Patent ID: 7483534
Filing Date: 2009-01-27
Classification: G06F,H04L,Y04S

Abstract:
1. A method for communicating securely over an insecure communication channel between a pair of correspondents who perform shared key cryptographic operations by implementing respective ones of a pair of complimentary mathematical operations utilizing the scalar multiplication of a shared key represented as a value and a base point, said method comprising the steps of: assembling a data string including information to be transferred from a sending correspondent to a receiving corresponding; performing a complimentary mathematical operation using points that satisfy an elliptic polynomial equation with more than one quadratic variable that are termed y-coordinates wherein all the corresponding coordinates of such points are elements of a finite field, F, and wherein the addition of any two of these elliptic points is defined over an extended dimensional that incorporates the additional y-coordinates, and wherein this point addition is computed using arithmetic over a finite field, F; and forwarding the defined set of points over a communication channel to the receiving correspondent and performing the other of the corresponding mathematical cryptographic operations to decrypt the data.