CRYPTOGRAPHY BY PARAMETRISATION ON AN ELLIPTICAL CURVE

摘要

A device is controlled by a controller on the basis of a password. A determination is made at the device or at the controller, on the basis of a random value r1, of a point P(X,Y) on an elliptic curve in a finite body Fq, q being an integer, according to: Ea,b(x, y):x3+ax+b=y2. First and second parameters k and k are obtained such that P(X,Y)=F(K,k), where F is a surjective function of Fq×Fq, in Fq. The first and second parameters are obtained in an encrypted format by encryption in accordance with the password. The first and second encrypted parameters are then transmitted to the controller. During the control, the function F is used, such that, whatever the values of z and z which are input elements of Fq, F(z,z) is a point on the elliptic curve and the input elements do not satisfy the equation.