If the unique value is secret, yes. Otherwise there is no need to store a table of values. If a home type PC is used for a year, there will be a finite amount

If the unique value is secret, yes. Otherwise there is no need to store a table of values. If a home type PC is used for a year, there will be a finite amount of randomness used from the HW generator in total. Probably under a terabyte I would guess. Maybe under a gigabyte. If you are doing something like looking for an encryption key, you know it's somewhere in that terabyte, which you can generate too, then put every possible block through your hash, and try it. You don't even need to store anything, you can just generate them since they're deterministic. And if the backdoor is based on a block cipher in in counter mode or something like that, you can do it all in parallel on FPGAs in seconds if you're a billionaire.