FE for Inner Products and Its Application to Decentralized ABE

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.

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