Abstract
Lossy trapdoor functions, introduced by Peikert and Waters (STOC’08), have received a lot of attention in the last years, because of their wide range of applications. The notion has been recently extended to the identity-based setting by Bellare et al. (Eurocrypt’12). An identity-based trapdoor function (IB-TDF) satisfying the lossy property introduced by Bellare et al. can be used to construct other cryptographic primitives in the identity-based setting: encryption schemes with semantic security under chosen-plaintext attacks, deterministic encryption schemes, and hedged encryption schemes that maintain some security when messages are encrypted using randomness of poor quality. However, the constructed primitives can be proved secure only against selective adversaries who select the target identity upfront.
Our first contribution is an alternative definition for the lossiness of an identity-based trapdoor function. We prove that an IB-TDF satisfying the new property can be used to construct all the aforementioned primitives, in the identity-based setting, with security against adaptive adversaries. We further consider the new definition and its implications in the more general scenario of hierarchical identity-based cryptography, which has proved very useful both for practical applications and to establish theoretical relations with other cryptographic primitives (including encryption with chosen-ciphertext security or with forward-security).
As a second contribution, we describe a pairing-based hierarchical IB-TDF satisfying the new definition of lossiness against either selective or, for hierarchies of constant depth, adaptive adversaries. This is also the first example of hierarchical trapdoor functions based on traditional (i.e., non-lattice-related) number theoretic assumptions. As a direct consequence of our two contributions, we obtain a hierarchical identity-based (HIB) encryption scheme with chosen-plaintext security, a HIB deterministic encryption scheme and a HIB hedged encryption scheme, all of them with security against adaptive adversaries.
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
Anderson, R.: Two Remarks on Public Key Cryptology. Invited lecture. In: ACM Conference on Computer and Communications Security (1997)
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., 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., Hofheinz, D., Yilek, S.: Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009)
Bellare, M., Kiltz, E., Peikert, C., Waters, B.: Identity-Based (Lossy) Trapdoor Functions and Applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 228–245. Springer, Heidelberg (2012)
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., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)
Boneh, D., Waters, B.: Conjunctive, Subset, and Range Queries on Encrypted Data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 535–554. Springer, Heidelberg (2007)
Boyen, X., Waters, B.: Anonymous Hierarchical Identity-Based Encryption (Without Random Oracles). In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 290–307. Springer, Heidelberg (2006)
Boyen, X., Waters, B.: Shrinking the Keys of Discrete-Log-Type Lossy Trapdoor Functions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 35–52. Springer, Heidelberg (2010)
Canetti, R., Halevi, S., Katz, J.: A Forward-Secure Public-Key Encryption Scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)
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., Peikert, C.: Bonsai Trees, or How to Delegate a Lattice Basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)
Dodis, Y., Reyzin, L., Smith, A.: Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 523–540. Springer, Heidelberg (2004)
Ducas, L.: Anonymity from Asymmetry: New Constructions for Anonymous HIBE. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 148–164. Springer, Heidelberg (2010)
Escala, A., Herranz, J., Libert, B., Ràfols, C.: Identity-Based Lossy Trapdoor Functions: New Definitions, Hierarchical Extensions, and Implications. Cryptology ePrint Archive: Report 2012/503 (2012)
Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More Constructions of Lossy and Correlation-Secure Trapdoor Functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010)
Gentry, C., Silverberg, A.: Hierarchical ID-Based Cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)
Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-Based Encryption for Fine-Grained Access Control of Encrypted Data. In: ACM CCS 2006 (2006)
Håstad, J., Impagliazzo, R., Levin, L., Luby, M.: A Pseudorandom Generator from any One-Way Function. SIAM Journal on Computing 28(4) (1999)
Hemenway, B., Ostrovsky, R.: Lossy Trapdoor Functions from Smooth Homomorphic Hash Proof Systems. Electronic Colloquium on Computational Complexity (ECCC) 16, 127 (2009)
Hofheinz, D.: All-But-Many Lossy Trapdoor Functions. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 209–227. Springer, Heidelberg (2012)
Katz, J., Sahai, A., Waters, B.: Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008)
Okamoto, T., Takashima, K.: Hierarchical Predicate Encryption for Inner-Products. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 214–231. Springer, Heidelberg (2009)
Peikert, C., Waters, B.: Lossy Trapdoor Functions and their Applications. In: STOC 2008. ACM Press (2008)
Sahai, A., Waters, B.: Fuzzy Identity-Based Encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)
Shi, E., Waters, B.: Delegating Capabilities in Predicate Encryption Systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 560–578. Springer, Heidelberg (2008)
Shamir, A.: Identity-Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)
Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
Wee, H.: Dual Projective Hashing and Its Applications — Lossy Trapdoor Functions and More. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 246–262. Springer, Heidelberg (2012)
Xie, X., Xue, R., Zhang, R.: Deterministic Public Key Encryption and Identity-Based Encryption from Lattices in the Auxiliary-Input Setting. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 1–18. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 International Association for Cryptologic Research
About this paper
Cite this paper
Escala, A., Herranz, J., Libert, B., Ràfols, C. (2014). Identity-Based Lossy Trapdoor Functions: New Definitions, Hierarchical Extensions, and Implications. In: Krawczyk, H. (eds) Public-Key Cryptography – PKC 2014. PKC 2014. Lecture Notes in Computer Science, vol 8383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54631-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-54631-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54630-3
Online ISBN: 978-3-642-54631-0
eBook Packages: Computer ScienceComputer Science (R0)