I'm trying to implement the zero-knowledge proof presented in this paper. The proof has a rejection step (page 14), which can be computed as follows:
Where B and Z are in $R^{m \times n}$ for some ring. Although I understand how it works for the ring $R=\mathbb{Z}$, I don't get the point of how could work when $R=\mathbb{Z}[x]/(x^{n}+1)$. If I am not misunderstanding something, the Frobenius product between two matrices would output an element in the ring, and thus, the previous algorithm could only operate over integers.
What I am missing? Thanks in advance for your help.