Federated　learning　has　become　prevalent　in　medical　diagnosis　due　to　its　effectiveness　in　training　a　federated　model　among　multiple　health　institutions　(i.e.,　Data　Islands　(DIs)).　However,　increasingly　massive　DI-level　poisoning　attacks　have　shed　light　on　a　vulnerability　in　federated　learning,　which　inject　poisoned　data　into　certain　DIs　to　corrupt　the　availability　of　the　federated　model.　Previous　works　on　federated　learning　have　been　inadequate　in　ensuring　the　privacy　of　DIs　and　the　availability　of　the　final　federated　model.　In　this　article,　we　design　a　secure　federated　learning　mechanism　with　multiple　keys　to　prevent　DI-level　poisoning　attacks　for　medical　diagnosis,　called　SFAP.　Concretely,　SFAP　provides　privacy-preserving　random　forest-based　federated　learning　by　using　the　multi-key　secure　computation,　which　guarantees　the　confidentiality　of　DI-related　information.　Meanwhile,　a　secure　defense　strategy　over　encrypted　locally-submitted　models　is　proposed　to　resist　DI-level　poisoning　attacks.　Finally,　our　formal　security　analysis　and　empirical　tests　on　a　public　cloud　platform　demonstrate　the　security　and　efficiency　of　SFAP　as　well　as　its　capability　of　resisting　DI-level　poisoning　attacks.