds) Progress in Cryptology – AFRICACRYPT 2010. AFRICACRYPT 2010. Lecture Notes in Computer Science, vol 6055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12678-9_18
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