In theory DRM could be mathematically perfect. However DRM relies on actual implementations both in software and hardware and shares a lot with broader security. Software implementations can have bugs but it’s relatively easy to ship fixes. The hardware level however is where it becomes very difficult to ensure a valid implementation of “secure compute” or “trusted zones” which are key to DRM and general security, particularly from an agent with physical access. It costs money to ship new fixed hardware, if it’s even possible. Then even if a given hardware implementation is correct there are ways to physically glitch the hardware to skip the checks. ESP32 chips had an issue like that where the hardware encryption was correct but simply “glitching” the voltage at the correct time could cause the processor to skip the encryption check entirely [1]. It’s very difficult and costly to make hardware immune to all such attacks. Small seemingly unrelated physical details can become novel ways to break the encryption system (like specter).
Ultimately I’ve come to believe that DRM and it’s cousin of system security is an economic game. So DRM useless in that it will probably be cracked after some time, but that time can translate to revenues or control until that point. It depends on how much money you have to throw at either hardening and cracking systems. It’ll likely become harder (i.e. more expensive) in the future to crack hardware DRM in the future as the technology becomes more sophisticated and classes of vulnerability are discovered and mitigated. But then the cracks become more valuable both for anti-DRM or anti-security.
How can DRM ever be perfect? It relies on your computer to be able to decrypt the data so it an never be "mathematically perfect" like regular encryption can be.
Current DRM is all about shoving the decryption part as deep in to a chip as possible and betting on the fact that it is physically too hard to extract that info. So it will always be exploitable with some amount of effort.
The DRM implementation and algorithm could be "perfect" in a mathematical sense, but as you point out they tend to rely on a PUF in the silicon hardware. Currently very hard to extract but not completely so. However, say a system had a quantum based PUF then it could be unclonable due to QM. Such a system could still be potentially cracked by causing issues in the processor itself like with the ESP32s. Which was my point, since there's a physical system to work in it'd be impossible in a practice to make perfect. Hence it boils down to economics.
It doesn't boil down to economics at all. Even if you push a googolplex dollars into perfecting it. If you wanted you can still relatively easily snoop the electrical signals that control an LCD to reconstruct the video. This is not possible to encrypt and never will be.
It could only be described as "mathematically perfect" in the sense that without the decryption key, the encrypted data is no more useful than random bytes.
But DRM fundamentally needs to have the decryption key available at the end user's device - which at least in my opinion, makes it better described as "provably mathematically impossible".
You still have to deliver the new keys to the clients. As long as the client can decrypt the file, the client can also decrypt and dump it to storage. And if the top pirates keep their methods secret, you can change the keys all you want and not know how they are extracting them each time.
Ultimately I’ve come to believe that DRM and it’s cousin of system security is an economic game. So DRM useless in that it will probably be cracked after some time, but that time can translate to revenues or control until that point. It depends on how much money you have to throw at either hardening and cracking systems. It’ll likely become harder (i.e. more expensive) in the future to crack hardware DRM in the future as the technology becomes more sophisticated and classes of vulnerability are discovered and mitigated. But then the cracks become more valuable both for anti-DRM or anti-security.
1: https://raelize.com/blog/espressif-systems-esp32-bypassing-s...