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Dynamic Collusion Bounded Functional Encryption from Identity-Based Encryption

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13276))

Abstract

Functional Encryption is a powerful notion of encryption in which each decryption key is associated with a function f such that decryption recovers the function evaluation f(m). Informally, security states that a user with access to function keys \(\mathsf {sk}_{f_1}, \mathsf {sk}_{f_2}, \ldots \) (and so on) can only learn \(f_1(m), f_2(m), \ldots \) (and so on) but nothing more about the message. The system is said to be q-bounded collusion resistant if the security holds as long as an adversary gets access to at most \(q = q(\lambda )\) function keys. A major drawback of such statically bounded collusion systems is that the collusion bound q must be declared at setup time and is fixed for the entire lifetime of the system.

We initiate the study of dynamically bounded collusion resistant functional encryption systems which provide more flexibility in terms of selecting the collusion bound, while reaping the benefits of statically bounded collusion FE systems (such as quantum resistance, simulation security, and general assumptions). Briefly, the virtues of a dynamically bounded scheme can be summarized as:

  • Fine-grained individualized selection. It lets each encryptor select the collusion bound by weighing the trade-off between performance overhead and the amount of collusion resilience.

  • Evolving encryption strategies. Since the system is no longer tied to a single collusion bound, thus it allows to dynamically adjust the desired collusion resilience based on any number of evolving factors such as the age of the system, or a number of active users, etc.

  • Ease and simplicity of updatability. None of the system parameters have to be updated when adjusting the collusion bound. That is, the same key \(\mathsf {sk}_f\) can be used to decrypt ciphertexts for collusion bound \(q = 2\) as well as \(q = 2^\lambda \).

We construct such a dynamically bounded functional encryption scheme for the class of all polynomial-size circuits under the general assumption of Identity-Based Encryption.

R. Goyal—Research supported in part by NSF CNS Award #1718161, an IBM-MIT grant, and by the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR00112020023. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

B. Waters—Supported by NSF CNS-1908611, CNS-1414082, Packard Foundation Fellowship, and Simons Investigator Award.

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Notes

  1. 1.

    Both works, this work and [3], were submitted to Crypto 2021.

  2. 2.

    However, note that it is essential that the master public-secret keys and every function key is resuable for all values of the collusion bound.

  3. 3.

    Technically, we compress the keys even further as we replace all the PKE key pairs with a single IBE key pair instead of a sequence of IBE key pairs. However, for the purpose of this overview, we present this simpler version.

  4. 4.

    One coud additionally consider the setup algorithm to take as input a sequence of functionality indices where the function class and message space are characterized by all such indices (e.g., having input length and circuit depth as functionality indices). For ease of notation, we keep a single functionality index in the above definition.

  5. 5.

    Although most prior works on bounded collusion security consider the collusion bound q to either be a global parameter, or given in unary to the setup algorithm. Here we instead pass it in binary for technical reasons as will become clear in the sequel. See Remark 1 for more details.

  6. 6.

    To be more precise, \(\varPi ^m\) should also contain the empty function and the evaluation of empty function on challenge message \((\epsilon _n, \epsilon _n(m))\). However, for ease of notation, throughout the paper we assume that to be implicitly added to the list of function-value pairs.

References

  1. Agrawal, S.: Stronger security for reusable garbled circuits, general definitions and attacks. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 3–35. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_1

    Chapter  Google Scholar 

  2. Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_28

    Chapter  MATH  Google Scholar 

  3. Agrawal, S., Maitra, M., Vempati, N.S., Yamada, S.: Functional encryption for turing machines with dynamic bounded collusion from LWE. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12828, pp. 239–269. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84259-8_9

    Chapter  Google Scholar 

  4. Agrawal, S., Rosen, A.: Functional encryption for bounded collusions, revisited. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 173–205. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_7

    Chapter  Google Scholar 

  5. 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 

  6. Ananth, P., Jain, K., Sahai, A.: Indistinguishability obfuscation from functional encryption for simple functions. Cryptology ePrint Archive, Report 2015/730 (2015)

