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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.

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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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Correspondence to Anshu Yadav .

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  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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