Abstract: A method for cryptographic signature of a datum comprises determining: a signature point equal to the addition of elements equal to a derived first point and of number equal to a first scalar; a second scalar by subtracting, from the product of the first scalar and of a selected scalar, the product of a third and of a fourth scalar; another signature point equal to the addition of elements equal to a selected point and of number equal to the second scalar, and of elements equal to a derived second point and of number equal to the fourth scalar; and a signature portion based on a private key, on the first scalar, on a coordinate of the signature point and on the datum. The derived first and second point are respectively equal to the addition of elements equal to a generator point and of number equal to a fifth and to the third scalar.