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Improved Inner-Product Encryption with Adaptive Security and Full Attribute-Hiding

  • Jie Chen
  • Junqing GongEmail author
  • Hoeteck Wee
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11273)

Abstract

In this work, we propose two IPE schemes achieving both adaptive security and full attribute-hiding in the prime-order bilinear group, which improve upon the unique existing result satisfying both features from Okamoto and Takashima [Eurocrypt ’12] in terms of efficiency.

  • Our first IPE scheme is based on the standard \(k\textsc {-lin}\) assumption and has shorter master public key and shorter secret keys than Okamoto and Takashima’s IPE under weaker \({\textsc {dlin} }=2\textsc {-lin}\) assumption.

  • Our second IPE scheme is adapted from the first one; the security is based on the \({\textsc {xdlin}}\) assumption (as Okamoto and Takashima’s IPE) but now it also enjoys shorter ciphertexts.

Technically, instead of starting from composite-order IPE and applying existing transformation, we start from an IPE scheme in a very restricted setting but already in the prime-order group, and then gradually upgrade it to our full-fledged IPE scheme. This method allows us to integrate Chen et al.’s framework [Eurocrypt ’15] with recent new techniques [TCC ’17, Eurocrypt ’18] in an optimized way.

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Notes

Acknowledgement

We thank the reviewers for their detailed and constructive feedback.

References

  1. 1.
    Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: generic constructions and simple assumptions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 4–24. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_3CrossRefGoogle Scholar
  2. 2.
    Agrawal, S., Chase, M.: A study of pair encodings: predicate encryption in prime order groups. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 259–288. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49099-0_10CrossRefzbMATHGoogle Scholar
  3. 3.
    Agrawal, S., Chase, M.: Simplifying design and analysis of complex predicate encryption schemes. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 627–656. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-56620-7_22CrossRefGoogle Scholar
  4. 4.
    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).  https://doi.org/10.1007/978-3-642-55220-5_31CrossRefGoogle Scholar
  5. 5.
    Attrapadung, N.: Dual system encryption framework in prime-order groups via computational pair encodings. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 591–623. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_20CrossRefzbMATHGoogle Scholar
  6. 6.
    Attrapadung, N., Yamada, S.: Duality in ABE: converting attribute based encryption for dual predicate and dual policy via computational encodings. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 87–105. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-16715-2_5CrossRefzbMATHGoogle Scholar
  7. 7.
    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 2007Google Scholar
  8. 8.
    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).  https://doi.org/10.1007/978-3-540-24676-3_14CrossRefGoogle Scholar
  9. 9.
    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_30CrossRefGoogle Scholar
  10. 10.
    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).  https://doi.org/10.1007/978-3-540-70936-7_29CrossRefGoogle Scholar
  11. 11.
    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).  https://doi.org/10.1007/978-3-662-46803-6_20CrossRefGoogle Scholar
  12. 12.
    Chen, J., Gong, J.: ABE with tag made easy. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 35–65. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70697-9_2CrossRefGoogle Scholar
  13. 13.
    Chen, J., Gong, J., Kowalczyk, L., Wee, H.: Unbounded ABE via bilinear entropy expansion, revisited. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 503–534. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78381-9_19CrossRefGoogle Scholar
  14. 14.
    Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_8CrossRefGoogle Scholar
  15. 15.
    Gay, R., Hofheinz, D., Kiltz, E., Wee, H.: Tightly CCA-secure encryption without pairings. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 1–27. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49890-3_1CrossRefGoogle Scholar
  16. 16.
    Gong, J., Chen, J., Dong, X., Cao, Z., Tang, S.: Extended nested dual system groups, revisited. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 133–163. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49384-7_6CrossRefGoogle Scholar
  17. 17.
    Gong, J., Dong, X., Chen, J., Cao, Z.: Efficient IBE with tight reduction to standard assumption in the multi-challenge setting. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 624–654. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_21CrossRefGoogle Scholar
  18. 18.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 545–554. ACM Press, June 2013Google Scholar
  19. 19.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 503–523. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_25CrossRefGoogle Scholar
  20. 20.
    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 2006/309Google Scholar
  21. 21.
    Ishai, Y., Wee, H.: Partial garbling schemes and their applications. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 650–662. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-43948-7_54CrossRefzbMATHGoogle Scholar
  22. 22.
    Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78967-3_9CrossRefGoogle Scholar
  23. 23.
    Lewko, A.: Tools for simulating features of composite order bilinear groups in the prime order setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318–335. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_20CrossRefzbMATHGoogle Scholar
  24. 24.
    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).  https://doi.org/10.1007/978-3-642-13190-5_4CrossRefGoogle Scholar
  25. 25.
    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).  https://doi.org/10.1007/978-3-642-32009-5_12CrossRefGoogle Scholar
  26. 26.
    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).  https://doi.org/10.1007/978-3-642-14623-7_11CrossRefGoogle Scholar
  27. 27.
    Okamoto, T., Takashima, K.: Adaptively attribute-hiding (hierarchical) inner product encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 591–608. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_35CrossRefGoogle Scholar
  28. 28.
    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).  https://doi.org/10.1007/978-3-642-34961-4_22CrossRefGoogle Scholar
  29. 29.
    Okamoto, T., Takashima, K.: Efficient (hierarchical) inner-product encryption tightly reduced from the decisional linear assumption. IEICE Trans. 96–A(1), 42–52 (2013)CrossRefGoogle Scholar
  30. 30.
    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 07, pp. 195–203. ACM Press, October 2007Google Scholar
  31. 31.
    Sahai, A., Waters, B.: 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_27CrossRefGoogle Scholar
  32. 32.
    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).  https://doi.org/10.1007/978-3-642-03356-8_36CrossRefGoogle Scholar
  33. 33.
    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_4CrossRefGoogle Scholar
  34. 34.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_7CrossRefGoogle Scholar
  35. 35.
    Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54242-8_26CrossRefGoogle Scholar
  36. 36.
    Wee, H.: Attribute-hiding predicate encryption in bilinear groups, revisited. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 206–233. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70500-2_8CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.East China Normal UniversityShanghaiChina
  2. 2.ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL)LyonFrance
  3. 3.CNRS and ENS, PSLParisFrance

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