Abstract
We present a technique for delegating a short lattice basis that has the advantage of keeping the lattice dimension unchanged upon delegation. Building on this result, we construct two new hierarchical identity-based encryption (HIBE) schemes, with and without random oracles. The resulting systems are very different from earlier lattice-based HIBEs and in some cases result in shorter ciphertexts and private keys. We prove security from classic lattice hardness assumptions.
Chapter PDF
Similar content being viewed by others
References
Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)
Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999)
Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: STACS, pp. 75–86 (2009)
Boneh, D., Boyen, X.: Efficient selective-id secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)
Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)
Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)
Boyen, X.: Lattices mixing and vanishing trapdoors: A framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010)
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)
Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-damgard revisited: how to construct a hash function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)
Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. J. Crypto 20(3), 265–294 (2007); Abstract in Eurocrypt 2003 (2003)
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)
Gentry, C., Halevi, S.: Hierarchical identity based encryption with polynomially many levels. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 437–456. Springer, Heidelberg (2009)
Gama, N., Nguyen, P.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008)
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC (2008)
Gentry, C., Silverberg, A.: Hierarchical id-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)
Horwitz, J., Lynn, B.: Toward hierarchical identity-based encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466–481. Springer, Heidelberg (2002)
Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: a cryptographic perspective, vol. 671. Kluwer Academic Publishers, Boston (March 2002)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM Journal on Computing (SICOMP) 37(1), 267–302 (2007); Extended abstract in FOCS 2004 (2004)
Peikert, C.: Bonsai trees (or, arboriculture in lattice-based cryptography). Cryptology ePrint Archive, Report (2009), /359, http://eprint.iacr.org/
Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: STOC, pp. 333–342 (2009)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6) (2009); Extended abstract in STOC 2005 (2005)
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)
Waters, B.: Dual key encryption: Realizing fully secure IBE and HIBE under simple assumption. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Agrawal, S., Boneh, D., Boyen, X. (2010). Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE. In: Rabin, T. (eds) Advances in Cryptology – CRYPTO 2010. CRYPTO 2010. Lecture Notes in Computer Science, vol 6223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14623-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-14623-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14622-0
Online ISBN: 978-3-642-14623-7
eBook Packages: Computer ScienceComputer Science (R0)