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FE for Inner Products and Its Application to Decentralized ABE

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Public-Key Cryptography – PKC 2019 (PKC 2019)

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Abstract

In this work, we revisit the primitive functional encryption (FE) for inner products and show its application to decentralized attribute-based encryption (ABE). Particularly, we derive an FE for inner products that satisfies a stronger notion, and show how to use such an FE to construct decentralized ABE for the class \(\{0,1\}\)-\(\mathsf {LSSS} \) against bounded collusions in the plain model. We formalize the FE notion and show how to achieve such an FE under the LWE or DDH assumption. Therefore, our resulting decentralized ABE can be constructed under the same standard assumptions, improving the prior construction by Lewko and Waters (Eurocrypt 2011). Finally, we also point out challenges to construct decentralized ABE for general functions by establishing a relation between such an ABE and witness encryption for general NP statements.

Z. Wang—This work was done when the author was visiting Florida Atlantic University.

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Notes

  1. 1.

    We will discuss the secret sharing in more details, but let us focus on the high level concepts at this point.

  2. 2.

    The work [31] can derive an IND adaptively secure scheme for challenge ciphertexts that encrypt a vector of messages, but as we discussed above, IND security seems not sufficient for our application.

  3. 3.

    In our setting, we consider a general case where there is no \(\mathsf {GID} \).

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Acknowledgements

We would like to thank Qiang Tang, Mingsheng Wang for their helpful discussions and suggestions. We also thank the anonymous reviewers of PKC 2019 for their insightful advices. Zhedong Wang is supported by the National Key R&D Program of China-2017YFB0802202. Xiong Fan is supported in part by IBM under Agreement 4915013672 and NSF Award CNS-1561209. Feng-Hao Liu is supported by the NSF Award CNS-1657040. 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 sponsors.

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Wang, Z., Fan, X., Liu, FH. (2019). FE for Inner Products and Its Application to Decentralized ABE. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_4

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