We present simpler and improved constructions of unbounded attribute-based encryption (ABE) schemes with constantsize public parameters under static assumptions in bilinear groups. Concretely, we obtain: - a simple and adaptively secure unbounded ABE scheme in composite-order groups, improving upon a previous construction of Lewko and Waters (Eurocrypt '11) which only achieves selective security; - an improved adaptively secure unbounded ABE scheme based on the k-linear assumption in prime-order groups with shorter ciphertexts and secret keys than those of Okamoto and Takashima (Asiacrypt '12); - the first adaptively secure unbounded ABE scheme for arithmetic branching programs under static assumptions. At the core of all of these constructions is a "bilinear entropy expansion" lemma that allows us to generate any polynomial amount of entropy starting from constant-size public parameters; the entropy can then be used to transform existing adaptively secure "bounded" ABE schemes into unbounded ones.
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