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Vendor trapdoor.tar.gz so repo stays self-contained
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intrigus-lgtm committed Jun 26, 2024
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Expand Up @@ -54,7 +54,7 @@ $$N_{L|K}(a) = \Pi_{\sigma \in GAL(L|K)} \sigma(a)$$. To explain what Galois gro

If we now go back to the challenge we get that for one instance the possible values for the flag are a line. If we took two instances and they would intersect we would have found the flag. Sadly they don't (again I don't remember that part of the solve that well, so it is left as an exercise).
But this essentially means we can combine multiple instances to get an iterator that skips more elements. This construction is basically a kind of Chinese remainder theorem.
My solve script especially the last part is hideous, so I won't publish it, but I have included the challenge handout [here](https://files.ctf.kitctf.de/trapdoor/a053f0f33932977546aa3e9720188e42cd8a1c6921ce95908f5f35766e2f53d6/trapdoor.tar.gz) so feel free to try to solve it yourself.
My solve script especially the last part is hideous, so I won't publish it, but I have included the challenge handout [here](/files/gpnctf-22/trapdoor.tar.gz) so feel free to try to solve it yourself.

### Related resources
If you want to know more about Galois theory, consider visiting a university course if you have the chance, otherwise there are many great online resources and books, such as [this](https://www.maths.ed.ac.uk/~tl/gt/gt.pdf) (be warned that most of Galois theory is not about finite fields), but you will probably want to start with an introduction to groups and algebra in general first.
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