Skip to main content
SpringerLink
Log in

Decentralized Multi-Authority Attribute-Based Inner-Product FE: Large Universe and Unbounded

  • Conference paper
  • First Online:
Public-Key Cryptography – PKC 2023 (PKC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13940))

Included in the following conference series:

  • 781 Accesses

Abstract

This paper presents the first decentralized multi-authority attribute-based inner product functional encryption \((\textsf{MA}\text {-}\textsf{ABIPFE})\) schemes supporting vectors of a priori unbounded lengths. The notion of \(\textsf{AB}\text {-}\textsf{IPFE}\), introduced by Abdalla et al. [ASIACRYPT 2020], combines the access control functionality of attribute-based encryption \((\textsf{ABE})\) with the possibility of evaluating linear functions on encrypted data. A decentralized \(\textsf{MA}\text {-}\textsf{ABIPFE}\) defined by Agrawal et al. [TCC 2021] essentially enhances the \(\textsf{ABE}\) component of \(\textsf{AB}\text {-}\textsf{IPFE}\) to the decentralized multi-authority setting where several authorities can independently issue user keys involving attributes under their control. In \(\textsf{MA}\text {-}\textsf{ABIPFE}\) for unbounded vectors \((\textsf{MA}\text {-}\textsf{ABUIPFE})\), encryptors can encrypt vectors of arbitrary length under access policies of their choice whereas authorities can issue secret keys to users involving attributes under their control and vectors of arbitrary lengths. Decryption works in the same way as for \(\textsf{MA}\text {-}\textsf{ABIPFE}\) provided the lengths of the vectors within the ciphertext and secret keys match.

We present two \(\textsf{MA}\text {-}\textsf{ABUIPFE}\) schemes supporting access policies realizable by linear secret sharing schemes \((\textsf{LSSS})\), in the significantly faster prime-order bilinear groups under decisional assumptions based on the target groups which are known to be weaker compared to their counterparts based in the source groups. The proposed schemes demonstrate different trade-offs between versatility and underlying assumptions. The first scheme allows each authority to control a bounded number of attributes and is proven secure under the well-studied decisional bilinear Diffie-Hellman \((\textsf{DBDH})\) assumption. On the other hand, the second scheme allows authorities to control exponentially many attributes and attributes are not required to be enumerated at the setup, that is, supports large attribute universe, and is proven secure under a non-interactive q-type variant of the \(\textsf{DBDH}\) assumption called L-\(\textsf{DBDH}\), similar to what was used in prior large-universe multi-authority \(\textsf{ABE}\) \((\textsf{MA}\text {-}\textsf{ABE})\) construction.

When compared with the only known \(\textsf{MA}\text {-}\textsf{ABIPFE}\) scheme due to Agrawal et al. [TCC 2021], our schemes offer significantly higher efficiency while offering greater flexibility and security under weaker assumptions at the same time. Moreover, unlike Agrawal et al., our schemes can support the appearance of the same attributes within an access policy arbitrarily many times. Since efficiency and practicality are the prime focus of this work, we prove the security of our constructions in the random oracle model against static adversaries similar to prior works on \(\textsf{MA}\text {-}\textsf{ABE}\) with similar motivations and assumptions. On the technical side, we extend the unbounded \(\textsf{IPFE}\) techniques of Dufour-Sans and Pointcheval [ACNS 2019] to the context of \(\textsf{MA}\text {-}\textsf{ABUIPFE}\) by introducing a novel hash-decomposition technique.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Very recently, Waters, Wee, and Wu [43] presented a lattice-based \(\textsf{MA}\text {-}\textsf{ABE}\) scheme that does not make use of random oracles. However, the scheme relies on a recently introduced complexity assumption called evasive \(\textsf{LWE}\) [44] which is a strong knowledge type assumption and is not yet cryptanalyzed in detail.

  2. 2.

    The ciphertext is re-randomized to ensure the distribution of its components is unharmed.

  3. 3.

    In particular, we consider a map \(\gamma : \mathcal {I}^* \rightarrow [n]\) and use \(\gamma (k) = \iota _k\) throughout the security analysis.

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., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733–751. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_33

    Chapter  Google Scholar 

  4. Abdalla, M., Bourse, F., Caro, A.D., Pointcheval, D.: Better security for functional encryption for inner product evaluations. Cryptology ePrint Archive, Paper 2016/011 (2016). https://eprint.iacr.org/2016/011

  5. Abdalla, M., Catalano, D., Gay, R., Ursu, B.: Inner-product functional encryption with fine-grained access control. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 467–497. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_16

    Chapter  Google Scholar 

  6. Agrawal, S., Bhattacherjee, S., Phan, D.H., Stehlé, D., Yamada, S.: Efficient public trace and revoke from standard assumptions: Extended abstract. CCS 2017, pp. 2277–2293, New York, NY, USA (2017). Association for Computing Machinery

    Google Scholar 

  7. 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 

  8. 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 

  9. Agrawal, S., Goyal, R., Tomida, J.: Multi-party functional encryption. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13043, pp. 224–255. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90453-1_8

    Chapter  Google Scholar 

  10. Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 333–362. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_12

    Chapter  Google Scholar 

  11. Benson, K., Shacham, H., Waters, B.: The k-BDH assumption family: bilinear map cryptography from progressively weaker assumptions. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 310–325. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36095-4_20

    Chapter  Google Scholar 

  12. Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_26

    Chapter  Google Scholar 

  13. 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 

  14. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_30

    Chapter  Google Scholar 

  15. 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 

  16. Chen, J., Gong, J., Kowalczyk, L., Wee, H.: Unbounded ABE via bilinear entropy expansion, revisited. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 503–534. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_19

