I don't know enough about the details of the build dependencies for any of these projects to give exact steps. To get a known-clean build (that is, a build guaranteed to match the source) of GCC 4.8.1, plug the GCC 4.8.1 into the procedure I gave above:

In case it wasn't clear, k is used for indexing, and I use "function application" f(x) to mean compilation of x by compiler f.

"Take one compiler source (GCC 4.8.1), and compile it with a diverse collection of compilers (Ck being a compiler in { C0 = GCC 4.8.1, C2 = LLVM, C3 = icc, C4 = visual c/c++, ...}[1]), producing a diverse collection of binaries that are compilations of GCC 4.8.1: (Bk = Ck(GCC 4.8.1)). Because the different compilers are almost certainly not functionally identical, the various Bk should not be expected to be bitwise identical. However, because they are compilations of the same source, they should be functionally identical, or one of the original compilers was broken (accidentally or deliberately). So now we can compile that original source with the Bk compilers, and because these compilers are functionally identical, the results (Bk(GCC 4.8.1)) should be bitwise identical. If there are any differences, you can manually inspect them to determine what the issue is and either issue a bug report to the appropriate compiler, change the source (GCC 4.8.1) to avoid undefined behavior, or notify people of the attack present in the compiler in question, depending on what you find. This does involve some binary digging, but quite targeted compared to a full audit and it may well not be necessary at all."

Likewise for any of the others, but note that once you've got a known-clean build of any (sufficiently capable) compiler you could use it to build known-clean builds of the others.

[1] the more compilers and the more diverse the background of the compilers, the better; it may well be worth using quite slow compilers that are proven correct and/or implemented in other (possibly interpreted) languages for a high degree of confidence.

One of the most useful forms of diversity is the "my opponent does not have access to time machine" defense. e.g. use some C compiler for amiga, or 1980's DEC unix, or whatever to bootstrap gcc3 for windows, and use that to bootstrap clang for linux, etc. The odds that hardware and binaries you've had for 30 years could carry a trojan that successfully applies to a compiler that was not written yet, for an architecture that was not designed yet, inserting a trojan for yet another such pair, seem low. Feel free to follow more than one such path if paranoia dictates. When you arrive at the end (some compiler, built with itself), the binaries should all match however you got there, presuming no undefined behavior in the compiler itself. If there is something, fix it.

And better yet if this chosen starting point(s), being old, are also small and simple.

I mostly agree, although careful about cross contamination if you're intending to actually use DDC - clang bootstrapped by gcc3 is not going to be independent of gcc3.

You're not giving a useful procedure for me. Let's say that only Gcc can compile itself and its own libraries (e.g version n-1 can compile version n). How can I make trusted GCC 4.8.1 if other compilers won't compile the sources of GCC? Do you agree that I have to implement all the features of GCC used in the sources of GCC in one or more other compilers? If not, don't I have to have a trusted GCC from the start? And if I have such GCC, then I don't need other implementations anyway?

I am not sure if gcc was able to compile itself always, but if it was, you can argue that there existed a smallest kernel of gcc sometime ago that did not depend on any of the "features" of gcc that makes it impossible for other compilers to compile gcc. Now, if there existed such a thing before, it probably exists now, because the incremental "features" that make it impossible for other compilers to compile gcc, would make it impossible for gcc too. My bet would be that there exists a logical separation somewhere, and there is still a small kernel in it, that you can bootstrap with other compilers, from which point you can do what your parent says.

You do need other compilers that can compile the GCC source. These do not need to be trusted, just diverse in origin so that they are unlikely to contain the same attacks.

If GCC is in fact the only thing that can compile GCC, then you cannot use DDC to get a trusted version of GCC.