We present a new approach to authentication using Trusted Execution Environments (TEEs), by changing the location of authentication from a remote device (e.g. remote authentication server) to user device(s) that are TEE enabled. The authentication takes place locally on the user device and only the outcome is sent back to the remote device. Our approach uses existing features and capabilities of TEEs to enhance the security of user authentication. We reverse the way traditional authentication schemes work: instead of the user presenting their authentication data to a remote device, we request the remote device to send the stored authentication template (s) to the local device. Almost paradoxically, this enhances security of authentication data by supplying it only to a trusted device, and so enabling users to authenticate the intended remote entity. This addresses issues related with bad SSL certificates on local devices, DNS poisoning, and counteracts certain threats posed by the presence of malware. We present a protocol to implement such authentication system discussing its strengths and limitations, before identifying available technologies to implement the architecture.