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Functional Encryption Against Probabilistic Queries: Definition, Construction and Applications

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Public-Key Cryptography – PKC 2023 (PKC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13941))

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Abstract

Functional encryption (FE for short) can be used to calculate a function output of a message, without revealing other information about the message. There are mainly two types of security definitions for FE, exactly simulation-based security (SIM-security) and indistinguishability-based security (IND-security). Both of them have some limitations: FE with SIM-security supporting all circuits cannot be constructed for unbounded number of ciphertext and/or key queries, while IND-security is sometimes not enough: there are examples where an FE scheme is IND-secure but not intuitively secure. In this paper, we present a new security definition which can avoid the drawbacks of both SIM-security and IND-security, called indistinguishability-based security against probabilistic queries (pIND-security for short), and we give an FE construction for all circuits which is secure for unbounded key/ciphertext queries under this new security definition. We prove that this new security definition is strictly between SIM-security and IND-security, and provide new applications for FE which were not known to be constructed from IND-secure or SIM-secure FE.

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Notes

  1. 1.

    We also note that a trapdoor may not only be hidden in the function, but also in the messages. We slightly modify the function in Example 1.2, and let f be defined as: \(f(pk,m,r)=\mathsf {PKE.Enc}(pk,m;r)\), and \(M_b=\{pk\}\times \{m_b\}\times \mathcal {R}\), so \(f(M_0)\) and \(f(M_1)\) are distributions with trapdoor, and the trapdoor is hidden in the message distribution, not the function.

  2. 2.

    Here we allows different distributions \(\bar{M'}_b^j\) to include the same randomness \(\bar{r}^*\), which means that there is a shared inner state between these sampling algorithms. We note that SIM-secure FE implies pIND-secure FE even considering stateful ciphertext queries like this, so it will not affect the validity of the proof.

References

  1. 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). https://doi.org/10.1007/978-3-662-48000-7_32

    Chapter  MATH  Google Scholar 

  2. Agrawal, S., Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption: new perspectives and lower bounds. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 500–518. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_28

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-662-47989-6_15

    Chapter  Google Scholar 

  4. Agrawal, S., Koppula, V., Waters, B.: Impossibility of simulation secure functional encryption even with random oracles. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 659–688. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_24

    Chapter  MATH  Google Scholar 

  5. Agrawal, S., Libert, B., Maitra, M., Titiu, R.: Adaptive simulation security for inner product functional encryption. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 34–64. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_2

    Chapter  Google Scholar 

  6. Agrawal, S., Maitra, M.: FE and iO for turing machines from minimal assumptions. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 473–512. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_18

    Chapter  Google Scholar 

  7. Agrawal, S., Wu, D.J.: Functional encryption: deterministic to randomized functions from simple assumptions. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 30–61. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_2

    Chapter  Google Scholar 

  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_14

    Chapter  Google Scholar 

  9. Bartusek, J., et al.: Public-key function-private hidden vector encryption (and more). In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 489–519. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_17

    Chapter  Google Scholar 

  10. Barbosa, M., Farshim, P.: On the semantic security of functional encryption schemes. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 143–161. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_10

    Chapter  Google Scholar 

  11. 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, Cham (2013). https://doi.org/10.1007/978-3-319-02937-5_12

    Chapter  Google Scholar 

  12. 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). https://doi.org/10.1007/978-3-642-40084-1_26

    Chapter  MATH  Google Scholar 

  13. Brakerski, Z., Segev, G.: Function-private functional encryption in the private-key setting. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 306–324. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_12

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-642-19571-6_16

    Chapter  Google Scholar 

  15. Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T., eds., Advances in Cryptology: Proceedings of CRYPTO ’82, Santa Barbara, California, USA, August 23–25, 1982, pp. 199–203. Plenum Press, New York (1982)

    Google Scholar 

  16. Döttling, N., Nishimaki, R.: Universal proxy re-encryption. In: Garay, J.A. (ed.) PKC 2021. LNCS, vol. 12710, pp. 512–542. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-75245-3_19

    Chapter  Google Scholar 

  17. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, 26–29 October, 2013, Berkeley, CA, USA, pp. 40–49. IEEE Computer Society (2013)

    Google Scholar 

  18. Gentry, C., Halevi, S., Raykova, M., Wichs, D.: Outsourcing private RAM computation. In: 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18–21, 2014, pp. 404–413. IEEE Computer Society (2014)

    Google Scholar 

  19. Goyal, V., Jain, A., Koppula, V., Sahai, A.: Functional encryption for randomized functionalities. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 325–351. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_13

    Chapter  Google Scholar 

  20. Gay, R., Pass, R.: Indistinguishability obfuscation from circular security. In: Samir Khuller and Virginia Vassilevska Williams, editors, STOC ’21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21–25, 2021, pp. 736–749. ACM (2021)

    Google Scholar 

  21. 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). https://doi.org/10.1007/978-3-642-32009-5_11

    Chapter  Google Scholar 

  22. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. In: Khuller, S., Williams, V.V., editors, STOC ’21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21–25, 2021, pp. 60–73. ACM (2021)

    Google Scholar 

  23. Kim, S., Lewi, K., Mandal, A., Montgomery, H., Roy, A., Wu, D.J.: Function-hiding inner product encryption is practical. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 544–562. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_29

    Chapter  Google Scholar 

  24. Lin, H., Pass, R., Seth, K., Telang, S.: Output-compressing randomized encodings and applications. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 96–124. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49096-9_5

    Chapter  Google Scholar 

  25. Marc, T., Stopar, M., Hartman, J., Bizjak, M., Modic, J.: Privacy-enhanced machine learning with functional encryption. In: Sako, K., Schneider, S., Ryan, P.Y.A. (eds.) ESORICS 2019. LNCS, vol. 11735, pp. 3–21. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29959-0_1

    Chapter  Google Scholar 

  26. O’Neill, A.: Definitional issues in functional encryption. In: IACR Cryptol. ePrint Arch., p. 556 (2010)

    Google Scholar 

  27. Patranabis, S., Mukhopadhyay, D., Ramanna, S.C.: Function private predicate encryption for low min-entropy predicates. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 189–219. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_7

    Chapter  Google Scholar 

  28. Ryffel, T., Sans, E.D., Gay, R., Bach, F.R., Pointcheval, D.: Partially encrypted machine learning using functional encryption. CoRR, abs/1905.10214 (2019)

    Google Scholar 

  29. Wee, H., Wichs, D.: Candidate obfuscation via oblivious LWE sampling. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 127–156. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77883-5_5

    Chapter  Google Scholar 

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Acknowledgement

This work is partially supported by the National Key R &D Program of China (No. 2020YFA0712300) and the National Natural Science Foundation of China (No. 62202294, No. 62272294).

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Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, P. R. China

    Geng Wang, Shi-Feng Sun, Zhedong Wang & Dawu Gu

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  1. Geng Wang
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Correspondence to Dawu Gu .

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  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Wang, G., Sun, SF., Wang, Z., Gu, D. (2023). Functional Encryption Against Probabilistic Queries: Definition, Construction and Applications. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13941. Springer, Cham. https://doi.org/10.1007/978-3-031-31371-4_15

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  • DOI: https://doi.org/10.1007/978-3-031-31371-4_15

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