public key private key

Since it is encryption, I definitely don’t want others to know my message, so only I can decrypt it, so it can be concluded that the public key is responsible for encryption, and the private key is responsible for decryption; in the same way, since it is a signature, I definitely don’t want anyone to pretend to be me. Send a message, only I can publish this signature, so it can be concluded that the private key is responsible for the signature, and the public key is responsible for the verification.