Devices, system, and methods of secure entry and handling of passwords and Personal Identification Numbers (PINs), as well as for secure local storage, secure user authentication, and secure payment via mobile devices and via payment terminals. A server includes: an authentication module to send, to a remote client device, a server authentication certificate; an accreditation certificate stored in a pre-defined location on the server, wherein the pre-defined location is accessible to the remote client device; wherein the accreditation certificate indicates a condition that the server authentication certificate needs to meet in order for the server authentication certificate to be accepted for authentication by the remote client device.