nach oben

Erschienen in:

2019 | OriginalPaper | Buchkapitel

FE for Inner Products and Its Application to Decentralized ABE

verfasst von : Zhedong Wang, Xiong Fan, Feng-Hao Liu

Erschienen in: Public-Key Cryptography – PKC 2019

Verlag: Springer International Publishing

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

In this work, we revisit the primitive functional encryption (FE) for inner products and show its application to decentralized attribute-based encryption (ABE). Particularly, we derive an FE for inner products that satisfies a stronger notion, and show how to use such an FE to construct decentralized ABE for the class \(\{0,1\}\)-\(\mathsf {LSSS} \) against bounded collusions in the plain model. We formalize the FE notion and show how to achieve such an FE under the LWE or DDH assumption. Therefore, our resulting decentralized ABE can be constructed under the same standard assumptions, improving the prior construction by Lewko and Waters (Eurocrypt 2011). Finally, we also point out challenges to construct decentralized ABE for general functions by establishing a relation between such an ABE and witness encryption for general NP statements.

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 Registration-Based Encryption from Standard Assumptions

Nächstes Kapitel Decentralizing Inner-Product Functional Encryption

We will discuss the secret sharing in more details, but let us focus on the high level concepts at this point.

The work [31] can derive an IND adaptively secure scheme for challenge ciphertexts that encrypt a vector of messages, but as we discussed above, IND security seems not sufficient for our application.

In our setting, we consider a general case where there is no \(\mathsf {GID} \).

Abdalla, M., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz [38], pp. 733–751

Abdalla, M., Gay, R., Raykova, M., Wee, H.: Multi-input inner-product functional encryption from pairings. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part I. LNCS, vol. 10210, pp. 601–626. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_21CrossRef

Agrawal, S.: Stronger security for reusable garbled circuits, general definitions and attacks. In: Katz and Shacham [40], pp. 3–35

Agrawal, S., Bhattacherjee, S., Phan, D.H., Stehlé, D., Yamada, S.: Efficient public trace and revoke from standard assumptions: extended abstract. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 2277–2293. ACM Press, New York (2017)

Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21–40. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_2CrossRef

Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw and Katz [50], pp. 333–362

Agrawal, S., Rosen, A.: Functional encryption for bounded collusions, revisited. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017, Part I. LNCS, vol. 10677, pp. 173–205. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_7CrossRef

Ananth, P., Fan, X.: Attribute based encryption for RAMs from LWE. Cryptology ePrint Archive, Report 2018/273 (2018). https://eprint.iacr.org/2018/273

Bellare, M., Hoang, V.T.: Adaptive witness encryption and asymmetric password-based cryptography. In: Katz [38], pp. 308–331

10.

Benhamouda, F., Bourse, F., Lipmaa, H.: CCA-secure inner-product functional encryption from projective hash functions. In: Fehr, S. (ed.) PKC 2017, Part II. LNCS, vol. 10175, pp. 36–66. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54388-7_2CrossRef

11.

Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: 2007 IEEE Symposium on Security and Privacy, pp. 321–334. IEEE Computer Society Press, May 2007

12.

Bishop, A., Jain, A., Kowalczyk, L.: Function-hiding inner product encryption. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 470–491. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_20CrossRef

13.

Boneh, D., et al.: Threshold cryptosystems from threshold fully homomorphic encryption. Cryptology ePrint Archive, Report 2017/956 (2017). https://eprint.iacr.org/2017/956

14.

Boneh, D., et al.: 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). https://doi.org/10.1007/978-3-642-55220-5_30CrossRef

15.

Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.): 45th ACM STOC. ACM Press, New York (2013)

16.

Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_16CrossRef

17.

Boyen, X.: Attribute-based functional encryption on lattices. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 122–142. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_8CrossRef

18.

Boyen, X., Li, Q.: Turing machines with shortcuts: efficient attribute-based encryption for bounded functions. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 267–284. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_15CrossRef

19.

Brakerski, Z., Jain, A., Komargodski, I., Passelegue, A., Wichs, D.: Non-trivial witness encryption and null-iO from standard assumptions. Cryptology ePrint Archive, Report 2017/874 (2017). https://eprint.iacr.org/2017/874

20.

Brakerski, Z., Vaikuntanathan, V.: Circuit-ABE from LWE: unbounded attributes and semi-adaptive security. In: Robshaw and Katz [50], pp. 363–384

21.

Canetti, R., Garay, J.A. (eds.): CRYPTO 2013, Part II. LNCS, vol. 8043. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1CrossRefMATH

22.

Chase, M.: Multi-authority attribute based encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 515–534. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_28CrossRef

23.

Chase, M., Chow, S.S.M.: Improving privacy and security in multi-authority attribute-based encryption. In: Al-Shaer, E., Jha, S., Keromytis, A.D. (eds.) ACM CCS 2009, pp. 121–130. ACM Press, New York (2009)

24.

