There is a statement in the paper "Asymptotically Efficient Lattice-Based Digital Signatures" by Lyubashevsky and Micciancio that says that "it is important that the ring of integers of $\mathbb{Q}(ζ)$, is efficiently samplable in practice - which is not known to be the case for particularly compact choices." Note that $\mathbb{Q}(ζ)$ is the number field where $ζ$ is the primitive root of $f(x)$, where $\mathbb{Z}[x]/\langle f(x) \rangle$ is the ring that we study in lattice-based cryptosystems. Why does the compactness of ring of integers affect the efficiency in sampling these distributions? Also, how does it affect our choices of the ring of integers?



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