This work is an extension of a research work presented at ICSIoT 2019. A suggested cryptographic primitive by Carnard et al. 2012 permits the checkability of a plaintext to a ciphertext to determine whether the ciphertext is an encryption of the plaintext. The proposed construction ensures a public plaintext query to a ciphertext. However, their proposed scheme is susceptible to data forgery and re-play attacks during data transmission. Therefore, we propose an improved scheme to resist data forgery and re-play attacks, and to achieve a simultaneous benefit of digital signature and public key encryption. Our proposed scheme achieves a desirable security property of EUF-CMA via the random oracle model.