That's related to the heartbleed bug. While my server (12.04 LTS) was configured to perform unattended install of all security updates, it seems that nginx was not restarted so it was still affected by the bug.
By manually performing the restart the problem was solved, but I am looking for an automatic solution to this kind of problem.
Note: I am using the nginx from nginx.org, not the one from Ubuntu which is, ancient.