Attribute-based signatures (ABS) allow users to simultaneously sign messages and prove their possession of some attributes while hiding the attributes and revealing only the fact that they satisfy a public policy. In this paper, we propose a generic construction of ABS for circuits of unbounded depth and size, with optimal parameter size—meaning the lengths of public parameters, keys, and signatures are all constant. Our construction can be instantiated from various standard assumptions, including LWE and DLIN. This substantially improves the state-of-the-art ABS scheme by Boyle, Goldwasser, and Ivan (PKC 2014), which, while achieving optimal parameter size, relies on succinct non-interactive arguments of knowledge that can only be constructed from non-standard assumptions. Our generic construction is based on RAM delegations. At a high level, we leverage the fact that the circuit associated with the signature can be made public and compress it using the power of RAM delegation. This allows us to achieve an overall optimal parameter size while simultaneously hiding the user’s attribute.