Patent ID: 7961874

Claim:
A method for communicating securely over an insecure communications channel between two communications devices that perform respective ones of a pair of complementary cryptographic operations, said method comprising: providing a communication system including a computer transmitting device, and a computer receiving device connected together using a communication channel to provide network online services, contents and resources to said computer receiving device and the user of said computer receiving device; assembling a data string including information to be transmitted from a transmitting device to a receiving device; encrypting the data string using a deterministic and non-iterative process for embedding bit strings into 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 decrypting the data using a complementary of the encrypting process, wherein the projective coordinates ensure that the projected elliptic curve and its twist are isomorphic to each other.