    Google Scholar 

  7. Ananth, P., Vaikuntanathan, V.: Optimal bounded-collusion secure functional encryption. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 174–198. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36030-6_8

    Chapter  Google Scholar 

  8. Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: CCS 2012 (2012)

    Google Scholar 

  9. Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: FOCS (2015)

    Google Scholar 

  10. Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  11. 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 

  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). https://doi.org/10.1007/978-3-540-70936-7_29

    Chapter  Google Scholar 

  13. Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: Miller, G.L. (ed.) STOC (1996)

    Google Scholar 

  14. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. J. Cryptol. 25(4), 601–639 (2011). https://doi.org/10.1007/s00145-011-9105-2

    Article  MathSciNet  MATH  Google Scholar 

  15. Chen, Y., Vaikuntanathan, V., Waters, B., Wee, H., Wichs, D.: Traitor-tracing from LWE made simple and attribute-based. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 341–369. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_13

    Chapter  Google Scholar 

  16. 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). https://doi.org/10.1007/3-540-45325-3_32

    Chapter  Google Scholar 

  17. Cramer, R., et al.: Bounded CCA2-secure encryption. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 502–518. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_31

    Chapter  Google Scholar 

  18. Diffie, W., Hellman, M.E.: New directions in cryptography (1976)

    Google Scholar 

  19. Dodis, Y., Katz, J., Xu, S., Yung, M.: Key-insulated public key cryptosystems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 65–82. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_5

    Chapter  Google Scholar 

  20. Garg, R., Goyal, R., Lu, G., Waters, B.: Dynamic collusion bounded functional encryption from identity-based encryption. Cryptology ePrint Archive (2021)

    Google Scholar 

  21. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS (2013)

    Google Scholar 

  22. Gentry, S., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206 (2008)

    Google Scholar 

  23. Goldwasser, S., Lewko, A., Wilson, D.A.: Bounded-collusion IBE from key homomorphism. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 564–581. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_32

    Chapter  Google Scholar 

  24. 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 

  25. Goyal, R., Koppula, V., Waters, B.: Semi-adaptive security and bundling functionalities made generic and easy. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 361–388. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_14

    Chapter  Google Scholar 

  26. Goyal, R., Koppula, V., Waters, B.: Collusion resistant traitor tracing from learning with errors. In: STOC (2018)

    Google Scholar 

  27. Goyal, R., Syed, R., Waters, B.: Bounded collusion abe for tms from ibe. Cryptology ePrint Archive, Report 2021/709 (2021)

    Google Scholar 

  28. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. In: STOC (2021)

    Google Scholar 

  29. 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). https://doi.org/10.1007/978-3-540-78967-3_9

    Chapter  Google Scholar 

  30. Kowalczyk, L., Malkin, T., Ullman, J., Wichs, D.: Hardness of non-interactive differential privacy from one-way functions. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 437–466. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_15

    Chapter  Google Scholar 

  31. Sahai, A., Seyalioglu, H.: Worry-free encryption: functional encryption with public keys. In: CCS (2010)

    Google Scholar 

  32. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27

    Chapter  Google Scholar 

  33. Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: STOC, pp. 475–484 (2014)

    Google Scholar 

  34. Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5

    Chapter  Google Scholar 

  35. Yao, A.: How to generate and exchange secrets. In: FOCS, pp. 162–167 (1986)

    Google Scholar 

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Acknowledgements

We thank the anonymous reviewers for CRYPTO 2021 for useful feedback regarding our abstractions.

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Authors and Affiliations

  1. UT Austin, Austin, USA

    Rachit Garg, George Lu & Brent Waters

  2. MIT, Cambridge, USA

    Rishab Goyal

  3. NTT Research, Palo Alto, USA

    Brent Waters

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  1. Rachit Garg
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Correspondence to Rachit Garg or Rishab Goyal .

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Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Garg, R., Goyal, R., Lu, G., Waters, B. (2022). Dynamic Collusion Bounded Functional Encryption from Identity-Based Encryption. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13276. Springer, Cham. https://doi.org/10.1007/978-3-031-07085-3_25

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