As a bank that has just started providing your customers with access to full service online banking, it is your job to provide them with the highest possible level of security for their accounts at all times. Given the high risk that exists in conducting any kind of business transaction online, you cannot afford to use anything less than the public key cryptography that is available from a Certificate Authority.
Public Key Cryptography Requires Two Halves of the Code
The reason that implementing public key cryptography is so successful is that it requires both parts of the security combination to be a perfect match or all of the information entered by your customers will remain fully encrypted and useless. The public key is used on the portal page to encrypt all of the information your client enters, the private key is held by you or by the Certificate Authority and is used to decrypt the information.