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This question is about secret key generation, based on section 4.7 in the design document: https://homenc.github.io/HElib/documentation/Design_Document/HElib-design.pdf

It seems that if $m$ is not a power of two, then we choose coefficients of the secret key such that the secret key is a polynomial of degree $m$. How is it reduced into a polynomial of degree $\phi(m)$? If we just reduce mod $\Phi_m(X)$ then the coefficients may be outside $\{-1,1\}$, so I assume based on the way it is written that there is some other method.

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  • $\begingroup$ Considering HElib's code, it seems that they really just reduce the polynomial modulo $\Phi_m(X)$. $\endgroup$ May 4 '21 at 6:40
  • $\begingroup$ But then the secret key has coefficients outside $\{-1,1\}$. Is this okay with the probability analysis they mention? $\endgroup$
    – jaykopp
    May 4 '21 at 7:35

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