Homomorphic encryption (HE) is a promising privacy-preserving technique for cross-silo federated learning (FL), where organizations perform collaborative model training on decentralized data. Despite the strong privacy guarantee, general HE schemes result in significant computation and communication overhead. Prior works employ batch encryption to address this problem, but it is still suboptimal in mitigating communication overhead and is incompatible with sparsification techniques. In this paper, we propose FLASHE, an HE scheme tailored for cross-silo FL. To capture the minimum requirements of security and functionality, FLASHE drops the asymmetric-key design and only involves modular addition operations with random numbers. Depending on whether to accommodate sparsification techniques, FLASHE is optimized in computation efficiency with different approaches. We have implemented FLASHE as a pluggable module atop FATE, an industrial platform for cross-silo FL. Compared to plaintext training, FLASHE slightly increases the training time by $\leq6\%$, with no communication overhead.