Public key encryption with equality test (PKEET) has been widely adopted in applications such as private health record management, secure outsourced data processing, and email filtering, owing to its ability to test equality on ciphertexts encrypted under different public keys. However, existing PKEET schemes often fall short in specialized settings, such as case-insensitive matching. Moreover, their security guarantees remain inadequate. In particular, many existing schemes are vulnerable to offline message recovery attacks (OMRA), which present a significant security challenge to PKEET. Furthermore, the existing IND-CCA security model is incomplete, as it fails to model all potential attacks that an adversary could exploit to execute the OMRA. To address these challenges, we propose a new variant of PKEET, termed public key encryption with case-insensitive fuzzy equality test (PKE-CIFET). To analyze security, we propose a unified security model that more closely aligns with IND-CCA security than previous works. This model includes more comprehensive oracles and considers adversaries launching the OMRA through multi-hop testing. Based on this model, we provide a comprehensive and rigorous security proof. Furthermore, experimental results demonstrate that the proposed PKE-CIFET scheme is efficient in terms of computational cost.