Abstract
A central question in the theory of public-key cryptography is to determine which minimal assumptions are sufficient to achieve security against chosen-ciphertext attacks (or CCA-security, for short). Following the large body of work on hardness and correctness amplification, we investigate how far we can weaken CCA security and still be able to efficiently transform any scheme satisfying such a weaker notion into a fully CCA-secure one.
More concretely, we consider a weak CCA-secure bit-encryption scheme with decryption error (1 − α)/2 where an adversary can distinguish encryptions of different messages with possibly large advantage β < 1 − 1/poly. We show that whenever α 2 > β, the weak correctness and security properties can be simultaneously amplified to obtain a fully CCA-secure encryption scheme with negligible decryption error. Our approach relies both on a new hardcore lemma for CCA security as well as on revisiting the recently proposed approach to obtain CCA security due to Hohenberger et al (EUROCRYPT ’12).
We note that such amplification results were only known in the simpler case of security against chosen-plaintext attacks.
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
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)
Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: 22nd ACM STOC. ACM Press (May 1990)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: 23rd ACM STOC, pp. 542–552. ACM Press (May 1991)
Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: 40th FOCS, pp. 543–553. IEEE Computer Society Press (October 1999)
Gertner, Y., Malkin, T., Myers, S.: Towards a separation of semantic and CCA security for public key encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 434–455. Springer, Heidelberg (2007)
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)
Wee, H.: Efficient chosen-ciphertext security via extractable hash proofs. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 314–332. Springer, Heidelberg (2010)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 187–196. ACM Press (May 2008)
Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)
Kiltz, E., Mohassel, P., O’Neill, A.: Adaptive trapdoor functions and chosen-ciphertext security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 673–692. Springer, Heidelberg (2010)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press (November 1993)
Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Yao, A.C.: Theory and applications of trapdoor functions. In: 23rd FOCS, pp. 80–91. IEEE Computer Society Press (November 1982)
Dwork, C., Naor, M., Reingold, O.: Immunizing encryption schemes from decryption errors. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 342–360. Springer, Heidelberg (2004)
Holenstein, T.: Key agreement from weak bit agreement. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 664–673. ACM Press (May 2005)
Holenstein, T., Renner, R.S.: One-way secret-key agreement and applications to circuit polarization and immunization of public-key encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 478–493. Springer, Heidelberg (2005)
Lenstra, A.K., Hughes, J.P., Augier, M., Bos, J.W., Kleinjung, T., Wachter, C.: Public keys. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 626–642. Springer, Heidelberg (2012)
Heninger, N., Durumeric, Z., Wustrow, E., Halderman, J.A.: Mining your ps and qs: Detection of widespread weak keys in network devices. In: Proceedings of the 21st USENIX Security Symposium (2012)
Kearns, M.J., Valiant, L.G.: Cryptographic limitations on learning boolean formulae and finite automata. J. ACM 41(1), 67–95 (1994)
Myers, S., Shelat, A.: Bit encryption is complete. In: 50th FOCS, pp. 607–616. IEEE Computer Society Press (October 2009)
Hohenberger, S., Lewko, A., Waters, B.: Detecting dangerous queries: A new approach for chosen ciphertext security. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 663–681. Springer, Heidelberg (2012)
Impagliazzo, R.: Hard-core distributions for somewhat hard problems. In: FOCS 1995, pp. 538–545 (1995)
Maurer, U.M.: Protocols for secret key agreement by public discussion based on common information. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 461–470. Springer, Heidelberg (1993)
Tessaro, S.: Security amplification for the cascade of arbitrarily weak pRPs: Tight bounds via the interactive hardcore lemma. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 37–54. Springer, Heidelberg (2011)
Impagliazzo, R., Luby, M.: One-way functions are essential for complexity-based cryptography. In: 30th FOCS, pp. 230–235. IEEE Computer Society Press (October / November 1989)
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)
Cramer, R., Hanaoka, G., Hofheinz, D., Imai, H., Kiltz, E., Pass, R., Shelat, A., Vaikuntanathan, V.: Bounded CCA2-secure encryption. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 502–518. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Lin, H., Tessaro, S. (2013). Amplification of Chosen-Ciphertext Security. In: Johansson, T., Nguyen, P.Q. (eds) Advances in Cryptology – EUROCRYPT 2013. EUROCRYPT 2013. Lecture Notes in Computer Science, vol 7881. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38348-9_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-38348-9_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38347-2
Online ISBN: 978-3-642-38348-9
eBook Packages: Computer ScienceComputer Science (R0)