We focus on the problem of how to boost greater confidence in computations outsourced to an untrusted cloud server. Naturally, we aim for solutions that cater for the following two security requirements: data confidentiality/privacy and verifiability of computations. This problem is addressed by the research community through an intriguing paradigm combining a verifiable computation (VC) and a fully homomorphic encryption (FHE). Despite continuing advances in achieving efficient VC and FHE, existing approaches that meet both requirements simultaneously are expensive and impractical for servers and clients. In this work, we first introduce an interesting primitive, called versatile message authenticators, to achieve a verifiable outsourced computation on encrypted data and then give a concrete construction. Without the involvement of FHE, our scheme mainly depends on a pseudo-random function and a adapted Homomorphic MAC scheme. Our solution is proven secure in a strong security model where the adversary is allowed to issue any verification queries. Furthermore, it allows for arbitrary composition and generates constant-size tags. However, our construction just supports linear functions. Finally, our security proof shows its semantic security and unforgeability.