US Patent 7961874 XZ-elliptic curve cryptography with secret key embedding

Secure communications over an insecure channel is provided using symmetric key elliptic curve cryptography. More specifically, a shared secret key and/or data bit string is embedded in the X-coordinate and the Z-coordinate of an elliptic curve point defined in projective coordinates, wherein the embedding process is deterministic and non-iterative. In addition, the base point may be blinded by making the base point dependant on the shared secret key.