We propose a Key-policy Attribute-based Encryption (KP-ABE) scheme for (monotone) Boolean circuits based on bilinear maps. The construction is based on secret sharing and just one bilinear map, and it is a proper extension of the KP-ABE scheme in [7] in the sense that it is practically efficient for a class of Boolean circuits which strictly includes all Boolean formulas. Selective security of the proposed scheme in the standard model is proved, and comparisons with the scheme in [5] based on leveled multilinear maps, are provided. Thus, for Boolean circuits representing multilevel access structures, our KP-ABE scheme is more efficient than the one in [5].
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