I don't think it's a mistake. I think this is actually a trapdoor in the cryptographic sense of the term, and the security hole is the result of them using a ze

I don't think it's a mistake. I think this is actually a trapdoor in the cryptographic sense of the term, and the security hole is the result of them using a zero-knowledge proof scheme based on these kind of trapdoor functions that relies on no-one having a copy of the trapdoor information, but incorrectly letting the untrusted party choose the trapdoor function.