CRYPTOGRAPHY WITH PARAMETRIZATION ON THE ELLIPTIC CURVE

摘要

1. A method for checking device (10) using a controller (11) based on a password (π), comprising the following steps performed on a device or controller: / 1 / based on a random number r determine the point P (X, Y) on an elliptic curve in the final field F, where q is an integer, and the curve is given by the equation: / 2 / get the first and second parameters k and k ′, such that P = F (k, k ′), where F is the surjective function FxFв F; / 3 / receive the first and second parameters in encrypted form through encryption in the form of a function depending on the password; and / 4 / pass the first and second parameters to the controller; the function F is such that, regardless of the input elements z and z ′ from F, F (z, z ′) is a point on the elliptic curve and the input elements do not satisfy equation (1 ) .2. The verification method according to claim 1, in which the function F has the form: F (k, k ′) = f (k ′) + f (k), where f is the invertible function, based on the coefficients a and b of the elliptic curve, to the input where the input parameter is fed and the output receives a point on the elliptic curve; f ′ is the function of generating a point on the elliptic curve, depending on the parameter; moreover, at step / 2 /, the parameters k and k ′ are obtained during the following steps: the value of the parameter k ; calculate the value of f ′ (k ′); determine the value of the parameter k from the following expression: .3. The verification method according to claim 2, in which the function f ′ has the form: f ′ (k ′) = k ′ · G, where G is the generator of the set of points on the elliptic curve; the value of the parameter k is determined from the following expression: 4. The verification method according to claim 2, in which the function f ′ has the form: f ′ (k ′) = f (k ′), and the value of the parameter k is determined from the following expression: 5. The verification method according to any one of claims 1 to 4, in which the function F contains at least one reversible