Authentication by on-line handwritten signature is one of the most accepted authentication way, this is due to its easy use and to our cultural habits. In order to improve performances of the authentication process, we propose to take into account, on one part, the global temporal aspect and the efficiency of the writing of the signature and, on the other part, the signature variability of a person by using the only available information, the training signatures. To improve the robustness of the process we propose a method which consists of selecting the representative points in the signature. Curves comparison is based on Dynamic Time Warping (DTW) in an original way. The different methods elaborated are tested on two databases of signatures and compared with the standard use of DTW. It shows the relevance of the improvements. All the modifications that we have presented will allow to obtain an improvement of more than 15%.