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Multi-authority ABE from Lattices Without Random Oracles

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13747))

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Abstract

Attribute-based encryption (ABE) extends public-key encryption to enable fine-grained control to encrypted data. However, this comes at the cost of needing a central trusted authority to issue decryption keys. A multi-authority ABE (MA-ABE) scheme decentralizes ABE and allows anyone to serve as an authority. Existing constructions of MA-ABE only achieve security in the random oracle model.

In this work, we develop new techniques for constructing MA-ABE for the class of subset policies (which captures policies such as conjunctions and DNF formulas) whose security can be based in the plain model without random oracles. We achieve this by relying on the recently-proposed “evasive” learning with errors (LWE) assumption by Wee (EUROCRYPT 2022) and Tsabury (CRYPTO 2022).

Along the way, we also provide a modular view of the MA-ABE scheme for DNF formulas by Datta et al.  (EUROCRYPT 2021) in the random oracle model. We formalize this via a general version of a related-trapdoor LWE assumption by Brakerski and Vaikuntanathan (ITCS 2022), which can in turn be reduced to the plain LWE assumption. As a corollary, we also obtain an MA-ABE scheme for subset policies from plain LWE with a polynomial modulus-to-noise ratio in the random oracle model. This improves upon the Datta et al. construction which relied on LWE with a sub-exponential modulus-to-noise ratio. Moreover, we are optimistic that the generalized related-trapdoor LWE assumption will also be useful for analyzing the security of other lattice-based constructions.

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Notes

  1. 1.

    As noted in [DKW21a, Remark 6.1], the MA-ABE scheme therein requires a monotone secret-sharing scheme where reconstruction has small coefficients and the joint distribution of the unauthorized shares are uniformly random; such a scheme is only known for subset policies and DNFs.

  2. 2.

    See the descriptions of Hybrid 5 and the analysis of Lemmas 5.5 and 6.5 in [DKW21a], where noise smuging is used for simulating secret keys.

  3. 3.

    In the selective security game, the adversary starts by committing to the set X associated with the challenge ciphertext. The reduction algorithm is then allowed to program X into the public parameters of the scheme.

  4. 4.

    Some restriction on \(\textbf{M}\) is also necessary. For instance, it is easy to distinguish if \(\textbf{M}= \textbf{u}^{\scriptscriptstyle \textsf{T}}\), or more generally, if \(\textbf{u}_0^{\scriptscriptstyle \textsf{T}} \textbf{M}= \textbf{u}\) for some \(\textbf{u}_0 \in \{0,1\}^k\).

  5. 5.

    Concretely, \(\textbf{u}^{\scriptscriptstyle \textsf{T}} = [1 ~|~ \textbf{x}^{\scriptscriptstyle \textsf{T}}]\) and \(\textbf{M}= [1 ~|~ \textbf{y}^{\scriptscriptstyle \textsf{T}}]\) for some \(\textbf{x},\textbf{y}\in \{0,1\}^{L-1}\). The adversary is restricted to queries \(\textbf{y}\ne \textbf{x}\), which is implied by our requirement that \(\bar{\textbf{M}}\) has full rank.

  6. 6.

    In the static security model [RW15], we require the adversary to commit to the set of corrupted authorities, the secret-key queries, and the challenge ciphertext query at the beginning of the security game. Previous lattice-based MA-ABE constructions were also analyzed in the static security model [DKW21a].

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Acknowledgments

We thanks the TCC reviewers for helpful suggestions. B. Waters is supported by NSF CNS-1908611, a Simons Investigator award, and the Packard Foundation Fellowship. D. J. Wu is supported by NSF CNS-2151131, CNS-2140975, a Microsoft Research Faculty Fellowship, and a Google Research Scholar award.

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Authors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Brent Waters & David J. Wu

  2. NTT Research, Sunnyvale, CA, USA

    Brent Waters & Hoeteck Wee

  3. CNRS, ENS, PSL, Paris, France

    Hoeteck Wee

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  1. Brent Waters
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Correspondence to David J. Wu .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Waters, B., Wee, H., Wu, D.J. (2022). Multi-authority ABE from Lattices Without Random Oracles. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13747. Springer, Cham. https://doi.org/10.1007/978-3-031-22318-1_23

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