Enables a real "Stay signed in"

Instead of trusting the php session, it uses a cookie. The php session
sooner or later is distroyed if not used. It depends upon the server
settings. Using a cookie git rid of this unwanted behaviour.

Dev notes: I wanted to avoid merge conflicts, stay with the main
developper standards and keep the "index.php" in one file. That's why
the code may look a bit shitty. My own dev level my also explain.

Please pay attention to the cryptographic part. The purpose is to
prevent reuse in case of cookie steal.