If that's what you want, you've got to encrypt with your own private key and pay some money to use the cloud.

His bank account details encrypted with the bank's public key.

The payment details encrypted with the bank's public key.

The customer's bank account details encrypted with the bank's public key.

The merchant sends the client the bank's response encrypted with the client's public key.

The merchant sends the bank a transaction request encrypted with the bank's public key.

That value is then encrypted with the sender's private key.

The problem is that traffic is still encrypted with their private key.

When you sign a transaction, you are encrypting the information with your private key.

But might be that web access is only available if you don't encrypt with your own key.