This system for executing a program to which access by a user is controlled by credentials includes a terminal (T), first memory means (F) associated with said program for storing at least first credentials specific to said user, access control means for authorizing access to said program in response to a match between said first credentials and second credentials applied via said terminal, and a security device (PSD) personal to said user, associated with said terminal and including second memory means (M) for secure storage of said second credentials. The terminal (T) includes at least some of credentials management means (CMP) including means for reading said second credentials and transmitting them to said access control means in response to presentation of a request to access said program, and credentials updating means for selectively commanding the generation and loading into said first and second memory means (F, M) of new credentials replacing the credentials previously stored.