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Decentralized Multi-authority ABE for \(\textsf{NC}^1\) from BDH

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Abstract

Decentralized multi-authority attribute-based encryption (\(\textsf{MA}\)-\(\textsf{ABE}\)) is a strengthening of standard ciphertext-policy attribute-based encryption so that there is no trusted central authority: Any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. Essentially, any party can act as an authority for some attribute by creating a public key of its own and issuing private keys to different users that reflect their attributes. This paper presents the first \(\textsf{MA}\)-\(\textsf{ABE}\) proven secure under the standard search variant of bilinear Diffie–Hellman (CBDH) and in the random oracle model. Our scheme supports all access policies captured by \(\textsf{NC}^1\) circuits. All previous constructions were proven secure in the random oracle model and additionally were based on decision assumptions such as the DLIN assumption, non-standard q-type assumptions, or subspace decision assumptions over composite-order bilinear groups.

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Notes

  1. The decision version of BDH asks to distinguish \(e(g,g)^{abc}\) from a random (target) group element given random \((g,g^a, g^b, g^c)\), while the search version asks to compute \(e(g,g)^{abc}\) given \((g,g^a, g^b, g^c)\).

  2. If \(e :{\mathbb {G}} \times {\mathbb {G}} \rightarrow {\mathbb {G}}_T\) is a bilinear map, then we refer to elements in \({\mathbb {G}}\) as being in the source group or bilinear group.

  3. In DLIN it is assumed to be hard to distinguish between \(g^{a+b}\) from a random (source) group element given random elements \((g,v,w,v^a,w^b)\) in the source group.

  4. Note that currently, the only known technique to achieve adaptive security for \(\textsf{ABE}\) is Waters’ “dual system encryption” methodology [55, 79] which crucially relies on the hidden subgroup or subspace structure.

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Authors and Affiliations

  1. NTT Research, Sunnyvale, CA, USA

    Pratish Datta, Ilan Komargodski & Brent Waters

  2. Hebrew University, Jerusalem, Israel

    Ilan Komargodski

  3. UT Austin, Austin, TX, USA

    Brent Waters

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  1. Pratish Datta
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Datta, P., Komargodski, I. & Waters, B. Decentralized Multi-authority ABE for \(\textsf{NC}^1\) from BDH. J Cryptol 36, 6 (2023). https://doi.org/10.1007/s00145-023-09445-7

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