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: encrypting a password using a deterministic and non-iterative process for embedding bit strings into the X coordinate and Z coordinate of points on a projected elliptic curve defined over a finite field and represented in projective coordinates; transmitting the encrypted data over the communication channel to the receiving device; and authenticating the password, wherein the projective coordinates ensure that the projected elliptic curve and its twist are isomorphic to each other.