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I'm studying post quantum cryptography and recently found McBits (PDF) that is a version of the Niederreiter cryptosystem.

I think I understand most of how the system works, but got a bit confused when I looked at the generation of the keys. In the Niederreiter scheme there is a non singular binary matrix S and a permutation matrix P which I cannot seem to find in McBits.

Do they not use these matrices or have I missed something? If not, does it work without them?

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