    Chapter  Google Scholar 

  17. 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 

  18. Datta, P., Dutta, R., Mukhopadhyay, S.: Functional encryption for inner product with full function privacy. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 164–195. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_7

    Chapter  Google Scholar 

  19. Datta, P., Komargodski, I., Waters, B.: Decentralized multi-authority ABE for DNFs from LWE. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 177–209. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77870-5_7

    Chapter  Google Scholar 

  20. Datta, P., Komargodski, I., Waters, B.: Fully adaptive decentralized multi-authority ABE. Cryptology ePrint Archive, Paper 2022/1311 (2022)

    Google Scholar 

  21. Datta, P., Komargodski, I., Waters, B.: Decentralized multi-authority ABE from \({\sf NC}^1\) from computational-BDH. Cryptology ePrint Archive, Paper 2021/1325, ePrint (2021)

    Google Scholar 

  22. Freeman, D.M.: Converting pairing-based cryptosystems from composite-order groups to prime-order groups. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 44–61. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_3

    Chapter  Google Scholar 

  23. Gay, R.: A new paradigm for public-key functional encryption for degree-2 polynomials. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 95–120. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_4

    Chapter  Google Scholar 

  24. 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, pp. 89–98 (2006)

    Google Scholar 

  25. Guillevic, A.: Comparing the pairing efficiency over composite-order and prime-order elliptic curves. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 357–372. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38980-1_22

    Chapter  Google Scholar 

  26. 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 

  27. Jain, A., Lin, H., Sahai, A.: Simplifying constructions and assumptions for \(i\cal{O}\). Cryptology ePrint Archive, Paper 2019/1252 (2019)

    Google Scholar 

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

    Google Scholar 

  29. Lee, J., Kim, D., Kim, D., Song, Y., Shin, J., Cheon, J.H.: Instant privacy-preserving biometric authentication for hamming distance. Cryptology ePrint Archive, Paper 2018/1214 (2018). https://eprint.iacr.org/2018/1214

  30. Lewko, A., Waters, B.: Decentralizing attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 568–588. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_31

    Chapter  Google Scholar 

  31. Lewko, A.: Tools for simulating features of composite order bilinear groups in the prime order setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318–335. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_20

    Chapter  MATH  Google Scholar 

  32. Nguyen, K., Phan, D.H., Pointcheval, D.: Multi-client functional encryption with fine-grained access control. In: Agrawal, S., Lin, D. (eds.) Advances in Cryptology–ASIACRYPT 2022. ASIACRYPT 2022. LNCS, vol 13791, pp. 95–125. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22963-3_4

  33. Okamoto, T., Takashima, K.: Decentralized attribute-based encryption and signatures. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 103-A(1), 41–73 (2020)

    Google Scholar 

  34. O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Paper 2010/556, ePrint (2010)

    Google Scholar 

  35. Pal, T., Dutta, R.: Attribute-based access control for inner product functional encryption from LWE. In: Longa, P., Ràfols, C. (eds.) LATINCRYPT 2021. LNCS, vol. 12912, pp. 127–148. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88238-9_7

    Chapter  Google Scholar 

  36. Rouselakis, Y., Waters, B.: Efficient statically-secure large-universe multi-authority attribute-based encryption. In: Böhme, R., Okamoto, T. (eds.) FC 2015. LNCS, vol. 8975, pp. 315–332. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47854-7_19

    Chapter  Google Scholar 

  37. 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 

  38. Dufour-Sans, E., Pointcheval, D.: Unbounded inner-product functional encryption with succinct keys. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 426–441. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_21

    Chapter  Google Scholar 

  39. Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_18

    Chapter  Google Scholar 

  40. 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 

  41. 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). https://doi.org/10.1007/978-3-642-03356-8_36

    Chapter  Google Scholar 

  42. Waters, B.: Ciphertext-policy attribute-based encryption: an expressive, efficient, and provably secure realization. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 53–70. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_4

    Chapter  Google Scholar 

  43. Waters, B., Wee, H., Wu, D.J.: Multi-authority ABE from lattices without random oracles. In: Kiltz, E., Vaikuntanathan, V. (eds.) Theory of Cryptography. TCC 2022. LNCS, vol. 13747, pp. 651–679. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22318-1_23

  44. Wee, H.: Optimal broadcast encryption and CP-ABE from evasive lattice assumptions. In: Dunkelman, O., Dziembowski, S. (eds.) Advances in Cryptology–EUROCRYPT 2022. EUROCRYPT 2022. LNCS, vol. 13276, pp. 217–241. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-07085-3_8

  45. Zhou, K., Ren, J.: PassBio: privacy-preserving user-centric biometric authentication. IEEE Trans. Inf. Forensics Secur. 13(12), 3050–3063 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Research, Inc., Sunnyvale, CA, 94085, USA

    Pratish Datta

  2. NTT Social Informatics Laboratories, Musashino-shi, Tokyo, 180-8585, Japan

    Tapas Pal

Authors
  1. Pratish Datta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tapas Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tapas Pal .

Editor information

Editors and Affiliations

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

    Alexandra Boldyreva

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

    Vladimir Kolesnikov

Rights and permissions

Reprints and permissions

Copyright information

© 2023 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Datta, P., Pal, T. (2023). Decentralized Multi-Authority Attribute-Based Inner-Product FE: Large Universe and Unbounded. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13940. Springer, Cham. https://doi.org/10.1007/978-3-031-31368-4_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-31368-4_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-31367-7

  • Online ISBN: 978-3-031-31368-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation