Public-key encryption with equality (PKEET) test enables testing if two ciphertexts, possibly under two different public keys, encrypt the same messages. Recent research on PKEET considers the setting where the testing ability is delegated to semi-trusted parties to negate unfettered chosen-plaintext attacks. In this work, we revise and enhance the PKEET security model, and introduce a new property of unmaskability which further prevents an attacker from skirting the test. We then propose a simple and efficient PKEET system with adaptive chosen-ciphertext security, provably secure under our revised security model, from either plain or ring lattice assumptions. The construction adopts a direct approach which significantly departs from the existing way of building such systems. Compared with existing literature, our system relies on weaker learning-with-errors assumptions while also being more efficient and providing better security.