A cryptography method for generating probabilistic digital signatures and/or for a key-exchange a protocol and/or for an encryption algorithm is based on the use of a public key algorithm on abnormal binary elliptic curve, such as a Koblitz curve. A point P (x, y) is selected, and pairs (k.sub.i, P.sub.i) are stored with P.sub.i being the point corresponding to the scalar multiplication of the point P by k.sub.i. A random variable (k) is generated and a point C is calculated that corresponds to the scalar multiplication of P by k. The generation of the random variable (k) and the calculation of the point C are performed simultaneously.