I have a client-side certificate in my browser. In theory, this should allow me to use strong authentication for access to my online banking account. All banks use SSL for online banking, but just don't require a client-side certificate for customer authentication.

I would like to use this stronger authentication method, instead of the authentication my bank currently uses.

Since SSL is used anyway for online banking, is there any reason why my bank couldn't link my client-side certificate to my account, and require this form of authentication for access to my account, instead of what they currently use? [Which is: enter loginID, see secret picture, then enter password, or if I've deleted my cookies, answer challenge questions]

When a bank begins making "one-off" exceptions they tend to change existing agreements, make exceptions to policy and set themselves up to fail.

Unless the bank is in the habit of making such exceptions and have a way to automate this, we don't see this happening.