Semi-adaptive Security and Bundling Functionalities Made Generic and Easy

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9986)

Abstract

Semi-adaptive security is a notion of security that lies between selective and adaptive security for Attribute-Based Encryption (ABE) and Functional Encryption (FE) systems. In the semi-adaptive model the attacker is forced to disclose the challenge messages before it makes any key queries, but is allowed to see the public parameters.

We show how to generically transform any selectively secure ABE or FE scheme into one that is semi-adaptively secure with the only additional assumption being public key encryption, which is already naturally included in almost any scheme of interest. Our technique utilizes a fairly simple application of garbled circuits where instead of encrypting directly, the encryptor creates a garbled circuit that takes as input the public parameters and outputs a ciphertext in the underlying selective scheme. Essentially, the encryption algorithm encrypts without knowing the ‘real’ public parameters. This allows one to delay giving out the underlying selective parameters until a private key is issued, which connects the semi-adaptive to selective security. The methods used to achieve this result suggest that the moral gap between selective and semi-adaptive security is in general much smaller than that between semi-adaptive and full security.

Finally, we show how to extend the above idea to generically bundle a family of functionalities under one set of public parameters. For example, suppose we had an inner product predicate encryption scheme where the length of the vectors was specified at setup and therefore fixed to the public parameters. Using our transformation one could create a system where for a single set of public parameters the vector length is not apriori bounded, but instead is specified by the encryption algorithm. The resulting ciphertext would be compatible with any private key generated to work on the same input length.

References

  1. 1.
    Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21–40. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Ananth, P., Brakerski, Z., Segev, G., Vaikuntanathan, V.: From selective to adaptive security in functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 657–677. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  3. 3.
    Ananth, P., Jain, A.: Indistinguishability obfuscation from compact functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 308–326. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  4. 4.
    Ananth, P., Jain, A., Sahai, A.: Achieving compactness generically: indistinguishability obfuscation from non-compact functional encryption. IACR Cryptology ePrint Archive (2015)Google Scholar
  5. 5.
    Ananth, P., Sahai, A.: Functional encryption for turing machines. In: Kushilevitz, E., et al. (eds.) TCC 2016-A. LNCS, vol. 9562, pp. 125–153. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49096-9_6 CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (Im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Proceedings of the 2012 ACM Conference on Computer and Communications Security, CCS 2012, pp. 784–796 (2012)Google Scholar
  9. 9.
    Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: FOCS (2015)Google Scholar
  10. 10.
    Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 213. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Boneh, D., Gentry, C., Gorbunov, S., Halevi, S., Nikolaenko, V., Segev, G., Vaikuntanathan, V., Vinayagamurthy, D.: 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)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    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
  16. 16.
    Brakerski, Z., Vaikuntanathan, V.: Circuit-abe from LWE: unbounded attributes and semi-adaptive security. IACR Cryptology ePrint Archive (2016)Google Scholar
  17. 17.
    Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    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
  20. 20.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indstinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)Google Scholar
  21. 21.
    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
  22. 22.
    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
  23. 23.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 162–179. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: STOC (2013)Google Scholar
  25. 25.
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006 (2006)Google Scholar
  26. 26.
    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
  27. 27.
    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
  28. 28.
    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
  29. 29.
    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
  30. 30.
    O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010)Google Scholar
  31. 31.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005Google Scholar
  32. 32.
    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
  33. 33.
    Sahai, A., Waters, B.: Slides on functional encryption. PowerPoint presentation (2008). http://www.cs.utexas.edu/~bwaters/presentations/files/functional.ppt
  34. 34.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)Google Scholar
  35. 35.
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    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)CrossRefGoogle Scholar
  38. 38.
    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)CrossRefGoogle Scholar
  39. 39.
    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
  40. 40.
    Yao, A.: How to generate and exchange secrets. In: FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA

Personalised recommendations