The use of elliptic curve cryptosystems on embedded systems has been becoming widespread for some years. Therefore the resistance of such cryptosystems to side-channel attacks is becoming crucial. Several techniques have recently been developed. One of these consists of finding a representation of the elliptic curve such that formulae for doubling and addition are the same. Until now, the best result has been obtained by using the Jacobi model. In this paper, we improve the arithmetic of elliptic curves in the Jacobi model and we relax some conditions required to work efficiently on this model. We thus obtained the fastest unified addition formulae for elliptic curve cryptography (assuming that the curve has a 2-torsion point)