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Multi-input Functional Encryption for Unbounded Inner Products

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Provable and Practical Security (ProvSec 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14217))

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Abstract

In this work, we propose a construction for Multi-Input Inner Product Encryption (MIPFE) that can handle vectors of variable length in different encryption slots. This construction is the first of its kind, as all existing MIPFE schemes allow only equal length vectors. The scheme is constructed in the private key setting, providing privacy for both message as well as the function, thereby achieving the so-called full-hiding security. Our MIPFE scheme uses bilinear groups of prime order and achieves security under well studied cryptographic assumptions, namely, the symmetric external Diffie-Hellman assumption.

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References

  1. 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 

  2. Boneh, D., Sahai, A., Waters, B.: Functional encryption: a new vision for public-key cryptography. Commun. ACM 55(11), 56–64 (2012)

    Article  Google Scholar 

  3. O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive (2010)

    Google Scholar 

  4. 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 

  5. 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 

  6. 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 

  7. Boneh, D., Lewi, K., Raykova, M., Sahai, A., Zhandry, M., Zimmerman, J.: Semantically secure order-revealing encryption: multi-input functional encryption without obfuscation. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 563–594. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_19

    Chapter  Google Scholar 

  8. Badrinarayanan, S., Gupta, D., Jain, A., Sahai, A.: Multi-input functional encryption for unbounded arity functions. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 27–51. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_2

    Chapter  Google Scholar 

  9. Brakerski, Z., Komargodski, I., Segev, G.: Multi-input functional encryption in the private-key setting: stronger security from weaker assumptions. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 852–880. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_30

    Chapter  MATH  Google Scholar 

  10. 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 

  11. 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 

  12. 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 

  13. 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 

  14. 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 

  15. Tomida, J.: Tightly secure inner product functional encryption: multi-input and function-hiding constructions. Theor. Comput. Sci. 833, 56–86 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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 

  17. 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 

  18. 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 

  19. Datta, P., Okamoto, T., Tomida, J.: Full-hiding (unbounded) multi-input inner product functional encryption from the k-linear assumption. IACR Cryptol. ePrint Arch., p. 61 (2018)

    Google Scholar 

  20. Lin, H.: Indistinguishability obfuscation from sxdh on 5-linear maps and locality-5 prgs. Cryptology ePrint Archive, Paper 2016/1096 (2016). https://eprint.iacr.org/2016/1096

  21. Tomida, J., Takashima, K.: Unbounded inner product functional encryption from bilinear maps. Jpn. J. Ind. Appl. Math. 37(3), 723–779 (2020). https://doi.org/10.1007/s13160-020-00419-x

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The first author expresses thanks to University Grants Commission (UGC), India for their support.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Bishnu Charan Behera & Somindu C. Ramanna

Authors
  1. Bishnu Charan Behera
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  2. Somindu C. Ramanna
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Correspondence to Bishnu Charan Behera .

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Editors and Affiliations

  1. Hubei University of Technology, Wuhan, China

    Mingwu Zhang

  2. Hong Kong Polytechnic University, Kowloon, Hong Kong

    Man Ho Au

  3. University of Wollongong, Wollongong, NSW, Australia

    Yudi Zhang

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Behera, B.C., Ramanna, S.C. (2023). Multi-input Functional Encryption for Unbounded Inner Products. In: Zhang, M., Au, M.H., Zhang, Y. (eds) Provable and Practical Security. ProvSec 2023. Lecture Notes in Computer Science, vol 14217. Springer, Cham. https://doi.org/10.1007/978-3-031-45513-1_15

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  • DOI: https://doi.org/10.1007/978-3-031-45513-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45512-4

  • Online ISBN: 978-3-031-45513-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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