Community　detection　is　an　effective　approach　to　unveiling　relationships　among　individuals　in　social　networks.　Detecting　communities　without　privacy　leakage　remains　an　area　of　ongoing　and　indispensable　focus.　Therefore,　anonymization　and　differential　privacy　based　community　detection　methods　are　proposed　to　protect　the　privacy　of　social　network　information.　However,　the　above　methods　cause　inevitable　accuracy　loss　in　some　way,　resulting　in　the　low　utility　in　the　final　community　division.　In　this　paper,　we　propose　a　secure　and　efficient　interaction　protocol　based　on　homomorphic　encryption　to　find　the　index　of　the　maximum　value　of　encrypted　floating-point　numbers.　Besides,　we　design　a　novel　federated　community　detection　framework,　using　user-server　interactions　to　adjust　and　construct　global　optimal　community　division　results,　which　could　not　only　get　an　effective　community　division　model　but　also　guarantee　strong　privacy　preservation.　Through　theoretical　analysis　and　empirical　experiments,　the　time　cost　of　our　proposed　secure　protocol　is　4　×　faster　than　previous　works.　Meanwhile,　our　framework　ensures　modularity　error　in　the　range　of　0.03　comparing　with　the　plaintext　framework,　and　modularity　improves　at　least　0.3　with　3　other　state-of-the-art　privacy-preserving　community　detection　schemes.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.