Patent ID: 8369517

Claim:
An elliptic curve cryptographic method performed by a device adapted to perform cryptographic operations, the method comprising: obtaining a point P on an elliptic curve, the point P representing material to be encrypted, the point P defined in a three-dimensional projective coordinate system by x, y, z reference coordinates, the direction of the z reference coordinate in the coordinate system determined by the cross product of the x and y reference coordinates; obtaining an n-bit integer k; computing points P 1 , P 2 on the elliptic curve as a function of P; performing a scalar multiplication operation using P 1 , P 2 , k and n, where during the scalar multiplication operation the point P is recomputed as a function of points P 1 and P 2 , the re-computing including addition and subtraction operations on points P 1 and P 2 , the re-computing resulting in the value of the z coordinate of P 1 being equal to the value of the z coordinate of P 2 ; and providing encrypted material [k]P resulting from the scalar multiplication operation.