Federated　collaborative　filtering　trains　models　by　uploading　gradients　to　achieve　privacy　protection.　Recent　studies　have　shown　that　gradients　have　the　risk　of　compromising　user　privacy.　To　address　this　problem,　this　paper　proposes　a　general　federal　framework　based　on　Paillier　semi-homomorphic　encryption　for　implicit　feedback　recommendation　with　privacy　protection.　First,　a　non-sampling　matrix　decomposition　model　based　on　the　federation　framework　is　designed,　and　alternating　least　squares　(ALS)　and　stochastic　gradient　descent　(SGD)　are　used　to　optimize　the　user　factor　and　item　factor,　respectively,　to　achieve　improved　recommendation　accuracy　and　recommendation　efficiency　while　ensuring　certain　privacy　protection.　Then,　the　privacy　protection　is　further　enhanced　by　encrypting　the　gradients　using　Paillier　semi-homomorphic　encryption　and　transmitting　the　encrypted　gradients　via　TLS/SSL　secure　channel.　Since　the　encryption　process　does　not　need　to　obfuscate　the　data,　the　method　is　lossless　and　ensures　the　accuracy　of　recommendations.　Finally,　experimental　analysis　is　performed　on　the　publicly　available　MovieLens　dataset.　The　experimental　results　show　that　the　method　is　able　to　enhance　privacy　protection　as　well　as　improve　recommendation　performance　with　higher　recommendation　efficiency　and　lower　time　overhead.