Patent ID: 7856101

Claim:
A method for elliptic curve scalar multiplication in an elliptic curve cryptosystem implemented over an insecure communications channel using a cryptographic device configured to carry out the steps of the method, comprising the steps of: (a) independently selecting integer exponents, n x and n y ; (b) separately raising a common base, g, to the n x power and to the n y power to form independent x-coordinate and y-coordinate transform parameters L x =g n x and L y =g n y , respectively, where L x ≧2 and L y ≧2; (c) representing coordinates of a point P=(x,y) on an elliptic curve of the form F(x,y)=y 2 −x 3 −ax−b=0 defined over a finite field as projective coordinates according to transforms x = X Z L x and y = Y Z L y , respectively; and (d) adding together K copies, K being a scalar, of the point P(X,Y,Z L x ,Z L y ) to obtain the scalar multiplication product KP.