# ZKPoK for RLWE secret and error

I came across How to validate the secret of a Ring Learning with Errors (RLWE) key paper by Ding et al., which seems to provide a ZK proof that the given $$p$$ is of the form $$as + e$$ with $$s, e$$ small and that the prover knows the corresponding $$s$$ value. However, their proof seems to be interactive. I was wondering whether there exists a non-interactive PoK for this, which in addition to proving knowledge of $$s$$ also proves knowledge of the error vector $$e$$?