It does not have to be absolutely trusted, in the sense of being perfect on all possible inputs. It can be subverted, and/or have bugs, as long as it will compile the compiler-under-test without triggering a subversion or bug.
> Do you think the "Fully" in the title of your thesis is perhaps unfortunate though? Your work seems to re-enforce Thompson's result rather than fully counter it, surely?
No, it's not unfortunate. It's intentional.
Thompson's "trusting trust" attack is dead. Thompson correctly points out a problem with compilers and other lower-level components, but his attack presumes that you can't easily use some other system that acts as a *check* on the first. It's not just that you can recompile something with a different compiler; people noted that in the 1980s.
A key is that DDC lets you *accumulate* evidence. If you want, you can use DDC 10 times, with 10 different trusted compilers; an attacker would have to subvert ALL TEN trusted compilers *AND* the original compiler-under-test executable to avoid detection. Fat chance.
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