Patent ID: 7729494

Claim:
A computer-implemented method for causing at least one processing unit to perform acts comprising: selecting an elliptic curve; determining a Squared Weil pairing based on the elliptic curve; and cryptographically processing selected information based on the Squared Weil pairing; wherein the elliptic curve includes an elliptic curve E over a field K, wherein E can be represented as an equation y 2 =x 3 +ax +b; wherein determining the Squared Weil pairing based on the elliptic curve further includes establishing a point id that is defined as a point at infinity on E, and wherein P, Q, R, X are points on E wherein X is an indeterminate denoting an independent variable of a function, and wherein x(X), y(X) are functions mapping the point X on E to its affine x and y coordinates, and wherein a line passes through the points P, Q, R if P +Q +R = id; wherein determining the Squared Weil pairing based on the elliptic curve further includes: with a first function ƒ j,P and a second function ƒ k,P for two integers j and k, deriving a third function ƒ −j−k,P based on the first and second functions.