Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
Apple's Developers Centre Was Target Of Attempted Hack for Information
Apple has today commented on the situation with the Developers portal which has been unavailable for the last couple of days.
Last Thursday, an intruder attempted to secure personal information of our registered developers from our developer website. Sensitive personal information was encrypted and cannot be accessed, however, we have not been able to rule out the possibility that some developers’ names, mailing addresses, and/or email addresses may have been accessed. In the spirit of transparency, we want to inform you of the issue. We took the site down immediately on Thursday and have been working around the clock since then.
In order to prevent a security threat like this from happening again, we’re completely overhauling our developer systems, updating our server software, and rebuilding our entire database. We apologize for the significant inconvenience that our downtime has caused you and we expect to have the developer website up again soon.”