unattend-upgrades is a debian package providing automatic security upgrades.
To use it, just install unattended-upgrades, modify /etc/apt/apt.conf.d/50unattended-upgrades to your needs like:
Unattended-Upgrade::Allowed-Origins { "Debian stable"; };
To automatically and unattended install security updates you also have to set
APT::Periodic::Update-Package-Lists "1"; APT::Periodic::Unattended-Upgrade "1";in /etc/apt/apt.conf or in a file located in /etc/apt/apt.conf.d/ (I use /etc/apt/apt.conf.d/60security)