Abstract
Traditional definitions of the security of encryption schemes assume that the messages encrypted are chosen independently of the randomness used by the encryption scheme. Recent works, implicitly by Myers and Shelat (FOCS’09) and Bellare et al (AsiaCrypt’09), and explicitly by Hemmenway and Ostrovsky (ECCC’10), consider randomness-dependent message (RDM) security of encryption schemes, where the message to be encrypted may be selected as a function—referred to as the RDM function—of the randomness used to encrypt this particular message, or other messages, but in a circular way. We carry out a systematic study of this notion. Our main results demonstrate the following:
-
Full RDM security—where the RDM function may be an arbitrary polynomial-size circuit—is not possible.
-
Any secure encryption scheme can be slightly modified, by just performing some pre-processing to the randomness, to satisfy bounded-RDM security, where the RDM function is restricted to be a circuit of a priori bounded polynomial size. The scheme, however, requires the randomness r needed to encrypt a message m to be slightly longer than the length of m (i.e., |r| > |m| + ω(logk), where k is the security parameter).
-
We present a black-box provability barrier to compilations of arbitrary public-key encryption into RDM-secure ones using just pre-processing of the randomness, whenever |m| > |r| + ω(logk). On the other hand, under the DDH assumption, we demonstrate the existence of bounded-RDM secure schemes that can encrypt arbitrarily “long” messages using “short” randomness.
We finally note that the existence of public-key encryption schemes imply the existence of a fully RDM-secure encryption scheme in an “ultra-weak” Random-Oracle Model—where the security reduction need not “program” the oracle, or see the queries made by the adversary to the oracle; combined with our impossibility result, this yields the first example of a cryptographic task that has a secure implementation in such a weak Random-Oracle Model, but does not have a secure implementation without random oracles.
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
Acar, T., Belenkiy, M., Bellare, M., Cash, D.: Cryptographic Agility and Its Relation to Circular Encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 403–422. Springer, Heidelberg (2010)
Akavia, A., Goldwasser, S., Vaikuntanathan, V.: Simultaneous Hardcore Bits and Cryptography against Memory Attacks. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 474–495. Springer, Heidelberg (2009)
Alwen, J., Dodis, Y., Wichs, D.: Leakage-Resilient Public-Key Cryptography in the Bounded-Retrieval Model. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 36–54. Springer, Heidelberg (2009)
Applebaum, B., Harnik, D., Ishai, Y.: Semantic security under related-key attacks and applications. In: ICS, pp. 45–60 (2011)
Barak, B.: How to go beyond the black-box simulation barrier. In: FOCS, pp. 106–115 (2001)
Barak, B., Haitner, I., Hofheinz, D., Ishai, Y.: Bounded Key-Dependent Message Security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 423–444. Springer, Heidelberg (2010)
Bellare, M., Rompel, J.: Randomness-efficient oblivious sampling. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 276–287 (1994)
Bellare, M., Boldyreva, A., O’Neill, A.: Deterministic and Efficiently Searchable Encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 535–552. Springer, Heidelberg (2007)
Bellare, M., Boldyreva, A., Palacio, A.: An Uninstantiable Random-Oracle-Model Scheme for a Hybrid-Encryption Problem. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004)
Bellare, M., Brakerski, Z., Naor, M., Ristenpart, T., Segev, G., Shacham, H., Yilek, S.: Hedged Public-Key Encryption: How to Protect against Bad Randomness. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 232–249. Springer, Heidelberg (2009)
Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 360–378. Springer, Heidelberg (2008)
Bellare, M., Keelveedhi, S.: Authenticated and Misuse-Resistant Encryption of Key-Dependent Data. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 610–629. Springer, Heidelberg (2011)
Berlekamp, E.R.: Factoring polynomials over finite fields. Bell System Technical Journal 46, 1853–1859 (1967)
Black, J., Rogaway, P., Shrimpton, T.: Encryption-Scheme Security in the Presence of Key-Dependent Messages. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003)
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)
Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-Secure Encryption from Decision Diffie-Hellman. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 108–125. Springer, Heidelberg (2008)
Brakerski, Z., Goldwasser, S.: Circular and Leakage Resilient Public-Key Encryption under Subgroup Indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010)
Brakerski, Z., Goldwasser, S., Kalai, Y.T.: Black-Box Circular-Secure Encryption beyond Affine Functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 201–218. Springer, Heidelberg (2011)
Brakerski, Z., Kalai, Y.T., Katz, J., Vaikuntanathan, V.: Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage. In: Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010, pp. 501–510 (2010)
Camenisch, J., Chandran, N., Shoup, V.: A Public Key Encryption Scheme Secure against Key Dependent Chosen Plaintext and Adaptive Chosen Ciphertext Attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 351–368. Springer, Heidelberg (2009)
Camenisch, J.L., Lysyanskaya, A.: An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93–118. Springer, Heidelberg (2001)
Canetti, R., Goldreich, O., Halevi, S.: On the Random-Oracle Methodology as Applied to Length-Restricted Signature Schemes. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 40–57. Springer, Heidelberg (2004)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)
Cash, D., Green, M., Hohenberger, S.: New Definitions and Separations for Circular Security. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 540–557. Springer, Heidelberg (2012)
Dodis, Y., Smith, A.: Correcting errors without leaking partial information. In: STOC, pp. 654–663 (2005)
Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 293–302 (2008)
Goldwasser, S., Kalai, Y.T.: On the (in)security of the fiat-shamir paradigm. In: FOCS, pp. 102–113 (2003)
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., 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)
Halevi, S., Krawczyk, H.: Security under key-dependent inputs. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, CCS 2007, pp. 466–475 (2007)
Hemenway, B., Ostrovsky, R.: Building injective trapdoor functions from oblivious transfer. Electronic Colloquium on Computational Complexity (ECCC) 17 (2010)
Hofheinz, D., Unruh, D.: Towards Key-Dependent Message Security in the Standard Model. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 108–126. Springer, Heidelberg (2008)
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)
Maurer, U.M., Renner, R.S., Holenstein, C.: Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)
Micali, S., Reyzin, L.: Physically Observable Cryptography (Extended Abstract). In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 278–296. Springer, Heidelberg (2004)
Myers, S., Shelat, A.: Bit encryption is complete. In: FOCS, pp. 607–616 (2009)
Naor, M.: On Cryptographic Assumptions and Challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg (2003)
Naor, M., Segev, G.: Public-Key Cryptosystems Resilient to Key Leakage. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 18–35. Springer, Heidelberg (2009)
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)
Pass, R.: On Deniability in the Common Reference String and Random Oracle Model. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 316–337. Springer, Heidelberg (2003)
Pass, R., Rosen, A., Tseng, W.l.D.: Public-coin parallel zero-knowledge for np (2011)
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)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. SIAM J. Comput. 40(6), 1803–1844 (2011)
Trevisan, L., Vadhan, S.: Extracting randomness from samplable distributions. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 32–42 (2000)
Unruh, D.: Random Oracles and Auxiliary Input. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 205–223. 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
Birrell, E., Chung, KM., Pass, R., Telang, S. (2013). Randomness-Dependent Message Security. In: Sahai, A. (eds) Theory of Cryptography. TCC 2013. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36594-2_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-36594-2_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36593-5
Online ISBN: 978-3-642-36594-2
eBook Packages: Computer ScienceComputer Science (R0)