I'm pretty sure forensic cameras already exist for this purpose. And as far as I can tell, there isn't really any bulletproof way to do this other than embed a signing key in the camera and hope no one manages to extract it, rendering the whole thing pointless.

I guess you could have a unique signing key per camera and blacklist known leaked keys.

Canon and Nikon both did this. You paid a premium for a “signature analysis” app. The target was for things like law enforcement, where authentication was important.

They got cracked with a year or two. Not sure if they still offer the capability.