Fueled by its successful commercialization, the recommender system (RS) has gained widespread attention. However, as the training data fed into the RS models are often highly sensitive, it ultimately leads to severe privacy concerns, especially when data are shared among different platforms. In this paper, we follow the tune of existing works to investigate the problem of secure sparse matrix multiplication for cross-platform RSs. Two fundamental while critical issues are addressed: preserving the training data privacy and breaking the data silo problem. Specifically, we propose two concrete constructions with significantly boosted efficiency. They are designed for the sparse location insensitive case and location sensitive case, respectively. State-of-the-art cryptography building blocks including homomorphic encryption (HE) and private information retrieval (PIR) are fused into our protocols with non-trivial optimizations. As a result, our schemes can enjoy the HE acceleration technique without privacy trade-offs. We give formal security proofs for the proposed schemes and conduct extensive experiments on both real and large-scale simulated datasets. Compared with state-of-the-art works, our two schemes compress the running time roughly by 10* and 2.8*. They also attain up to 15* and 2.3* communication reduction without accuracy loss.