Algorithm 1: Federated Learning Security Mechanism in Round b

Input: Number of clients: N;

Number of participants in the last round: K;

Local multi−dimensional data;

Round b − 1.

Output: Global model parameter $\omega$(t):

1.fort = 1 to T do

2.   client1 to clientN ← pk1, pk2 and Score(Q, p) rules

3.   for i = 1 to N do

4.      Qi ← arg max U (Qi) − c(Qi,$\theta$i) in Equation (17)

5.      p i ←$c\left(Qi, \theta i\right)+{\int }_{\theta }^{\overline{\theta }}{c}_{\theta }\left(Q,t\right){(\frac{1-F\left(t\right)}{1-F\left(\theta \right)})}^{N-1}dt$ in Equation (18)

6.      E(Qi) ← encrypt with pk1

7.      E(pi) ← encrypt with pk2

8.      submit bid(E(Qi), E(pi))

9.   end for

10.   $E\left(Score\right)\leftarrow E_{p{k}_1, p{k}_2}\left(U\left(q_1,\cdots ,q_m\right)-p\right)$

11.$Score\leftarrow { \mathrm{D}}_{s{k}_1, s{k}_2}(E\left(Score\right)$

12.   win← 0 or 1

13.   Add winner to round b − 1 for federated learning

14.   Complete the auction

15.   for i = 1 to K + 1 do

16.      clienti ← pk3, p i, global $\omega$(t) from server

17.      ${\omega }_i\left(t + 1\right)$ ← trains the clienti

18.      server ← Epk3($\omega$i(t + 1))

19.   end for

20.   $\omega$(t + 1) ← $\omega \left(t+1\right)=\frac{{\sum }_{i=1}^N{C}_i{D}_{s{k}_3}{\omega }_i\left(t+1\right)}{{\sum }_{i=1}^N{C}_i}$ in Equation (8)

21.end for