Patent ID: 8102998
Filing Date: 2012-01-24
Classification: G06F,H04L

Abstract:
1. A method for elliptic curve scalar multiplication in an elliptic curve cryptosystem implemented over an insecure communications channel, comprising the steps of: (a) selecting positive integers L (b) storing the positive integers L (c) selecting a projective coordinate system; (d) representing coordinates of a point P=(x,y) on an elliptic curve of the form F(x,y)=y respectively, wherein X, Y and Z are orthogonal projective coordinates in the selected projective coordinate system, and wherein the orthogonal projective coordinates are defined by expressing the elliptic curve in the orthogonal projective coordinates as Y 2 Z 3L -2 =X 3 +aXZ 2L +bZ 3L ; (e) adding together K copies, K being a scalar, of the point P(X,Y (f) storing the scalar multiplication product KP in the computer readable memory; (g) converting the scalar multiplication product from parameterized projective coordinates P(X, Y,Z (h) maintaining the scalar K as private and making the point P(x,y) and the scalar multiplication product KP public for establishing elliptic curve public-key agreement; (i) embedding a plaintext message onto a point on the elliptic curve to form a message point; and (j) adding the message point to the scalar multiplication product KP in order to encrypt the plaintext message, the encrypted plaintext message being stored in the computer readable memory.