Abstract: The present invention relates to a process for remote authentication of a user (7) for local access to a local machine (4) of a network (5) having a server (3) managed by an administrator (8). The local machine (4) creates a challenge (D) which is communicated to the administrator (8), together with elements known by the user via communication means (9) independent from the network (5). A predetermined calculation is performed by means of the server (3) in order to obtain a first response (RD) to the challenge (D). The response (RD) is first transmitted to the user (7) obtained through the communication means (9). A calculation is performed by means of the local machine (4) in the same way as the server (3) in order to obtain a second response (RD1) to the challenge (D). The first and second responses (RD) and (RD1) and the local connection are authorized based on the result.