With the rapid advancements in innovative technologies like cloud computing, internet of things, and mobile computing, the paradigm to delegate the heavy computational tasks from trusted and resource-constrained devices to potentially untrusted and more powerful services has gained a lot of attention. Ensuring the verifiability of the outsourced computation along with the security and privacy requirements is an active research area. Several cryptographic protocols have been proposed by using pairing-based cryptographic techniques based on bilinear maps of suitable elliptic curves. However, the computational overhead of bilinear maps forms the most expensive part of those protocols. In this paper, we propose a new 1–checkable algorithm under the one-malicious version of a two-untrusted-program model. Our solution is approximately twice as efficient as the single comparably efficient 1–checkable solution in the literature, and requires only 4 elliptic curve point additions in the preimage and 6 field multiplications in the image of the bilinear map.