Datta, P., Okamoto, T., Tomida, J.: Full-hiding (unbounded) multi-input inner product functional encryption from the k-linear assumption. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part II. LNCS, vol. 10770, pp. 245–277. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_9CrossRef

25.

Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40–49. IEEE Computer Society Press, October 2013

26.

Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti and Garay [21], pp. 479–499

27.

Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Functional encryption without obfuscation. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016, Part II. LNCS, vol. 9563, pp. 480–511. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0_18CrossRef

28.

Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Boneh et al. [15], pp. 467–476

29.

Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: How to run turing machines on encrypted data. In: Canetti and Garay [21], pp. 536–553

30.

Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)MathSciNetCrossRef

31.

Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini and Canetti [52], pp. 162–179

32.

Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Boneh et al. [15], pp. 545–554

33.

Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro, R., Robshaw, M.J.B. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 503–523. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_25CrossRef

34.

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., Vimercati, S. (eds.) ACM CCS 2006, pp. 89–98. ACM Press, October/November 2006. Cryptology ePrint Archive Report 2006/309

35.

Green, M., Hohenberger, S., Waters, B.: Outsourcing the decryption of ABE ciphertexts. In: USENIX Security Symposium, vol. 2011 (2011)

36.

Jafargholi, Z., Kamath, C., Klein, K., Komargodski, I., Pietrzak, K., Wichs, D.: Be adaptive, avoid overcommitting. In: Katz and Shacham [40], pp. 133–163

37.

Katsumata, S., Yamada, S.: Partitioning via non-linear polynomial functions: more compact IBEs from ideal lattices and bilinear maps. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 682–712. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_23CrossRef

38.

Katz, J. (ed.): PKC 2015. LNCS, vol. 9020. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2CrossRefMATH

39.

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). https://doi.org/10.1007/978-3-540-78967-3_9CrossRef

40.

Katz, J., Shacham, H. (eds.): CRYPTO 2017, Part I. LNCS, vol. 10401. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7CrossRefMATH

41.

Lewko, A., Waters, B.: Decentralizing attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 568–588. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_31CrossRef

42.

Lewko, A.B., 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). https://doi.org/10.1007/978-3-642-13190-5_4CrossRef

43.

Lin, H., Cao, Z., Liang, X., Shao, J.: Secure threshold multi authority attribute based encryption without a central authority. In: Chowdhury, D.R., Rijmen, V., Das, A. (eds.) INDOCRYPT 2008. LNCS, vol. 5365, pp. 426–436. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89754-5_33CrossRef

44.

Liu, Z., Cao, Z., Huang, Q., Wong, D.S., Yuen, T.H.: Fully secure multi-authority ciphertext-policy attribute-based encryption without random oracles. In: Atluri, V., Diaz, C. (eds.) ESORICS 2011. LNCS, vol. 6879, pp. 278–297. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23822-2_16CrossRef

45.

Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions from worst-case complexity assumptions. In: 43rd FOCS, pp. 356–365. IEEE Computer Society Press, November 2002

46.

Müller, S., Katzenbeisser, S., Eckert, C.: Distributed attribute-based encryption. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 20–36. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00730-9_2CrossRef

47.

Muller, S., Katzenbeisser, S., Eckert, C.: On multi-authority ciphertext-policy attribute-based encryption. Bull. Korean Math. Soc. 46(4), 803–819 (2009)MathSciNetCrossRef

48.

O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010). http://eprint.iacr.org/2010/556

49.

Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.) ACM CCS 2007, pp. 195–203. ACM Press, New York (2007)

50.

Robshaw, M., Katz, J. (eds.): CRYPTO 2016, Part III. LNCS, vol. 9816. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3CrossRefMATH

51.

Rouselakis, Y., Waters, B.: Practical constructions and new proof methods for large universe attribute-based encryption. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 463–474. ACM Press, New York (2013)

52.

Safavi-Naini, R., Canetti, R. (eds.): CRYPTO 2012. LNCS, vol. 7417. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5CrossRefMATH

53.

Sahai, A., Waters, B.R.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27CrossRef

54.

Waters, B.: Ciphertext-policy attribute-based encryption: an expressive, efficient, and provably secure realization. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 53–70. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_4CrossRef

55.

Waters, B.: Functional encryption for regular languages. In: Safavi-Naini and Canetti [52], pp. 218–235

56.

Xagawa, K.: Improved (hierarchical) inner-product encryption from lattices. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 235–252. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_15CrossRef

Titel: FE for Inner Products and Its Application to Decentralized ABE
verfasst von: Zhedong Wang
Xiong Fan
Feng-Hao Liu
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2019
Print ISBN: 978-3-030-17258-9

Electronic ISBN: 978-3-030-17259-6

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-17259-6_4

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