Attribute-based signatures allow us to sign anonymously, in such a way that the signature proves that the signer's attributes satisfy some predicate, but it hides any other information on the signer's attributes beyond that fact. As well as any cryptographic primitive, one of the important goals of the research on this primitive is to construct a scheme that is expressive (supports a wide class of predicates), is practically efficient, and is based on well-studied cryptographic assumptions. The authors construct attribute-based signature schemes that support any Boolean circuit of unbounded depth and number of gates, are practically efficient, from the symmetric bilinear Diffie-Hellman assumption. Toward this end, they combine the Groth-Sahai proof system, which serve as an efficient proof system for algebraic equations, and the Groth-Ostrovsky-Sahai proof system, which are still inefficient, but can prove any NP language via a Karp reduction to circuit satisfiability.