By　combining　user　feedback　on　items　with　social　networks,　cross-domain　social　recommendations　provide　users　with　more　accurate　recommendation　results.　However,　traditional　cross-domain　social　recommendations　require　holding　both　data　of　ratings　and　social　networks,　which　is　not　easy　to　achieve　for　both　information-oriented　and　social-oriented　websites.　To　promote　cross-domain　social　network　collaboration　among　the　institutions　holding　different　data,　this　chapter　proposes　a　federated　cross-domain　social　recommendation　(FCSR)　algorithm.　The　main　innovation　is　applying　Random　Response　mechanism　to　achieve　sparsely　maintained　differential　privacy　for　user　connections　and　proposing　Matrix　Confusion　Method　to　achieve　efficient　encrypted　user　feature　vector　updates.　Our　experiments　on　three　datasets　show　the　practicality　of　FCSR　in　social　recommendation　and　significantly　outperforms　baselines.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.