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A Study of Pair Encodings: Predicate Encryption in Prime Order Groups

  • Shashank Agrawal
  • Melissa Chase
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9563)

Abstract

Pair encodings and predicate encodings, recently introduced by Attrapadung [2] and Wee [36] respectively, greatly simplify the process of designing and analyzing predicate and attribute-based encryption schemes. However, they are still somewhat limited in that they are restricted to composite order groups, and the information theoretic properties are not sufficient to argue about many of the schemes. Here we focus on pair encodings, as the more general of the two. We first study the structure of these objects, then propose a new relaxed but still information theoretic security property. Next we show a generic construction for predicate encryption in prime order groups from our new property; it results in either semi-adaptive or full security depending on the encoding, and gives security under SXDH or DLIN. Finally, we demonstrate the range of our new property by using it to design the first semi-adaptively secure CP-ABE scheme with constant size ciphertexts.

Keywords

Predicate encryption Attribute-based encryption Pair encoding schemes Dual system technique Short ciphertexts 

References

  1. 1.
    Akinyele, J.A., Pagano, M.W., Green, M.D., Lehmann, C.U., Peterson, Z.N.J., Rubin, A.D.: Securing electronic medical records using attribute-based encryption on mobile devices. In: SPSM 2011, ACM Workshop Security and Privacy in Smartphones and Mobile Devices 2011, pp. 75–86 (2011)Google Scholar
  2. 2.
    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. 3.
    Attrapadung, N.: Dual system encryption framework in prime-order groups. Cryptology ePrint Archive, Report 2015/390 (2015). http://eprint.iacr.org/2015/390
  4. 4.
    Attrapadung, N., Hanaoka, G., Yamada, S.: Conversions among several classes of predicate encryption and their applications. Cryptology ePrint Archive, Report 2015/431 (2015). http://eprint.iacr.org/2015/431
  5. 5.
    Attrapadung, N., Libert, B., de Panafieu, E.: Expressive key-policy attribute-based encryption with constant-size ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 90–108. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  6. 6.
    Baden, R., Bender, A., Spring, N., Bhattacharjee, B., Starin, D.: Persona: an online social network with user-defined privacy. In: ACM SIGCOMM 2009 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 135–146 (2009)Google Scholar
  7. 7.
    Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  8. 8.
    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 (2007)Google Scholar
  9. 9.
    Boneh, D., Raghunathan, A., Segev, G.: Function-private identity-based encryption: hiding the function in functional encryption. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 461–478. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    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) CrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    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
  13. 13.
    Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 435–460. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  14. 14.
    Chen, J., Wee, H.: Dual system groups and its applications – compact HIBE and more. Cryptology ePrint Archive, Report 2014/265 (2014). http://eprint.iacr.org/2014/265
  15. 15.
    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) Google Scholar
  16. 16.
    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, Part II. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  17. 17.
    Freeman, D.M.: Converting pairing-based cryptosystems from composite-order groups to prime-order groups. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 44–61. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  18. 18.
    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 (2006). Available as Cryptology ePrint Archive Report 2006/309Google Scholar
  19. 19.
    Guillevic, A.: Comparing the pairing efficiency over composite-order and prime-order elliptic curves. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 357–372. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  20. 20.
    Herold, G., Hesse, J., Hofheinz, D., Ràfols, C., Rupp, A.: Polynomial spaces: a new framework for composite-to-prime-order transformations. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 261–279. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  21. 21.
    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
  22. 22.
    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) CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    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) CrossRefGoogle 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) CrossRefGoogle 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) CrossRefGoogle Scholar
  27. 27.
    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) CrossRefGoogle Scholar
  28. 28.
    Pirretti, M., Traynor, P., McDaniel, P., Waters, B.: Secure attribute-based systems. In: Juels, A., Wright, R.N., Vimercati, S. (eds.) ACM CCS 2006, pp. 99–112. ACM Press (2006)Google Scholar
  29. 29.
    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 (2013)Google Scholar
  30. 30.
    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
  31. 31.
    Santos, N., Rodrigues, R., Gummadi, K.P., Saroiu, S.: Policy-sealed data: a new abstraction for building trusted cloud services. In: USENIX Security Symposium 2012, pp. 175–188 (2012)Google Scholar
  32. 32.
    Shen, E., Shi, E., Waters, B.: Predicate privacy in encryption systems. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 457–473. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  33. 33.
    Takashima, K.: Expressive attribute-based encryption with constant-size ciphertexts from the decisional linear assumption. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 298–317. Springer, Heidelberg (2014) Google Scholar
  34. 34.
    Traynor, P., Butler, K.R.B., Enck, W., McDaniel, P.: Realizing massive-scale conditional access systems through attribute-based cryptosystems. In: NDSS 2008. The Internet Society (2008)Google Scholar
  35. 35.
    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
  36. 36.
    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
  37. 37.
    Yamada, S., Attrapadung, N., Hanaoka, G., Kunihiro, N.: A framework and compact constructions for non-monotonic attribute-based encryption. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 275–292. Springer, Heidelberg (2014) CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.University of Illinois Urbana-ChampaignChampaignUSA
  2. 2.Microsoft ResearchRedmondUSA

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