Given many proofs for linear statements, it should be possible to run batch verification.
Let ${(\vec K_i, c_i, \vec r_i)}_i$ be a sequence of sigma protocols transcripts for the statement $M_i \vec x_i = \vec X_i$. Then, for a $\mu$ be the hash of all the transcripts, we can check all of them at once via
$$
\sum_i \mu^i M_i \vec r_i = \sum_i \mu^i \vec K_i + \mu^i c_i \vec X_i
$$
The batch function can implement this using multi-scalar multiplication. The implementation should be smart enough to recognize when simplifications can be applied because the matrix $M_i$, or the challenge $c_i$, or the instance $\vec X_i$ is repeated.
