1. A method for authenticating the identity of a device over an unsecured communications channel using a selected elliptic curve and a base point, the method comprising: providing a communication system including a client computer device and a host computer device connected to said client computer device using a communication channel to provide network online services, contents and resources to one or more client devices and their users; encrypting a password using a deterministic and non-iterative process for embedding bit strings into the X coordinates and Z coordinates of points on a projected elliptic curve defined over a finite field and represented in projective coordinates; transmitting the encrypted data from said host computer device over the communication channel to the receiving computer device; and authenticating the password, wherein the projective coordinates ensure that the projected elliptic curve and its twist are isomorphic to each other.