Byzantine-robust Federated Learning (FL) aims to counter malicious clients and train an accurate global model while maintaining an extremely low attack success rate. Most existing systems, however, are only robust when most of the clients are honest. FLTrust (NDSS '21) and Zeno++ (ICML '20) do not make such an honest majority assumption but can only be applied to scenarios where the server is provided with an auxiliary dataset used to filter malicious updates. FLAME (USENIX '22) and EIFFeL (CCS '22) maintain the semi-honest majority assumption to guarantee robustness and the confidentiality of updates. It is, therefore, currently impossible to ensure Byzantine robustness and confidentiality of updates without assuming a semi-honest majority. To tackle this problem, we propose a novel Byzantine-robust and privacy-preserving FL system, called MUDGUARD, to capture malicious minority and majority for server and client sides, respectively. Our experimental results demonstrate that the accuracy of MUDGUARD is practically close to the FL baseline using FedAvg without attacks (≈0.8% gap on average). Meanwhile, the attack success rate is around 0%-5% even under an adaptive attack tailored to MUDGUARD. We further optimize our design by using binary secret sharing and polynomial transformation, leading to communication overhead and runtime decreases of 67%-89.17% and 66.05%-68.75%, respectively.