Advertisement

Simplifying Design and Analysis of Complex Predicate Encryption Schemes

  • Shashank Agrawal
  • Melissa Chase
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10210)

Abstract

Wee (TCC’14) and Attrapadung (Eurocrypt’14) introduced predicate and pair encodings, respectively, as a simple way to construct and analyze attribute-based encryption schemes, or more generally predicate encryption. However, many schemes do not satisfy the simple information theoretic property proposed in those works, and thus require much more complicated analysis. In this paper, we propose a new simple property for pair encodings called symbolic security. Proofs that pair encodings satisfy this property are concise and easy to verify. We show that this property is inherently tied to the security of predicate encryption schemes by arguing that any scheme which is not trivially broken must satisfy it. Then we use this property to discuss several ways to convert between pair encodings to obtain encryption schemes with different properties like small ciphertexts or keys. Finally, we show that any pair encoding satisfying our new property can be used to construct a fully secure predicate encryption scheme. The resulting schemes are secure under a new q-type assumption which we show follows from several of the assumptions used to construct such schemes in previous work.

Keywords

Encryption Scheme Security Property Regular Language Full Version Symbolic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    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). doi: 10.1007/978-3-662-49099-0_10 CrossRefGoogle 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). doi: 10.1007/978-3-642-55220-5_31 CrossRefGoogle Scholar
  3. 3.
    Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully-secure functional encryption for regular languages, and more. Cryptology ePrint Archive, Report 2014/428 (2014). http://eprint.iacr.org/2014/428
  4. 4.
    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). doi: 10.1007/978-3-662-53890-6_20 CrossRefGoogle Scholar
  5. 5.
    Attrapadung, N., Hanaoka, G., Yamada, S.: Conversions among several classes of predicate encryption and applications to ABE with various compactness tradeoffs. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 575–601. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48797-6_24 CrossRefGoogle Scholar
  6. 6.
    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). doi: 10.1007/978-3-642-13013-7_23 CrossRefGoogle Scholar
  7. 7.
    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). doi: 10.1007/978-3-642-19379-8_6 CrossRefGoogle Scholar
  8. 8.
    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). doi: 10.1007/978-3-319-16715-2_5 Google Scholar
  9. 9.
    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). doi: 10.1007/978-3-642-20901-7_2 CrossRefGoogle Scholar
  10. 10.
    Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: IEEE Symposium on Security and Privacy, pp. 321–334 (2007)Google Scholar
  11. 11.
    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. LNCS, vol. 8043, pp. 461–478. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40084-1_26 CrossRefGoogle Scholar
  12. 12.
    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). doi: 10.1007/978-3-540-70936-7_29 CrossRefGoogle Scholar
  13. 13.
    Boyen, X.: Attribute-based functional encryption on lattices. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 122–142. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-36594-2_8 CrossRefGoogle Scholar
  14. 14.
    Chase, M.: Multi-authority attribute based encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 515–534. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-70936-7_28 CrossRefGoogle Scholar
  15. 15.
    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). doi: 10.1007/978-3-662-46803-6_20 Google Scholar
  16. 16.
    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
  17. 17.
    Chen, J., Wee, H.: Semi-adaptive attribute-based encryption and improved delegation for boolean formula. In: Abdalla, M., Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 277–297. Springer, Cham (2014). doi: 10.1007/978-3-319-10879-7_16 Google Scholar
  18. 18.
    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). doi: 10.1007/978-3-642-13190-5_3 CrossRefGoogle Scholar
  19. 19.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40–49 (2013)Google Scholar
  20. 20.
    Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Functional encryption without obfuscation. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 480–511. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49099-0_18 CrossRefGoogle Scholar
  21. 21.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: ACM STOC, pp. 545–554 (2013)Google Scholar
  22. 22.
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS, pp. 89–98 (2006). Available as Cryptology ePrint Archive Report 2006/309Google Scholar
  23. 23.
    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). doi: 10.1007/978-3-642-38980-1_22 CrossRefGoogle Scholar
  24. 24.
    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. LNCS, vol. 8616, pp. 261–279. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44371-2_15 CrossRefGoogle Scholar
  25. 25.
    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). doi: 10.1007/978-3-540-78967-3_9 CrossRefGoogle Scholar
  26. 26.
    Kowalczyk, L., Lewko, A.B.: Bilinear entropy expansion from the decisional linear assumption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 524–541. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48000-7_26 CrossRefGoogle Scholar
  27. 27.
    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). doi: 10.1007/978-3-642-29011-4_20 CrossRefGoogle Scholar
  28. 28.
    Lewko, A., Waters, B.: Decentralizing attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 568–588. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-20465-4_31 CrossRefGoogle Scholar
  29. 29.
    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). doi: 10.1007/978-3-642-20465-4_30 CrossRefGoogle Scholar
  30. 30.
    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). doi: 10.1007/978-3-642-32009-5_12 CrossRefGoogle Scholar
  31. 31.
    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). doi: 10.1007/978-3-642-34961-4_22 CrossRefGoogle Scholar
  32. 32.
    Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: ACM CCS, pp. 195–203 (2007)Google Scholar
  33. 33.
    Rouselakis, Y., Waters, B.: Practical constructions and new proof methods for large universe attribute-based encryption. In: ACM CCS, pp. 463–474 (2013)Google Scholar
  34. 34.
    Sahai, A., Seyalioglu, H., Waters, B.: Dynamic credentials and ciphertext delegation for attribute-based encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 199–217. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32009-5_13 CrossRefGoogle Scholar
  35. 35.
    Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). doi: 10.1007/11426639_27 CrossRefGoogle Scholar
  36. 36.
    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). doi: 10.1007/978-3-642-00457-5_27 CrossRefGoogle Scholar
  37. 37.
    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). doi: 10.1007/978-3-642-03356-8_36 CrossRefGoogle Scholar
  38. 38.
    Waters, B.: Functional encryption for regular languages. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 218–235. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32009-5_14 CrossRefGoogle Scholar
  39. 39.
    Waters, B.: A punctured programming approach to adaptively secure functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 678–697. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48000-7_33 CrossRefGoogle Scholar
  40. 40.
    Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-54242-8_26 CrossRefGoogle Scholar
  41. 41.
    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). doi: 10.1007/978-3-642-54631-0_16 CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.Visa ResearchPalo AltoUSA
  2. 2.Microsoft ResearchRedmondUSA

Personalised recommendations