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Actually, we do trust many (but obviously not all) post-quantum cryptosystems more than traditional schemes. We haven't been using them because they fail to meet practical space and time trade-offs. When elliptic curve cryptography was first being deployed no one was suggesting using elliptic curve cryptography with classical RSA or Diffie-Hellman in a ...

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Actually, we do trust many (but obviously not all) post-quantum cryptosystems more than traditional schemes. We haven't been using them because they fail to meet practical space and time trade-offs. We start pessimistic with high parameters, then gradually cut down the space by filtering out bad or slow parameter classes until we have reasonable space and ...

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Trusting the algorithms is not a black and white issue. Given that we cannot unequivocally prove the hardness of the problems underlying basic cryptographic primitives, we have no choice but to assume that they are hard. A vast amount of effort in cryptographic research is spent on minimising these assumptions and analysing their hardness. We already have a ...

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convert $v-u \cdot s$ to centered representation as described here seems to work

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Let's answer my question after revisiting the research. Start by quoting the following text from [2]. Note that I've changed the variables names to fit my description. Here $P(X) = T \circ F \circ S(X)$. An open question is to know whether or not these schemes remain secure if the set of polynomials $\mathcal{F}$ is public. In this situation, the ...

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