nach oben

Erschienen in:

2016 | OriginalPaper | Buchkapitel

Circuit-ABE from LWE: Unbounded Attributes and Semi-adaptive Security

verfasst von : Zvika Brakerski, Vinod Vaikuntanathan

Erschienen in: Advances in Cryptology – CRYPTO 2016

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We construct an LWE-based key-policy attribute-based encryption (ABE) scheme that supports attributes of unbounded polynomial length. Namely, the size of the public parameters is a fixed polynomial in the security parameter and a depth bound, and with these fixed length parameters, one can encrypt attributes of arbitrary length. Similarly, any polynomial size circuit that adheres to the depth bound can be used as the policy circuit regardless of its input length (recall that a depth d circuit can have as many as \(2^d\) inputs). This is in contrast to previous LWE-based schemes where the length of the public parameters has to grow linearly with the maximal attribute length.

We prove that our scheme is semi-adaptively secure, namely, the adversary can choose the challenge attribute after seeing the public parameters (but before any decryption keys). Previous LWE-based constructions were only able to achieve selective security. (We stress that the “complexity leveraging” technique is not applicable for unbounded attributes).

We believe that our techniques are of interest at least as much as our end result. Fundamentally, selective security and bounded attributes are both shortcomings that arise out of the current LWE proof techniques that program the challenge attributes into the public parameters. The LWE toolbox we develop in this work allows us to delay this programming. In a nutshell, the new tools include a way to generate an a-priori unbounded sequence of LWE matrices, and have fine-grained control over which trapdoor is embedded in each and every one of them, all with succinct representation.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Fully Secure Functional Encryption for Inner Products, from Standard Assumptions

Nächstes Kapitel Design in Type-I, Run in Type-III: Fast and Scalable Bilinear-Type Conversion Using Integer Programming

We follow, here and after, the convention that \(f(x)=0\) signifies the ability to decrypt. This is the opposite of the standard convention, and is done purely for our convenience in the technical sections.

One can modify the circuit-ABE constructions of [9, 20] to support unbounded attributes in the (programmable) random oracle model. Our focus in this paper is on constructions in the standard model.

Note that this “negated policy” formulation is obviously equivalent to the standard formulation in the literature wherein decryption succeeds if \(f(x)=1\). From this point and on, purely for our convenience in the technical sections, we will assume that a ciphertext should be decryptable if \(f(x)=0\) and not decryptable otherwise.

The proofs of the other circuit-ABE schemes from standard assumptions, namely [14, 19], follow along similar lines.

Recall our convention that \(f(x) = 0\) is the event when decryption succeeds.

Abdalla, M., Catalano, D., Dent, A.W., Malone-Lee, J., Neven, G., Smart, N.P.: Identity-based encryption gone wild. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 300–311. Springer, Heidelberg (2006)CrossRef

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)CrossRef

Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010)CrossRef

Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: Miller, G.L. (ed.) Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, 22–24 May 1996, pp. 99–108. ACM (1996)

Alekhnovich, M.: More on average case vs. approximation complexity. In: Proceedings of the 44th Symposium on Foundations of Computer Science (FOCS 2003), Cambridge, MA, USA, 11–14 October 2003, pp. 298–307. IEEE Computer Society (2003)

Ananth, P., Brakerski, Z., Segev, G., Vaikuntanathan, V.: From selective to adaptive security in functional encryption. In: Gennaro and Robshaw [16], pp. 657–677 (2015)

Ananth, P., Sahai, A.: Functional encryption for turing machines. IACR Cryptology ePrint Archive 2015:776 (2015)

Blum, A., Furst, M.L., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994)CrossRef

Boneh, D., Gentry, C., Gorbunov, S., Halevi, S., Nikolaenko, V., Segev, G., Vaikuntanathan, V., Vinayagamurthy, D.: Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 533–556. Springer, Heidelberg (2014)CrossRef

10.

Boyen, X.: Attribute-based functional encryption on lattices. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 122–142. Springer, Heidelberg (2013)CrossRef

11.

Brakerski, Z., Vaikuntanathan, V.: Constrained key-homomorphic PRFs from standard lattice assumptions. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 1–30. Springer, Heidelberg (2015)CrossRef

12.

Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. J. Cryptol. 25(4), 601–639 (2012)MathSciNetCrossRefMATH

13.

Chen, J., Wee, H.: Semi-adaptive attribute-based encryption and improved delegation for Boolean formula. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 277–297. Springer, Heidelberg (2014)

14.

Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 479–499. Springer, Heidelberg (2013)CrossRef

15.

Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Fully secure attribute based encryption from multilinear maps. IACR Cryptology ePrint Archive 2014:622 (2014)

16.

Gennaro, R., Robshaw, M. (eds.): CRYPTO 2015. LNCS, vol. 9216. Springer, Heidelberg (2015)MATH

17.

Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC (2008)

18.

Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)CrossRef

19.

Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) Symposium on Theory of Computing Conference, STOC 2013, Palo Alto, CA, USA, 1–4 June 2013, pp. 545–554. ACM (2013)

20.

Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro and Robshaw [16], pp. 503–523 (2015)

21.

Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: Servedio, R.A., Rubinfeld, R. (eds.) Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, 14–17 June 2015, pp. 469–477. ACM (2015)

22.

Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Juels, A., Wright, R.N., di Vimercati, S.D.C. (eds.) Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006, Alexandria, VA, USA, 30 October–3 November 2006, pp. 89–98. ACM (2006)

23.

Hohenberger, S., Waters, B.: Attribute-based encryption with fast decryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 162–179. Springer, Heidelberg (2013)CrossRef

24.

Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: Jajodia, S., Atluri, V., Jaeger, T. (eds.) Proceedings of the 10th ACM Conference on Computer and Communications Security, CCS 2003, Washington, DC, USA, 27–30 October 2003, pp. 155–164. ACM (2003)

25.

Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010)CrossRef

26.

Lewko, A., Waters, B.: Unbounded HIBE and attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 547–567. Springer, Heidelberg (2011)CrossRef

27.

Lewko, A., Waters, B.: New proof methods for attribute-based encryption: achieving full security through selective techniques. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 180–198. Springer, Heidelberg (2012)CrossRef

28.

Micciancio, D., Mol, P.: Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 465–484. Springer, Heidelberg (2011)CrossRef

29.

Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012)CrossRef

30.

Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010)CrossRef

31.

Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012)CrossRef

32.

Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, 31 May–2 June 2009, pp. 333–342 (2009)

33.

Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 22–24 May 2005, pp. 84–93 (2005)

34.

Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)CrossRef

35.

Schnorr, C.: A hierarchy of polynomial time lattice basis reduction algorithms. Theor. Comput. Sci. 53, 201–224 (1987)MathSciNetCrossRefMATH

36.

Waters, B.: Functional encryption for regular languages. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 218–235. Springer, Heidelberg (2012)CrossRef

37.

Waters, B.: A punctured programming approach to adaptively secure functional encryption. In: Gennaro and Robshaw [16], pp. 678–697 (2015)

Titel: Circuit-ABE from LWE: Unbounded Attributes and Semi-adaptive Security
verfasst von: Zvika Brakerski
Vinod Vaikuntanathan
Verlag: Springer Berlin Heidelberg
Buch: Advances in Cryptology – CRYPTO 2016
Print ISBN: 978-3-662-53014-6

Electronic ISBN: 978-3-662-53015-3

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-662-53015-3_13

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner