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Multi-input Attribute Based Encryption and Predicate Encryption

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13507))

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Abstract

Motivated by several new and natural applications, we initiate the study of multi-input predicate encryption (\(\textsf{miPE}\)) and further develop multi-input attribute based encryption (\(\textsf{miABE}\)). Our contributions are:

  1. 1.

    Formalizing Security: We provide definitions for \(\textsf{miABE}\) and \(\textsf{miPE}\) in the symmetric key setting and formalize security in the standard indistinguishability (IND) paradigm, against unbounded collusions.

  2. 2.

    Two-input \({\textsf{ABE}}\) for \({\textsf{NC}}_1\) from \(\textsf{LWE}\) and Pairings: We provide the first constructions for two-input key-policy \({\textsf{ABE}}\) for \({\textsf{NC}}_1\) from \(\textsf{LWE}\) and pairings. Our construction leverages a surprising connection between techniques recently developed by Agrawal and Yamada (Eurocrypt, 2020) in the context of succinct single-input ciphertext-policy \({\textsf{ABE}}\), to the seemingly unrelated problem of two-input key-policy \({\textsf{ABE}}\). Similarly to Agrawal-Yamada, our construction is proven secure in the bilinear generic group model. By leveraging inner product functional encryption and using (a variant of) the KOALA knowledge assumption, we obtain a construction in the standard model analogously to Agrawal, Wichs and Yamada (TCC, 2020).

  3. 3.

    Heuristic two-input \({\textsf{ABE}}\) for \(\textsf{P}\) from Lattices: We show that techniques developed for succinct single-input ciphertext-policy \({\textsf{ABE}}\) by Brakerski and Vaikuntanathan (ITCS 2022) can also be seen from the lens of \(\textsf{miABE}\) and obtain the first two-input key-policy \({\textsf{ABE}}\) from lattices for \(\textsf{P}\).

  4. 4.

    Heuristic three-input \({\textsf{ABE}}\) and \({\textsf{PE}}\) for \({\textsf{NC}}_1\) from Pairings and Lattices: We obtain the first three-input \({\textsf{ABE}}\) for \({\textsf{NC}}_1\) by harnessing the powers of both the Agrawal-Yamada and the Brakerski-Vaikuntanathan constructions.

  5. 5.

    Multi-input \({\textsf{ABE}}\) to multi-input \({\textsf{PE}}\) via Lockable Obfuscation: We provide a generic compiler that lifts multi-input \({\textsf{ABE}}\) to multi-input \({\textsf{PE}}\) by relying on the hiding properties of Lockable Obfuscation (\(\textsf{LO}\)) by Wichs-Zirdelis and Goyal-Koppula-Waters (FOCS 2018), which can be based on \(\textsf{LWE}\). Our compiler generalises such a compiler for single-input setting to the much more challenging setting of multiple inputs. By instantiating our compiler with our new two and three-input \({\textsf{ABE}}\) schemes, we obtain the first constructions of two and three-input \({\textsf{PE}}\) schemes.

Our constructions of multi-input \({\textsf{ABE}}\) provide the first improvement to the compression factor of non-trivially exponentially efficient Witness Encryption defined by Brakerski et al. (SCN 2018) without relying on compact functional encryption or indistinguishability obfuscation. We believe that the unexpected connection between succinct single-input ciphertext-policy \({\textsf{ABE}}\) and multi-input key-policy \({\textsf{ABE}}\) may lead to a new pathway for witness encryption. We remark that our constructions provide the first candidates for a nontrivial class of \({\textsf{miFE}}\) without needing \(\textsf{LPN}\) or low depth \(\textsf{PRG}\).

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Notes

  1. 1.

    We note that a message m separate from attribute \(\textbf{x}\) is not required in the definition of \(\textsf{FE}\), but we include it here for simpler comparison with \({\textsf{PE}}\) and \({\textsf{ABE}}\).

  2. 2.

    The length of the attribute is set to \(2\ell \) to match our two-input setting.

