We propose several new methods to protect the scalar multi- plication on an elliptic curve against Dieren tial Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm. The solutions we suggest complement and improve the state-of-the-art, but also provide a practical toolbox of ecien t countermeasures. These should suit most of the needs for protecting implementations of crypto- algorithm based on elliptic curves.