We propose a practical zero-knowledge proof system for proving knowledge of short solutions to linear relations which gives the most efficient solution for two naturally-occurring classes of problems. The first is when is very “tall”, which corresponds to a large number of LWE instances that use the same secret . In this case, we show that the proof size is independent of the height of the matrix (and thus the length of the error vector ) and rather only linearly depends on the length of . The second case is when is of the form , which corresponds to proving many LWE instances (with different secrets) that use the same samples . The length of this second proof is square root in the length of , which corresponds to a square root of the length of all the secrets. Our constructions combine recent advances in “purely” lattice-based zero-knowledge proofs with the Reed-Solomon proximity testing ideas present in some generic zero-knowledge proof systems – with the main difference that the latter are applied directly to lattice instances without going through intermediate problems.