Federated Learning (FL) enables collaborative model training without exposing clients' private data, and has been widely adopted in privacy-sensitive scenarios. However, FL faces two critical security threats: curious servers that may launch inference attacks to reconstruct clients' private data, and compromised clients that can launch poisoning attacks to disrupt model aggregation. Existing solutions mitigate these attacks by combining mainstream privacy-preserving techniques with defensive aggregation strategies. However, they either incur high computation and communication overhead or perform poorly under non-independent and identically distributed (Non-IID) data settings. To tackle these challenges, we propose SRFed, an efficient Byzantine-robust and privacy-preserving FL framework for Non-IID scenarios. First, we design a decentralized efficient functional encryption (DEFE) scheme to support efficient model encryption and non-interactive decryption. DEFE also eliminates third-party reliance and defends against server-side inference attacks. Second, we develop a privacy-preserving defensive model aggregation mechanism based on DEFE. This mechanism filters poisonous models under Non-IID data by layer-wise projection and clustering-based analysis. Theoretical analysis and extensive experiments show that SRFed outperforms state-of-the-art baselines in privacy protection, Byzantine robustness, and efficiency.