Fully Secure Functional Encryption with General Relations from the Decisional Linear Assumption

  • Tatsuaki Okamoto
  • Katsuyuki Takashima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6223)

Abstract

This paper presents a fully secure functional encryption scheme for a wide class of relations, that are specified by non-monotone access structures combined with inner-product relations. The security is proven under a well-established assumption, the decisional linear (DLIN) assumption, in the standard model. The proposed functional encryption scheme covers, as special cases, (1) key-policy and ciphertext-policy attribute-based encryption with non-monotone access structures, and (2) (hierarchical) predicate encryption with inner-product relations and functional encryption with non-zero inner-product relations.

References

  1. 1.
    Beimel, A.: Secure schemes for secret sharing and key distribution. PhD Thesis, Israel Institute of Technology, Technion, Haifa, Israel (1996)Google Scholar
  2. 2.
    Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: 2007 IEEE Symposium on Security and Privacy, pp. 321–334. IEEE Press, Los Alamitos (2007)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Boneh, D., Boyen, X., Goh, E.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Hamburg, M.: Generalized identity based and broadcast encryption scheme. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Boneh, D., Katz, J.: Improved efficiency for CCA-secure cryptosystems built using identity based encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM Conference on Computer and Communication Security 2006, pp. 89–98. ACM, New York (2006)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Lewko, A.B., Waters, B.: New techniques for dual system encryption and fully secure HIBE with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010)Google Scholar
  20. 20.
    Okamoto, T., Takashima, K.: Homomorphic encryption and signatures from vector decomposition. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 57–74. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  21. 21.
    Okamoto, T., Takashima, K.: Hierarchical predicate encryption for inner-products. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 114–231. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: ACM Conference on Computer and Communication Security 2007, pp. 195–203. ACM, New York (2007)CrossRefGoogle Scholar
  23. 23.
    Pirretti, M., Traynor, P., McDaniel, P., Waters, B.: Secure attribute-based systems. In: ACM Conference on Computer and Communication Security 2006, pp. 99–112. ACM, New York (2006)CrossRefGoogle Scholar
  24. 24.
    Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)Google Scholar
  25. 25.
    Shi, E., Waters, B.: Delegating capability in predicate encryption systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldørsson, M.M., Ingølfsdøttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 560–578. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Waters, B.: Efficient identity based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)Google Scholar
  27. 27.
    Waters, B.: Ciphertext-policy attribute-based encryption: an expressive, efficient, and provably secure realization. ePrint, IACR, http://eprint.iacr.org/2008/290
  28. 28.
    Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tatsuaki Okamoto
    • 1
  • Katsuyuki Takashima
    • 2
  1. 1.NTTTokyoJapan
  2. 2.Mitsubishi ElectricKanagawaJapan

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