In this paper, as a measure to respond to public key attacks that commonly occur in existing asymmetric watermarking systems, we propose a method to additionally generate and distribute public keys for the verification and detection of public key attacks. To configure an effective asymmetric watermarking system, public keys and private keys were generated based on a linear transformation method using special matrixes. The system was designed to be able to generate many public keys that can effectively detect correlations with the same private key when an attack has occurred, so that the system can effectively respond to public key attacks. Based on the results of the experiments, the system was able to effectively detect correlations using public and private keys in images where watermarks had been inserted. In addition, it was found that the system could effectively detect correlations in images under public key attacks by using additionally issued public keys for verification.