Registration-based encryption (RBE) effectively addresses the key escrow problem in identity-based encryption. However, existing post-quantum RBE schemes suffer from prohibitive ciphertext sizes in the gigabyte range for systems with registered users. This poor scalability is a major obstacle to the large-scale implementation of RBE in society. In this work, we propose a framework for constructing efficient RBE schemes that can be instantiated from the learning with errors (LWE) assumption. Specifically, the ciphertext size remains around 221 MB even as the number of registered users increases. The core techniques involve introducing decomposable laconic encryption and integrating it with a refined snapshotting trick. Our work represents an important milestone towards achieving practical post-quantum RBEs.