Abstract
Public-key encryption schemes with non-interactive opening (PKENO) allow a receiver to non-interactively convince third parties that a ciphertext decrypts to a given plaintext or, alternatively, that such a ciphertext is invalid. Two practical generic constructions for PKENO have been proposed so far, starting from either identity-based encryption or public-key encryption with witness-recovering decryption (PKEWR). We show that the known transformation from PKEWR to PKENO fails to provide chosen-ciphertext security; only the transformation from identity-based encryption remains thus valid. Next, we prove that PKENO can alternatively be built out of robust non-interactive threshold public-key cryptosystems, a primitive that differs from identity-based encryption. Using the new transformation, we construct two efficient PKENO schemes: one based on the Decisional Diffie-Hellman assumption (in the Random-Oracle Model) and one based on the Decisional Linear assumption (in the standard model). Last but not least, we propose new applications of PKENO in protocol design. Motivated by these applications, we reconsider proof soundness for PKENO and put forward new definitions that are stronger than those considered so far. We give a taxonomy of all definitions and demonstrate them to be satisfiable.
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References
Agrawal, S., Boyen, X.: Identity-based encryption from lattices in the standard model (July 2009) (manuscript)
An, J.H., Dodis, Y., Rabin, T.: On the security of joint signature and encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 83–107. Springer, Heidelberg (2002)
Arita, S., Tsurudome, K.: Construction of threshold public-key encryptions through tag-based encryptions. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 186–200. Springer, Heidelberg (2009)
Boneh, D., Boyen, X., Halevi, S.: Chosen ciphertext secure public key threshold encryption without random oracles. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 226–243. Springer, Heidelberg (2006)
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., Gentry, C., Hamburg, M.: Space-efficient identity based encryption without pairings. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), pp. 647–657 (2007)
Boyen, X., Mei, Q., Waters, B.: Direct chosen ciphertext security from identity-based techniques. In: ACM Conference on Computer and Communications Security 2005, pp. 320–329 (2005)
Boyen, X.: Miniature cca2 pk encryption: Tight security without redundancy. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 485–501. Springer, Heidelberg (2007)
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)
Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)
Cash, D., Hofheinz, D., Kiltz, E.: How to delegate a lattice basis. Cryptology ePrint Archive: Report 2009/351 (July 2009)
Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)
Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)
Damgård, I., Hofheinz, D., Kiltz, E., Thorbek, R.: Public-key encryption with non-interactive opening. In: Malkin, T.G. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 239–255. Springer, Heidelberg (2008)
Dodis, Y., Katz, J.: Chosen-ciphertext security of multiple encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 188–209. Springer, Heidelberg (2005)
Damgård, I., Thorbek, R.: Non-interactive proofs for integer multiplication. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 412–429. Springer, Heidelberg (2007)
Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)
Fouque, P.-A., Pointcheval, D.: Threshold cryptosystems secure against chosen-ciphertext attacks. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 351–368. Springer, Heidelberg (2001)
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)
Goldreich, O.: Foundations of Cryptography - Basic Tools. Cambridge University Press, Cambridge (2001)
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: 40th Annual ACM Symposium on Theory of Computing (STOC 2008), pp. 197–206 (2008)
Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007)
Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006)
Kiltz, E.: Chosen-ciphertext secure key-encapsulation based on gap hashed diffie-hellman. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 282–297. Springer, Heidelberg (2007)
Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attack. In: Proc. of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 427–437. ACM, New York (1990)
Peikert, C.: Bonsai trees (or, arboriculture in lattice-based cryptography). Cryptology ePrint Archive: Report 2009/359 (July 2009)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC, pp. 187–196. ACM, New York (2008)
Rosen, A., Segev, G.: Efficient lossy trapdoor functions based on the composite residuosity assumption. Cryptology ePrint Archive, Report 2008/134 (2008), http://eprint.iacr.org/
Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: 40th Annual Symposium on Foundations of Computer Science, pp. 543–553. IEEE Computer Society Press, Los Alamitos (1999)
Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 1–16. Springer, Heidelberg (1998)
Shoup, V.: Draft ISO/IEC 18033-2: An emerging standard for public-key encryption. Technical report, ISO/IEC (2004), http://www.shoup.net/iso
Waters, B.: 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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Galindo, D. et al. (2010). Public-Key Encryption with Non-Interactive Opening: New Constructions and Stronger Definitions. 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_20
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DOI: https://doi.org/10.1007/978-3-642-12678-9_20
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