In the article "Short factoring proofs" under "Security parameters:" you list among others "$m$, and $K$". However, $K$ is never used in the rest of the article. Instead, $m$ takes the role of $K$ (from the original paper [PS00]), denoting the number of $z_i$'s. I suggest to rename $m$ to $K$, or vice versa, so that there are no more redundant security parameters.
Also, it would be nice to give more details on the choice of $K$/$m$ in the respective section "Choice of security parameters". For example, you write "$B$ and $\ell$ should satisfy $\ell \cdot \log B = \theta(k)$", so you could add something like "$K$/$m$ should be approximately equal to $k$" (or, heuristically, even smaller, cf. [PS00]).
In the article "Short factoring proofs" under "Security parameters:" you list among others "$m$, and$K$ ". However, $K$ is never used in the rest of the article. Instead, $m$ takes the role of $K$ (from the original paper [PS00]), denoting the number of $z_i$ 's. I suggest to rename $m$ to $K$ , or vice versa, so that there are no more redundant security parameters.$K$ /$m$ in the respective section "Choice of security parameters". For example, you write "$B$ and $\ell$ should satisfy $\ell \cdot \log B = \theta(k)$ ", so you could add something like "$K$/$m$ should be approximately equal to $k$ " (or, heuristically, even smaller, cf. [PS00]).
Also, it would be nice to give more details on the choice of