Abstract
This paper develops a theory of multi-instance (mi) security and applies it to provide the first proof-based support for the classical practice of salting in password-based cryptography. Mi-security comes into play in settings (like password-based cryptography) where it is computationally feasible to compromise a single instance, and provides a second line of defense, aiming to ensure (in the case of passwords, via salting) that the effort to compromise all of some large number m of instances grows linearly with m. The first challenge is definitions, where we suggest LORX-security as a good metric for mi security of encryption and support this claim by showing it implies other natural metrics, illustrating in the process that even lifting simple results from the si setting to the mi one calls for new techniques. Next we provide a composition-based framework to transfer standard single-instance (si) security to mi-security with the aid of a key-derivation function. Analyzing password-based KDFs from the PKCS#5 standard to show that they meet our indifferentiability-style mi-security definition for KDFs, we are able to conclude with the first proof that per password salts amplify mi-security as hoped in practice. We believe that mi-security is of interest in other domains and that this work provides the foundation for its further theoretical development and practical application.
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
Abadi, M., Warinschi, B.: Password-Based Encryption Analyzed. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 664–676. Springer, Heidelberg (2005)
Baudron, O., Pointcheval, D., Stern, J.: Extended Notions of Security for Multicast Public Key Cryptosystems. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 499–511. Springer, Heidelberg (2000)
Bellare, M., Boldyreva, A., Micali, S.: Public-Key Encryption in a Multi-user Setting: Security Proofs and Improvements. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 259–274. Springer, Heidelberg (2000)
Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th FOCS, pp. 394–403. IEEE Computer Society Press (October 1997)
Bellare, M., Pointcheval, D., Rogaway, P.: Authenticated Key Exchange Secure against Dictionary Attacks. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 139–155. Springer, Heidelberg (2000)
Bellare, M., Ristenpart, T., Tessaro, S.: Multi-instance security and its application to password-based cryptography. Cryptology ePrint Archive, Report 2012/196 (2012), http://eprint.iacr.org/
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)
Boyen, X.: Halting password puzzles: hard-to-break encryption from human-memorable keys. In: Proceedings of 16th USENIX Security Symposium on USENIX Security Symposium, p. 9. USENIX Association (2007)
Boyen, X.: New Paradigms for Password Security (Abstract from the Keynote Lecture). In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 1–5. Springer, Heidelberg (2008)
Canetti, R., Halevi, S., Katz, J., Lindell, Y., MacKenzie, P.: Universally Composable Password-Based Key Exchange. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 404–421. Springer, Heidelberg (2005)
Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-Damgård Revisited: How to Construct a Hash Function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)
Dodis, Y., Gennaro, R., Håstad, J., Krawczyk, H., Rabin, T.: Randomness Extraction and Key Derivation Using the CBC, Cascade and HMAC Modes. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 494–510. Springer, Heidelberg (2004)
Dodis, Y., Impagliazzo, R., Jaiswal, R., Kabanets, V.: Security Amplification for Interactive Cryptographic Primitives. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 128–145. Springer, Heidelberg (2009)
Gennaro, R., Lindell, Y.: A Framework for Password-Based Authenticated Key Exchange. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 524–543. Springer, Heidelberg (2003)
Goldreich, O.: Three XOR-Lemmas — An exposition (1995), http://www.wisdom.weizmann.ac.il/
Goldreich, O., Impagliazzo, R., Levin, L.A., Venkatesan, R., Zuckerman, D.: Security preserving amplification of hardness. In: 31st FOCS, pp. 318–326. IEEE Computer Society Press (October 1990)
Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st ACM STOC, pp. 25–32. ACM Press (May 1989)
Goldreich, O., Nisan, N., Wigderson, A.: On Yao’s XOR-Lemma. In: Goldreich, O. (ed.) Studies in Complexity and Cryptography. LNCS, vol. 6650, pp. 273–301. Springer, Heidelberg (2011)
Haitner, I., Harnik, D., Reingold, O.: On the Power of the Randomized Iterate. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 22–40. Springer, Heidelberg (2006)
Impagliazzo, R., Kabanets, V.: Constructive Proofs of Concentration Bounds. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX and RANDOM 2010, LNCS, vol. 6302, pp. 617–631. Springer, Heidelberg (2010)
Kelsey, J., Schneier, B., Hall, C., Wagner, D.: Secure Applications of Low-Entropy Keys. In: Okamoto, E., Davida, G., Mambo, M. (eds.) ISW 1997. LNCS, vol. 1396, pp. 121–134. Springer, Heidelberg (1998)
Kohno, T.: Attacking and repairing the winZip encryption scheme. In: Atluri, V., Pfitzmann, B., McDaniel, P. (eds.) ACM CCS 2004, pp. 72–81. ACM Press (October 2004)
Krawczyk, H.: Cryptographic Extraction and Key Derivation: The HKDF Scheme. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 631–648. Springer, Heidelberg (2010)
Luby, M., Rackoff, C.: A Study of Password Security. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 392–397. Springer, Heidelberg (1988)
Maurer, U.M., Pietrzak, K., Renner, R.: Indistinguishability Amplification. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 130–149. Springer, Heidelberg (2007)
Maurer, U.M., Renner, R., 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)
Maurer, U., Tessaro, S.: Computational Indistinguishability Amplification: Tight Product Theorems for System Composition. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 355–373. Springer, Heidelberg (2009)
Maurer, U., Tessaro, S.: A Hardcore Lemma for Computational Indistinguishability: Security Amplification for Arbitrarily Weak PRGs with Optimal Stretch. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 237–254. Springer, Heidelberg (2010)
Morris, R., Thompson, K.: Password security: a case history. Commun. ACM 22, 594–597 (1979)
Myers, S.: Efficient amplification of the security of weak pseudo-random function generators. Journal of Cryptology 16(1), 1–24 (2003)
Panconesi, A., Srinivasan, A.: Randomized distributed edge coloring via an extension of the chernoff-hoeffding bounds. SIAM J. Comput. 26(2), 350–368 (1997)
PKCS #5: Password-based cryptography standard (rfc 2898). RSA Data Security Inc, Version 2.0 (September 2000)
Ristenpart, T., Shacham, H., Shrimpton, T.: Careful with Composition: Limitations of the Indifferentiability Framework. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 487–506. Springer, Heidelberg (2011)
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)
Unger, F.: A probabilistic inequality with applications to threshold direct-product theorems. In: 50th FOCS, pp. 221–229. IEEE Computer Society Press (October 2009)
Wagner, D., Goldberg, I.: Proofs of Security for the Unix Password Hashing Algorithm. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 560–572. Springer, Heidelberg (2000)
Yao, A.C.: Theory and applications of trapdoor functions. In: 23rd FOCS, pp. 80–91. IEEE Computer Society Press (November 1982)
Yao, F.F., Yin, Y.L.: Design and Analysis of Password-Based Key Derivation Functions. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 245–261. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 International Association for Cryptologic Research 2012
About this paper
Cite this paper
Bellare, M., Ristenpart, T., Tessaro, S. (2012). Multi-instance Security and Its Application to Password-Based Cryptography. In: Safavi-Naini, R., Canetti, R. (eds) Advances in Cryptology – CRYPTO 2012. CRYPTO 2012. Lecture Notes in Computer Science, vol 7417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32009-5_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-32009-5_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32008-8
Online ISBN: 978-3-642-32009-5
eBook Packages: Computer ScienceComputer Science (R0)