  3. 3.

    The construction described here is simplified. For example, we omit the additional message carrying part in the construction, which is not necessary for the overview.

References

  1. Abdalla, M., Benhamouda, F., Gay, R.: From single-input to multi-client inner-product functional encryption. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 552–582. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_19

    Chapter  Google Scholar 

  2. Abdalla, M., Benhamouda, F., Kohlweiss, M., Waldner, H.: Decentralizing inner-product functional encryption. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 128–157. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_5

    Chapter  Google Scholar 

  3. Abdalla, M., Catalano, D., Fiore, D., Gay, R., Ursu, B.: Multi-input functional encryption for inner products: function-hiding realizations and constructions without pairings. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 597–627. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_20

    Chapter  Google Scholar 

  4. Abdalla, M., Gay, R., Raykova, M., Wee, H.: Multi-input inner-product functional encryption from pairings. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 601–626. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_21

    Chapter  Google Scholar 

  5. Agrawal, S.: Indistinguishability obfuscation without multilinear maps: new techniques for bootstrapping and instantiation. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 191–225. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_7

    Chapter  Google Scholar 

  6. 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). https://doi.org/10.1007/978-3-642-25385-0_2

    Chapter  Google Scholar 

  7. Agrawal, S., Goyal, R., Tomida, J.: Multi-input quadratic functional encryption from pairings. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12828, pp. 208–238. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84259-8_8

    Chapter  Google Scholar 

  8. Agrawal, S., Wichs, D., Yamada, S.: Optimal broadcast encryption from LWE and pairings in the standard model. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12550, pp. 149–178. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64375-1_6

    Chapter  Google Scholar 

  9. Agrawal, S., Yadav, A., Yamada, S.: Multi-input attribute based encryption and predicate encryption. IACR Cryptology ePrint Archive (2022)

    Google Scholar 

  10. Agrawal, S., Yamada, S.: Optimal broadcast encryption from pairings and LWE. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 13–43. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_2

    Chapter  Google Scholar 

  11. 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 

  12. Ananth, P., Jain, A., Lin, H., Matt, C., Sahai, A.: Indistinguishability obfuscation without multilinear maps: iO from LWE, bilinear maps, and weak pseudorandomness. In: CRYPTO (2019)

    Google Scholar 

  13. 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). https://doi.org/10.1007/978-3-642-55220-5_31

    Chapter  Google Scholar 

  14. Barak, B., et al.: On the (Im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1

    Chapter  Google Scholar 

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

    Google Scholar 

  16. Boneh, D., et al.: 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). https://doi.org/10.1007/978-3-642-55220-5_30

    Chapter  Google Scholar 

  17. 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 

  18. 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 

  19. Brakerski, Z., Jain, A., Komargodski, I., Passelègue, A., Wichs, D.: Non-trivial witness encryption and Null-iO from standard assumptions. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 425–441. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_23

    Chapter  MATH  Google Scholar 

  20. Brakerski, Z., Vaikuntanathan, V.: Circuit-ABE from LWE: unbounded attributes and semi-adaptive security. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 363–384. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_13

    Chapter  Google Scholar 

  21. Brakerski, Z., Vaikuntanathan, V.: Lattice-inspired broadcast encryption and succinct ciphertext policy ABE. In: ITCS (2022)

    Google Scholar 

  22. 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, Cham (2014). https://doi.org/10.1007/978-3-319-10879-7_16

    Chapter  Google Scholar 

  23. Chotard, J., Dufour Sans, E., Gay, R., Phan, D.H., Pointcheval, D.: Decentralized multi-client functional encryption for inner product. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 703–732. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_24

    Chapter  Google Scholar 

  24. Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 630–656. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_31

    Chapter  Google Scholar 

  25. Datta, P., Okamoto, T., Tomida, J.: Full-hiding (Unbounded) multi-input inner product functional encryption from the k-linear assumption. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 245–277. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_9

