Abstract : Attribute-based cryptography is a natural solution for fine-grained access control with respect to security policies. In the case of attribute-based signatures (ABS), users obtain from an authority their secret keys as a function of the attributes they hold, with which they can later sign messages for any predicate satisfied by their attributes. A verifier will be convinced of the fact that the signer's attributes satisfy the signing predicate while remaining completely ignorant of the identity of the signer. In many scenarios where authentication and anonymity are required, like distributed access control mechanisms in ad hoc networks, the bandwidth is a crucial and sensitive concern. The signature size of all previous ABS schemes grows linearly in the number of attributes involved in the signing predicate. We propose the first two attribute-based signature schemes with constant size signatures. Their security is proven in the selective-predicate and adaptive-message setting, in the standard model, under chosen message attacks, with respect to some algorithmic assumptions related to bilinear groups. The described schemes are for the case of threshold predicates, but they can be extended to admit some other (more expressive) kinds of monotone predicates.