If someone has physical access to your shut-down computer, they can probably break the hard-drive's encryption. This is a "cold boot" attack, and one we thought solved. We have not:
To carry out the attack, the F-Secure researchers first sought a way to defeat the the industry-standard cold boot mitigation. The protection works by creating a simple check between an operating system and a computer's firmware, the fundamental code that coordinates hardware and software for things like initiating booting. The operating system sets a sort of flag or marker indicating that it has secret data stored in its memory, and when the computer boots up, its firmware checks for the flag. If the computer shuts down normally, the operating system wipes the data and the flag with it. But if the firmware detects the flag during the boot process, it takes over the responsibility of wiping the memory beafore anything else can happen.
Looking at this arrangement, the researchers realized a problem. If they physically opened a computer and directly connected to the chip that runs the firmware and the flag, they could interact with it and clear the flag. This would make the computer think it shut down correctly and that the operating system wiped the memory, because the flag was gone, when actually potentially sensitive data was still there.
So the researchers designed a relatively simple microcontroller and program that can connect to the chip the firmware is on and manipulate the flag. From there, an attacker could move ahead with a standard cold boot attack. Though any number of things could be stored in memory when a computer is idle, Segerdahl notes that an attacker can be sure the device's decryption keys will be among them if she is staring down a computer's login screen, which is waiting to check any inputs against the correct ones.