Method for cryptographic signature of a datum (m), implemented within an electronic device based on a private key (d) and on a finite group of points of an elliptic curve, said group being provided with an operation of adding two points of the elliptic curve and comprising a generator point, the method comprising the following steps: - determining a first signature point (R 1) through the combination, by way of said operation, of elements equal to a derived first generator point (T 0) of the curve and of number equal to a first intermediate scalar (k), and - determining (E12, E112) a second intermediate scalar (k') by adding or subtracting, to or from a scalar resulting from a product of the first intermediate scalar (k) and of a selected scalar, a scalar resulting from a product of a first derivation scalar (t 1) and of a third intermediate scalar (k"), - determining (E14, E114) a second signature point (R 0) through the combination, by way of said operation, of elements equal to a selected point of the curve and of number equal to the second intermediate scalar (k'), and of other elements equal to a point from among a derived second generator point (T 1) or the opposite of the derived second generator point (T 1) for said operation and of number equal to the third intermediate scalar (k"), - determining a signature portion (s) based on the private key (d), on the first intermediate scalar (k), on an affine coordinate (r 1) of the first signature point (R 1) and on the datum (m), and wherein: - the derived first generator point (T 0) is equal to the combination, by way of said operation, of elements equal to the generator point of the curve and of number equal to a second derivation scalar (t 0), - the derived second generator point (T 1) is equal to the combination, by way of said operation, of elements equal to the selected point of the curve and of number equal to the first derivation scalar (t 1), - the signature of the datum comprises the signature portion (s) and another signature portion determined based on an affine coordinate (r 0) of the second signature point (R 0), - the first signature point and the second signature point are equal, - the other elements are equal to the derived second generator point (T 1) and the step (E12, E112) of determining the second intermediate scalar (k') is based on subtraction, or - the other elements are equal to the opposite of said derived second generator point and the step (E12, E112) of determining the second intermediate scalar (k') is based on addition. - determining a first signature point (R 1) through the combination, by way of said operation, of elements equal to a derived first generator point (T 0) of the curve and of number equal to a first intermediate scalar (k), and - determining (E12, E112) a second intermediate scalar (k') by adding or subtracting, to or from a scalar resulting from a product of the first intermediate scalar (k) and of a selected scalar, a scalar resulting from a product of a first derivation scalar (t 1) and of a third intermediate scalar (k"), - determining (E14, E114) a second signature point (R 0) through the combination, by way of said operation, of elements equal to a selected point of the curve and of number equal to the second intermediate scalar (k'), and of other elements equal to a point from among a derived second generator point (T 1) or the opposite of the derived second generator point (T 1) for said operation and of number equal to the third intermediate scalar (k"), - determining a signature portion (s) based on the private key (d), on the first intermediate scalar (k), on an affine coordinate (r 1) of the first signature point (R 1) and on the datum (m), - the derived first generator point (T 0) is equal to the combination, by way of said operation, of elements equal to the generator point of the curve and of number equal to a second derivation scalar (t 0), - the derived second generator point (T 1) is equal to the combination, by way of said operation, of elements equal to the selected point of the curve and of number equal to the first derivation scalar (t 1), - the signature of the datum comprises the signature portion (s) and another signature portion determined based on an affine coordinate (r 0) of the second signature point (R 0), - the first signature point and the second signature point are equal, - the other elements are equal to the derived second generator point (T 1) and the step (E12, E112) of determining the second intermediate scalar (k') is based on subtraction, or - the other elements are equal to the opposite of said derived second generator point and the step (E12, E112) of determining the second intermediate scalar (k') is based on addition.