Multi-input Functional Encryption

  • Shafi Goldwasser
  • S. Dov Gordon
  • Vipul Goyal
  • Abhishek Jain
  • Jonathan Katz
  • Feng-Hao Liu
  • Amit Sahai
  • Elaine Shi
  • Hong-Sheng Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8441)

Abstract

We introduce the problem of Multi-Input Functional Encryption, where a secret key skf can correspond to an n-ary function f that takes multiple ciphertexts as input. We formulate both indistinguishability-based and simulation-based definitions of security for this notion, and show close connections with indistinguishability and virtual black-box definitions of obfuscation.

Assuming indistinguishability obfuscation for circuits, we present constructions achieving indistinguishability security for a large class of settings. We show how to modify this construction to achieve simulation-based security as well, in those settings where simulation security is possible.

References

  1. 1.
    Agrawal, S., Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption: New perspectives and lower bounds. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 500–518. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Bellare, M., O’Neill, A.: Semantically-secure functional encryption: Possibility results, impossibility results and the quest for a general definition. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 218–234. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Boldyreva, A., Chenette, N., Lee, Y., O’Neill, A.: Order-preserving symmetric encryption. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 224–241. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Boldyreva, A., Chenette, N., O’Neill, A.: Order-preserving encryption revisited: Improved security analysis and alternative solutions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 578–595. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    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
  8. 8.
    De Caro, A., Iovino, V., Jain, A., O’Neill, A., Paneth, O., Persiano, G.: On the achievability of simulation-based security for functional encryption. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 519–535. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013), http://eprint.iacr.org/2013/451
  10. 10.
    Goldwasser, S., Goyal, V., Jain, A., Sahai, A.: Multi-input functional encryption. Cryptology ePrint Archive, Report 2013/727 (2013), http://eprint.iacr.org/
  11. 11.
    Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: STOC (2013)Google Scholar
  12. 12.
    Gordon, S.D., Katz, J., Liu, F.-H., Shi, E., Zhou, H.-S.: Multi-input functional encryption. Cryptology ePrint Archive, Report 2013/774 (2013), http://eprint.iacr.org/
  13. 13.
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM Conference on Computer and Communications Security (2006)Google Scholar
  14. 14.
    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
  15. 15.
    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
  16. 16.
    O’Neill, A.: Definitional issues in functional encryption. IACR Cryptology ePrint Archive, 2010 (2010)Google Scholar
  17. 17.
    Pandey, O., Rouselakis, Y.: Property preserving symmetric encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 375–391. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Sahai, A., Seyalioglu, H.: Worry-free encryption: functional encryption with public keys. In: ACM Conference on Computer and Communications Security, pp. 463–472 (2010)Google Scholar
  19. 19.
    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
  20. 20.
    Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. IACR Cryptology ePrint Archive, 2013 (2013)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Shafi Goldwasser
    • 1
  • S. Dov Gordon
    • 2
  • Vipul Goyal
    • 3
  • Abhishek Jain
    • 4
  • Jonathan Katz
    • 5
  • Feng-Hao Liu
    • 5
  • Amit Sahai
    • 6
  • Elaine Shi
    • 5
  • Hong-Sheng Zhou
    • 7
  1. 1.MIT and WeizmannIsrael
  2. 2.Applied Communication SciencesUSA
  3. 3.Microsoft ResearchIndia
  4. 4.Boston University and MITUSA
  5. 5.University of MarylandUSA
  6. 6.UCLAUSA
  7. 7.Virginia Commonwealth UniversityUSA

Personalised recommendations