    Chapter  Google Scholar 

  26. Gay, R., Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from simple-to-state hard problems: new assumptions, new techniques, and simplification. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 97–126. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77883-5_4

    Chapter  Google Scholar 

  27. Goldwasser, S., et al.: Multi-input functional encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578–602. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_32

    Chapter  Google Scholar 

  28. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute based encryption for circuits. In: STOC (2013)

    Google Scholar 

  29. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 503–523. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_25

    Chapter  Google Scholar 

  30. Gorbunov, S., Vinayagamurthy, D.: Riding on asymmetry: efficient ABE for branching programs. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 550–574. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_23

    Chapter  Google Scholar 

  31. Goyal, R., Koppula, V., Waters, B.: Lockable obfuscation. In: FOCS (2017)

    Google Scholar 

  32. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS (2006)

    Google Scholar 

  33. Jain, A., Lin, H., Matt, C., Sahai, A.: How to leverage hardness of constant-degree expanding polynomials over \(\mathbb{R}\) to build \(i\cal{O}\). In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 251–281. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_9

    Chapter  Google Scholar 

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

    Google Scholar 

  35. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from LPN over large fields, DLIN, and constant depth PRGs. In: EUROCRYPT (2022)

    Google Scholar 

  36. 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 

  37. 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). https://doi.org/10.1007/978-3-642-13190-5_4

    Chapter  Google Scholar 

  38. 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). https://doi.org/10.1007/978-3-642-20465-4_30

    Chapter  Google Scholar 

  39. 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). https://doi.org/10.1007/978-3-642-32009-5_12

    Chapter  Google Scholar 

  40. Libert, B., Ţiţiu, R.: Multi-client functional encryption for linear functions in the standard model from LWE. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 520–551. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_18

    Chapter  MATH  Google Scholar 

  41. Lin, H.: Indistinguishability obfuscation from constant-degree graded encoding schemes. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 28–57. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49890-3_2

    Chapter  Google Scholar 

  42. Lin, H.: Indistinguishability obfuscation from SXDH on 5-linear maps and locality-5 PRGs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 599–629. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_20

    Chapter  Google Scholar 

  43. Lin, H., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: FOCS (2016)

    Google Scholar 

  44. López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: STOC (2012)

    Google Scholar 

  45. Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_26

    Chapter  Google Scholar 

  46. 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). https://doi.org/10.1007/978-3-642-14623-7_11

    Chapter  Google Scholar 

  47. Okamoto, T., Takashima, K.: Adaptively attribute-hiding (Hierarchical) inner product encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 591–608. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_35

    Chapter  Google Scholar 

  48. 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 

  49. Shi, E., Bethencourt, J., Chan, T.H., Song, D., Perrig, A.: Multi-dimensional range query over encrypted data. In: SP (2007)

    Google Scholar 

  50. Tomida, J.: Tightly secure inner product functional encryption: multi-input and function-hiding constructions. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 459–488. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_16

    Chapter  Google Scholar 

  51. 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). https://doi.org/10.1007/978-3-642-32009-5_14

    Chapter  Google Scholar 

  52. Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_26

    Chapter  Google Scholar 

  53. Wichs, D., Zirdelis, G.: Obfuscating compute-and-compare programs under LWE. In: FOCS (2017)

    Google Scholar 

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Acknowledgements

The third author was partially supported by JST AIP Acceleration Research JPMJCR22U5 and JSPS KAKENHI Grant Number 19H01109, Japan.

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Authors and Affiliations

  1. IIT Madras, Chennai, India

    Shweta Agrawal & Anshu Yadav

  2. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Shota Yamada

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  1. Shweta Agrawal
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  2. Anshu Yadav
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  3. Shota Yamada
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Correspondence to Anshu Yadav .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Agrawal, S., Yadav, A., Yamada, S. (2022). Multi-input Attribute Based Encryption and Predicate Encryption. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13507. Springer, Cham. https://doi.org/10.1007/978-3-031-15802-5_21

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