Attribute Based Signatures for Circuits from Bilinear Map
In attribute based signatures, each signer receives a signing key from the authority, which is associated with the signer's attribute, and using the signing key, the signer can issue a signature on any message under a predicate, if his attribute satisfies the predicate. One of the ultimate goals in this area is to support a wide class of predicates, such as the class of arbitrary circuits, with practical efficiency from a simple assumption, since these three aspects determine the usefulness of the scheme. We present an attribute based signature scheme which allows us to use an arbitrary circuit as the predicate with practical efficiency from the symmetric external Diffie Hellman assumption. We achieve this by combining the efficiency of Groth Sahai proofs, which allow us to prove algebraic equations efficiently, and the expressiveness of Groth Ostrovsky Sahai proofs, which allow us to prove any NP relation via circuit satisfiability.
Public Key Cryptography