Functional encryption, as introduced by Boneh, Sahai, and Waters (TCC\'11),generalizes public-key encryption systems to include functional decryption

capabilities. Recently, Boyle et al. as well as Bellare and

Fuchsbauer (both PKC\'14) formalized analogous notions for signature schemes. Here

we discuss that both their notions are limited in terms of expressiveness in the

sense that they cannot cast known signature schemes supporting operations on

data in their frameworks. We therefore propose a notion of what we call, for

sake of distinctiveness, operational signature schemes which captures

functional signatures, policy-based signatures, sanitizable signatures, P-homomorphic signatures, ring

signatures, aggregate signatures etc., and also their message authentication code counterparts.

We discuss possible instantiations for operational signatures.

We give some positive result about achieving our general notion of operational signatures presenting a

compact construction that relies on a new combination of indistinguishability

obfuscation and random oracles. We then indicate that it is unlikely to be able to instantiate

operational signature schemes in general using one-wayness and, under some

circumstances, even using specific ``non-interactive\'\' assumptions like RSA.