Abstract
Let a sender Alice computes a ciphertext C of a message M by using a receiver Bob’s public key pk B . Damgård, Hofheinz, Kiltz, and Thorbek (CT-RSA2008) has proposed the notion public key encryption with non-interactive opening (PKENO), where Bob can make an non-interactive proof π that proves the decryption result of C under sk B is M, without revealing sk B itself. When Bob would like to prove the correctness of (C, M) (e.g., the information M sent to Bob is not the expected one), PKENO turns out to be an effective cryptographic primitive. A PKENO scheme for the KEM/DEM framework has also been proposed by Galindo (CT-RSA2009). Bob can make a non-interactive proof π that proves the decapsulation result of C under sk B is K without revealing sk B itself, where K is an encapsulation key of the DEM part. That is, no verifier can verify π without knowing K. This setting is acceptable if K is an ephemeral value. However, PKENO is not applicable if an encryption key is shared among certain users beforehand, and is used for a relatively long period before re-running the key agreement protocol, such as symmetric cryptosystems. In this paper, we define the notion secret key encryption with non-interactive opening (SKENO), and give a generic construction of SKENO from verifiable random function (VRF) and the Berbain-Gilbert IV-dependent stream cipher construction (FSE2007). Bob can make a non-interactive proof π that proves the decryption result of C under K is M, without revealing K itself.
Chapter PDF
References
ISO CD 18033-2. Encryption algorithms part 2: asymmetric ciphers (2004)
Abdalla, M., Catalano, D., Fiore, D.: Verifiable Random Functions from Identity-based Key Encapsulation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 554–571. Springer, Heidelberg (2009)
Belenkiy, M., Chase, M., Kohlweiss, M., Lysyanskaya, A.: Compact E-cash and Simulatable VRFs Revisited. In: Shacham, H., Waters, B. (eds.) Pairing 2009. LNCS, vol. 5671, pp. 114–131. Springer, Heidelberg (2009)
Bellare, M., Shi, H., Zhang, C.: Foundations of Group Signatures: The Case of Dynamic Groups. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 136–153. Springer, Heidelberg (2005)
Bellare, M., Shoup, S.: Two-tier Signatures, Strongly Unforgeable Signatures, and Fiat-shamir without Random Oracles. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 201–216. Springer, Heidelberg (2007)
Berbain, C., Gilbert, H.: On the Security of IV Dependent Stream Ciphers. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 254–273. Springer, Heidelberg (2007)
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Sponge-based Pseudo-random Number Generators. In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 33–47. Springer, Heidelberg (2010)
Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13(4), 850–864 (1984)
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., Katz, J.: Improved Efficiency for CCA-secure Cryptosystems Built Using Identity-based Encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)
Brakerski, Z., Goldwasser, S., Rothblum, G.N., Vaikuntanathan, V.: Weak Verifiable Random Functions. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 558–576. Springer, Heidelberg (2009)
Camenisch, J.L., Hohenberger, S., Lysyanskaya, A.: Compact E-cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005)
Damgård, I., Hofheinz, D., Kiltz, E., Thorbek, R.: Public-Key Encryption with Non-interactive Opening. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 239–255. Springer, Heidelberg (2008)
Dodis, Y.: Efficient Construction of (Distributed) Verifiable Random Functions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 1–17. Springer, Heidelberg (2002)
Dodis, Y., Yampolskiy, A.: A Verifiable Random Function with Short Proofs and Keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)
Dwork, C., Naor, M.: Zaps and their applications. SIAM J. Comput. 36(6), 1513–1543 (2007)
Emura, K., Hanaoka, G., Sakai, Y.: Group Signature Implies PKE with Non-interactive Opening and Threshold PKE. In: Echizen, I., Kunihiro, N., Sasaki, R. (eds.) IWSEC 2010. LNCS, vol. 6434, pp. 181–198. Springer, Heidelberg (2010)
Fiore, D., Schröder, D.: Uniqueness is a different story: Impossibility of verifiable random functions from trapdoor permutations. Cryptology ePrint Archive, Report 2010/648 (2010), http://eprint.iacr.org/
Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword Search and Oblivious Pseudorandom Functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005)
Galindo, D.: Breaking and Repairing Damgård et al. Public Key Encryption Scheme with Non-interactive Opening. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 389–398. Springer, Heidelberg (2009)
Galindo, D., Libert, B., Fischlin, M., Fuchsbauer, G., Lehmann, A., Manulis, M., Schröder, D.: Public-Key Encryption with Non-Interactive Opening: New Constructions and Stronger Definitions. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 333–350. Springer, Heidelberg (2010)
Goldreich, O.: Foundations of Cryptography. Basic Tools, vol. 1. Cambridge University Press, New York (2001)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
Hazay, C., Lindell, Y.: Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 155–175. Springer, Heidelberg (2008)
Hohenberger, S., Waters, B.: Constructing Verifiable Random Functions with Large Input Spaces. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 656–672. Springer, Heidelberg (2010)
Jarecki, S., Liu, X.: Efficient Oblivious Pseudorandom Function with Applications to Adaptive OT and Secure Computation of Set Intersection. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 577–594. Springer, Heidelberg (2009)
Lai, J., Deng, R.H., Liu, S., Kou, W.: Efficient CCA-secure PKE from Identity-based Techniques. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 132–147. Springer, Heidelberg (2010)
Liskov, M.: Updatable Zero-knowledge Databases. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 174–198. Springer, Heidelberg (2005)
Lysyanskaya, A.: Unique Signatures and Verifiable Random Functions from the DH-DDH Separation. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 597–612. Springer, Heidelberg (2002)
Matsuda, T., Hanaoka, G., Matsuura, K., Imai, H.: An Efficient Encapsulation Scheme from Near Collision Resistant Pseudorandom Generators and its Application to IBE-to-PKE Transformations. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 16–31. Springer, Heidelberg (2009)
Matsuda, T., Matsuura, K.: On Black-box Separations among Injective One-way Functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 597–614. Springer, Heidelberg (2011)
Micali, S., Rabin, M.O., Vadhan, S.P.: Verifiable random functions. In: FOCS, pp. 120–130 (1999)
Micali, S., Reyzin, L.: Soundness in the Public-key Model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 542–565. Springer, Heidelberg (2001)
Micali, S., Rivest, R.L.: Micropayments Revisited. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 149–163. Springer, Heidelberg (2002)
Yao, A.C.-C.: Theory and applications of trapdoor functions (extended abstract). In: FOCS, pp. 80–91 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, J., Emura, K., Miyaji, A. (2011). Non-interactive Opening for Ciphertexts Encrypted by Shared Keys. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds) Information and Communications Security. ICICS 2011. Lecture Notes in Computer Science, vol 7043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25243-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-25243-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25242-6
Online ISBN: 978-3-642-25243-3
eBook Packages: Computer ScienceComputer Science (R0)