Abstract
The existence of encryption and commitment schemes secure under selective opening attack (SOA) has remained open despite considerable interest and attention. We provide the first public key encryption schemes secure against sender corruptions in this setting. The underlying tool is lossy encryption. We then show that no non-interactive or perfectly binding commitment schemes can be proven secure with black-box reductions to standard computational assumptions, but any statistically hiding commitment scheme is secure. Our work thus shows that the situation for encryption schemes is very different from the one for commitment schemes.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-642-01001-9_35
Chapter PDF
References
Barak, B.: How to go beyond the black-box simulation barrier. In: 42nd Annual Symposium on Foundations of Computer Science, Proceedings of FOCS 2001, pp. 106–115. IEEE Computer Society, Los Alamitos (2001)
Barak, B., Goldreich, O.: Universal arguments and their applications. In: 17th Annual IEEE Conference on Computational Complexity, Proceedings of CoCo 2002, pp. 194–203. IEEE Computer Society, Los Alamitos (2002)
Barak, B., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero-knowledge. In: 47th Annual Symposium on Foundations of Computer Science, Proceedings of FOCS 2006, pp. 345–354. IEEE Computer Society, Los Alamitos (2006)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: 1st ACM Conference on Computer and Communications Security, Proceedings of CCS 1993, pp. 62–73. ACM Press, New York (1993)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption—how to encrypt with RSA. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Bellare, M., Rogaway, P.: Robust computational secrete sharing and a unified account of classical secret-sharing goals. In: 14th ACM Conference on Computer and Communications Security, Proceedings of CCS 2007, pp. 172–184. ACM Press, New York (2007)
Bellare, M., Yilek, S.: Encryption schemes secure under selective opening attack. IACR ePrint Archive (2009)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: 20th ACM Symposium on Theory of Computing, Proceedings of STOC 1988, pp. 1–10. ACM, New York (1988)
Blum, M.: Coin flipping by telephone. In: Gersho, A. (ed.) Advances in Cryptology, A report on CRYPTO 1981, number 82-04 in ECE Report, pp. 11–15. University of California, Electrical and Computer Engineering (1982)
Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science, Proceedings of FOCS 2001, pp. 136–145. IEEE Computer Society, Los Alamitos (2001)
Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)
Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: Twenty-Eighth Annual ACM Symposium on Theory of Computing, Proceedings of STOC 1995, pp. 639–648. ACM Press, New York (1996)
Canetti, R., Dwork, C., Naor, M., Ostrovsky, R.: Deniable encryption. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 90–104. Springer, Heidelberg (1997)
Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Concurrent zero-knowledge requires \(\tilde\Omega(\log n)\) rounds. In: 33rd Annual ACM Symposium on Theory of Computing, Proceedings of STOC 2001, pp. 570–579. ACM Press, New York (2001)
Canetti, R., Halevi, S., Katz, J.: Adaptively-secure, non-interactive public-key encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 150–168. Springer, Heidelberg (2005)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: 20th ACM Symposium on Theory of Computing, Proceedings of STOC 1988, pp. 11–19. ACM Press, New York (1988)
Damgård, I., Nielsen, J.B.: Improved non-committing encryption schemes based on general complexity assumptions. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 432–450. Springer, Heidelberg (2000)
Damgård, I.B., Pedersen, T.P., Pfitzmann, B.: On the existence of statistically hiding bit commitment schemes and fail-stop sigantures. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 250–265. Springer, Heidelberg (1994)
Dodis, Y., Oliveira, R., Pietrzak, K.: On the generic insecurity of the full domain hash. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 449–466. Springer, Heidelberg (2005)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: Twenty-Third Annual ACM Symposium on Theory of Computing, Proceedings of STOC 1991, pp. 542–552. ACM Press, New York (1991) (Extended abstract)
Dwork, C., Naor, M., Reingold, O., Stockmeyer, L.: Magic functions. Journal of the ACM 50(6), 852–921 (2003)
Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. Journal of the ACM 51(6), 851–898 (2004)
Gennaro, R., Micali, S.: Independent zero-knowledge sets. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 34–45. Springer, Heidelberg (2006)
Goldreich, O.: Foundations of Cryptography (Basic Tools), vol. 1. Cambridge University Press, Cambridge (2001)
Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM Journal on Computing 25(1), 169–192 (1996)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2) (1984)
Haitner, I., Holenstein, T.: On the (im)possibility of key dependent encryption. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 202–219. Springer, Heidelberg (2009)
Haitner, I., Reingold, O.: Statistically-hiding commitment from any one-way function. In: 39th Annual ACM Symposium on Theory of Computing, Proceedings of STOC 2007, pp. 1–10. ACM Press, New York (2007)
Haitner, I., Hoch, J.J., Reingold, O., Segev, G.: Finding collisions in interactive protocols – a tight lower bound on the round complexity of statistically-hiding commitments. In: 48th Annual Symposium on Foundations of Computer Science, Proceedings of FOCS 2007, pp. 669–679. IEEE Computer Society, Los Alamitos (2007)
Hofheinz, D.: Possibility and impossibility results for selective decommitments. IACR ePrint Archive (April 2008)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Twenty-First Annual ACM Symposium on Theory of Computing, Proceedings of STOC 1989, pp. 44–61. ACM Press, New York (1989) (Extended abstract)
Kilian, J., Petrank, E.: Concurrent and resettable zero-knowledge in poly-logarithmic rounds. In: 33rd Annual ACM Symposium on Theory of Computing, Proceedings of STOC 2001, pp. 560–569. ACM Press, New York (2001)
Kol, G., Naor, M.: Cryptography and game theory: Designing protocols for exchanging information. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 320–339. Springer, Heidelberg (2008)
Naor, M.: Bit commitment using pseudo-randomness. Journal of Cryptology 4(2), 151–158 (1991)
Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Twelfth Annual Symposium on Discrete Algorithms, Proceedings of SODA 2001, pp. 448–457. ACM/SIAM (2001)
Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: Twenty-First Annual ACM Symposium on Theory of Computing, Proceedings of STOC 1989, pp. 33–43. ACM Press, New York (1989)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: The non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
Panjwani, S.: Tackling adaptive corruptions in multicast encryption protocols. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 21–40. Springer, Heidelberg (2007)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Fotieth Annual ACM Symposium on Theory of Computing, Proceedings of STOC 2008, pp. 187–196. ACM Press, New York (2008)
Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)
Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round complexity. In: 43rd Annual Symposium on Foundations of Computer Science, Proceedings of FOCS 2002, pp. 366–375. IEEE Computer Society Press, Los Alamitos (2002)
Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004)
Richardson, R., Kilian, J.: On the concurrent composition of zero-knowledge proofs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 415–431. Springer, Heidelberg (1999)
Rosen, A., Segev, G.: Efficient lossy trapdoor functions based on the composite residuosity assumption. IACR ePrint Archive (March 2008)
Simon, D.R.: Findings collisions on a one-way street: Can secure hash functions be based on general assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)
Wee, H.M.: One-way permutations, interactive hashing and statistically hiding commitments. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 419–433. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bellare, M., Hofheinz, D., Yilek, S. (2009). Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening. In: Joux, A. (eds) Advances in Cryptology - EUROCRYPT 2009. EUROCRYPT 2009. Lecture Notes in Computer Science, vol 5479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01001-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-01001-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01000-2
Online ISBN: 978-3-642-01001-9
eBook Packages: Computer ScienceComputer Science (R0)