We extend a commitment scheme based on the learning with errors over rings (\(\mathsf{RLWE}\)) problem, and present efficient companion zero-knowledge proofs of knowledge. Our scheme maps elements from the ring (or equivalently, n elements from \(\mathbb F_q\)) to a small constant number of ring elements. We then construct \(\varSigma \)-protocols for proving, in a zero-knowledge manner, knowledge of the message contained in a commitment. We are able to further extend our basic protocol to allow us to prove additive and multiplicative relations among committed values. Our protocols have a communication complexity of \(\mathcal {O}(Mn\log q)\) and achieve a negligible knowledge error in one run. Here M is the constant from a rejection sampling technique that we employ, and can be set close to 1 by adjusting other parameters. Previously known \(\varSigma \)-protocols for LWE-related languages only achieved a noticeable or even constant knowledge error (thus requiring many repetitions of the protocol), or relied on “smudging” out the error (which necessitates working over large fields, resulting in poor efficiency).