Recently, we introduced an interesting cryptographic primitive: CCA Secure Publicly verifiable Public Key Encryption Without Pairings In the Standard Model (PVPKE) and discussed its application in constructing of chosen cipher text secure proxyre-encryption (PRE) and chosen cipher text secure threshold public key encryption (TPKE) [32]. Recently Hofheiz and Kiltz[16] proposed a practical chosen cipher text secure encryption from factoring assumption in the signed quadratic residues group(HK09 scheme). In this paper, we try to modify the HK09 scheme to meet the requirements of PVPKE, that is, how to publicly verify the cipher text's validity. Towards this goal, we propose three schemes and roughly analysis its feature and security. We believe our results will be useful to guide a final good result.