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non-prime modulus for Ring-SIS

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Consider the Ring-SIS problem for $R_q=\mathbb{Z}_q[x]/(x^n+1)$ when $n$ is power of $2$ and $q=1 \mod 2n$. Does the modulus $q$ need to be prime? if yes, it seems that it is mainly because of the way that we prove the hardness of Ring-SIS by reducing it to a lattice-problem. This means that it might be possible to choose $q$ non-prime, is there any attack to the case that $q$ is not prime.?

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