More Efficient Constructions for Inner-Product Encryption

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9696)

Abstract

We propose new constructions for inner product encryption – Open image in new window and Open image in new window, both secure under the eXternal Diffie-Hellman assumption (SXDH) in asymmetric pairing groups. The first scheme has constant-size ciphertexts whereas the second one is weakly attribute hiding. Open image in new window is derived from the identity-based encryption scheme of Jutla Roy (Asiacrypt 2013), that was extended from tag-based quasi-adaptive non-interactive zero-knowledge (QA-NIZK) proofs for linear subspaces of vector spaces over bilinear groups. The verifier common reference string (CRS) in these tag-based systems are split into two parts, that are combined during verification. We consider an alternate form of the tag-based QA-NIZK proof with a single verifier CRS that already includes a tag, different from the one defining the language. The verification succeeds as long as the two tags are unequal. Essentially, we embed a two-equation revocation mechanism in the verification. The new QA-NIZK proof system leads to Open image in new window, a constant-sized ciphertext IPE scheme with very short ciphertexts. Both the IPE schemes are obtained by applying the n-equation revocation technique of Attrapadung and Libert (PKC 2010) to the corresponding identity based encryption schemes and proved secure under SXDH assumption. As an application, we show how our schemes can be specialised to obtain the first fully secure identity-based broadcast encryption based on SXDH with a trade-off among the public parameters, ciphertext and key sizes, all of them being sub-linear in the maximum number of recipients of a broadcast.

Keywords

Inner-product encryption Attribute-hiding Constant-size ciphertexts Quasi-adaptive non-interactive zero knowledge proofs 

References

  1. [AL10]
    Attrapadung, N., Libert, B.: Functional encryption for inner product: achieving constant-size ciphertexts with adaptive security or support for negation. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 384–402. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. [Att14]
    Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully secure functional encryption for regular languages, and more. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 557–577. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  3. [Att15]
    Attrapadung, N.: Dual system encryption framework in prime-order groups. IACR Cryptology ePrint Archive 2015:390 (2015)Google Scholar
  4. [BKP14]
    Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 408–425. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  5. [Boy13]
    Boyen, X.: Attribute-based functional encryption on lattices. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 122–142. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. [BSW07]
    Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: IEEE Symposium on Security and Privacy, pp. 321–334. IEEE Computer Society (2007)Google Scholar
  7. [CG13]
    Canetti, R., Garay, J.A. (eds.): CRYPTO 2013, Part II. LNCS, vol. 8043. Springer, Heidelberg (2013)MATHGoogle Scholar
  8. [CGW15]
    Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015)Google Scholar
  9. [CW13]
    Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups. In: Canetti, Garay (eds.) [CG13], pp. 435–460. Full version available as IACR Technical Report, 2013/803. http://eprint.iacr.org/2013/803
  10. [GGH+13]
    Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, Garay (eds.) [CG13], pp. 479–499Google Scholar
  11. [GPSW06]
    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., De Capitani di Vimercati, S. (eds.) ACM Conference on Computer and Communications Security, pp. 89–98. ACM (2006)Google Scholar
  12. [GVW13]
    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)Google Scholar
  13. [GW09]
    Gentry, C., Waters, B.: Adaptive security in broadcast encryption systems (with short ciphertexts). In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 171–188. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. [JR13]
    Jutla, C.S., Roy, A.: Shorter quasi-adaptive NIZK proofs for linear subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 1–20. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. [JR15]
    Jutla, C.S., Roy, A.: Dual-system simulation-soundness with applications to UC-PAKE and more. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 628–653. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48797-6_26 Google Scholar
  16. [KSW08]
    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
  17. [LSW08]
    Lewko, A.B., Sahai, A., Waters, B.: Revocation systems with very small private keys. IACR Cryptology ePrint Archive 2008:309 (2008)Google Scholar
  18. [LW12]
    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)CrossRefGoogle Scholar
  19. [OSW07]
    Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: Ning, P., De Capitani di Vimercati, S., Syverson, P.F. (eds.) ACM Conference on Computer and Communications Security, pp. 195–203. ACM (2007)Google Scholar
  20. [OT08]
    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. [OT09]
    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)CrossRefGoogle Scholar
  22. [OT10]
    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)CrossRefGoogle Scholar
  23. [OT11]
    Okamoto, T., Takashima, K.: Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption. In: Lin, D., Tsudik, G., Wang, X. (eds.) CANS 2011. LNCS, vol. 7092, pp. 138–159. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  24. [Ram16]
    Ramanna, S.C.: More efficient constructions for inner-product encryption. Cryptology ePrint Archive, Report 2016/356 (2016). http://eprint.iacr.org/
  25. [RS14a]
    Ramanna, S.C., Sarkar, P.: Efficient adaptively secure IBBE from standard assumptions. IACR Cryptology ePrint Archive 2014:380 (2014)Google Scholar
  26. [RS14b]
    Ramanna, S.C., Sarkar, P.: Efficient (anonymous) compact HIBE from standard assumptions. In: Chow, S.S.M., Liu, J.K., Hui, L.C.K., Yiu, S.M. (eds.) ProvSec 2014. LNCS, vol. 8782, pp. 243–258. Springer, Heidelberg (2014)Google Scholar
  27. [SW05]
    Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  28. [Wat09]
    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
  29. [Wat11]
    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)CrossRefGoogle Scholar
  30. [Wee14]
    Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire LIPENS de LyonLyonFrance

Personalised recommendations