We design homomorphic signatures that support arbitrary homomorphic computations from a wide variety of standard falsifiable assumptions (such as decision-linear, or DDH, or learning with errors). Unlike known folklore solutions, we do not put any artificial restrictions on the evaluator, and support homomorphic evaluation on any combination of evaluated signatures. The size of evaluated signatures and verification key grows polynomially in the circuit depth, but is otherwise independent of the circuit/data size. Our designs naturally generalize to multi-key homomorphism. This gives the first multi-key homomorphic signature system with full succinctness under the same set of assumptions. We also achieve full context hiding without sacrificing homomorphism, under the hardness of learning with errors. All our constructions satisfy full (adaptive) security.