Abstract
In 2008, Groth and Sahai proposed a powerful suite of techniques for constructing non-interactive zero-knowledge proofs in bilinear groups. Their proof systems have found numerous applications, including group signature schemes, anonymous voting, and anonymous credentials. In this paper, we demonstrate that the notion of smooth projective hash functions can be useful to design round-optimal privacy-preserving interactive protocols. We show that this approach is suitable for designing schemes that rely on standard security assumptions in the standard model with a common-reference string and are more efficient than those obtained using the Groth-Sahai methodology. As an illustration of our design principle, we construct an efficient oblivious signature-based envelope scheme and a blind signature scheme, both round-optimal.
CNRS – UMR 8548 and INRIA – EPI Cascade, Université Paris Diderot.
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., Chevalier, C., Pointcheval, D.: Smooth Projective Hashing for Conditionally Extractable Commitments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 671–689. Springer, Heidelberg (2009)
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)
Balfanz, D., Durfee, G., Shankar, N., Smetters, D., Staddon, J., Wong, H.-C.: Secret handshakes from pairing-based key agreements. In: IEEE Symposium on Security and Privacy, pp. 180–196 (2003)
Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th Annual Symposium on Foundations of Computer Science, pp. 394–403. IEEE Computer Society Press (October 1997)
Blazy, O., Fuchsbauer, G., Pointcheval, D., Vergnaud, D.: Signatures on Randomizable Ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 403–422. Springer, Heidelberg (2011)
Blazy, O., Pointcheval, D., Vergnaud, D.: Round-Optimal Privacy-Preserving Protocols with Smooth Projective Hash Functions. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 94–110. Springer, Heidelberg (2012)
Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boyen, X., Waters, B.: Compact Group Signatures Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 427–444. Springer, Heidelberg (2006)
Boyen, X., Waters, B.: Full-Domain Subgroup Hiding and Constant-Size Group Signatures. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 1–15. Springer, Heidelberg (2007)
Bradshaw, R.W., Holt, J.E., Seamons, K.E.: Concealing complex policies with hidden credentials. In: Atluri, V., Pfitzmann, B., McDaniel, P. (eds.) ACM CCS 2004: 11th Conference on Computer and Communications Security, pp. 146–157. ACM Press (October 2004)
Castelluccia, C., Jarecki, S., Tsudik, G.: Secret Handshakes from CA-Oblivious Encryption. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 293–307. Springer, Heidelberg (2004)
Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology – CRYPTO 1982, pp. 199–203. Plenum Press, New York (1983)
Cramer, R., Shoup, V.: Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002)
Dwork, C., Naor, M.: Zaps and their applications. SIAM J. Comput. 36(6), 1513–1543 (2007)
Fischlin, M.: Round-Optimal Composable Blind Signatures in the Common Reference String Model. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 60–77. Springer, Heidelberg (2006)
Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Applied Mathematics 156(16), 3113–3121 (2008)
Garg, S., Rao, V., Sahai, A., Schröder, D., Unruh, D.: Round Optimal Blind Signatures. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 630–648. Springer, Heidelberg (2011)
Gennaro, R., Lindell, Y.: A Framework for Password-Based Authenticated Key Exchange. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 524–543. Springer, Heidelberg (2003), http://eprint.iacr.org/2003/032.ps.gz
Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. ACM Transactions on Information and System Security 9(2), 181–234 (2006)
Groth, J.: Fully Anonymous Group Signatures Without Random Oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007)
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)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM Journal on Computing 28(4), 1364–1396 (1999)
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)
Juels, A., Guajardo, J.: RSA Key Generation with Verifiable Randomness. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 357–374. Springer, Heidelberg (2002)
Kalai, Y.T.: Smooth Projective Hashing and Two-Message Oblivious Transfer. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005)
Li, N., Du, W., Boneh, D.: Oblivious signature-based envelope. In: 22nd ACM Symposium Annual on Principles of Distributed Computing, pp. 182–189. ACM Press (July 2003)
Shacham, H.: A Cramer-Shoup encryption scheme from the Linear Assumption and from progressively weaker Linear variants. Cryptology ePrint Archive, Report 2007/074 (February 2007), http://eprint.iacr.org/
Shoup, V.: OAEP reconsidered. Journal of Cryptology 15(4), 223–249 (2002)
Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blazy, O., Pointcheval, D., Vergnaud, D. (2012). Round-Optimal Privacy-Preserving Protocols with Smooth Projective Hash Functions. In: Cramer, R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28914-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-28914-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28913-2
Online ISBN: 978-3-642-28914-9
eBook Packages: Computer ScienceComputer Science (R0)