# Privacy-Preserving Federated Singular Value Decomposition
## Appendix A Practical Secure Aggregation
* If the server receives at least \(t\) messages from individual node devices (denoted by \(\mathcal{U}_{2}\subseteq\mathcal{U}_{1}\) this set of node devices), then it shares to each node device \(u\in\mathcal{U}_{2}\) all ciphertexts for it \(\{e_{u,v}\}_{v\in\mathcal{U}_{2}}\). * Round 2 (MaskedInputCollection):
* For the node device \(u\in\mathcal{U}_{2}\), once the ciphertexts are received, it computes \(s_{u,v}\leftarrow\mathsf{KA\_agree}(s^{SK}_{u},s^{PK}_{v})\), where \(v\in\mathcal{U}_{2}\setminus\{u\}\). * \(s_{u,v}\) is expanded using PRG into a random vector \(p_{u,v}=\Delta_{u,v}\cdot\mathsf{PRG}(s_{u,v})\), where \(\Delta_{u,v}=1\) when \(u>v\) and \(\Delta_{u,v}=-1\) when \(u<v\); moreover, define \(p_{u,u}=0\). * The node device \(u\) computes its own private mask vector \(p_{u}=\mathsf{PRG}(b_{u})\) and the masked input vector \(x_{u}\) into \(y_{u}\gets x_{u}+p_{u}+\sum_{v\in\mathcal{U}_{2}}p_{u,v}\) (mod \(R\)); then, \(y_{u}\) is sent to the server. * If the server receives at least \(t\) messages (denote with \(\mathcal{U}_{3}\subseteq\mathcal{U}_{2}\) this set of node devices), share the node device set \(\mathcal{U}_{3}\) with all node devices in \(\mathcal{U}_{3}\). * Round 3 (ConsistencyCheck):
* Round 3 (ConsistencyCheck  
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