The authors construct statistical zero-knowledge authentication protocols for smart cards based on general assumptions. The main protocol is only secure against active attacks, but they present a modification based on trapdoor commitments that can resist concurrent attacks as well. Both protocols are instantiated using lattice-based primitives, which are secure against quantum attacks. To the best of their knowledge, this is the first construction of trapdoor commitments based on lattices. They illustrate the practicality of their main protocol on smart cards in terms of storage, computation, communication, and round complexities, and compare it to other lattice-based authentication protocols, which are either zero-knowledge or have a similar structure.