Patent ID: 7483533
Filing Date: 2009-01-27
Classification: G06F,H04L

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 representing as a scalar 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 correspondent; performing a complimentary mathematical operation using points that satisfy an elliptic polynomial equation with more than one cubic variable that are termed x-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 space that incorporates the additional x-coordinates, and wherein this point addition is computed using arithmetic over a finite filed 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.