Algorithm 1: Carpooling matching scheme based on BF-PSI

Input: $Q M_{P_{i}}, S M_{V_{i}}, δ_{S M_{V_{i}}}$

Output: Result = “successful matching” or “failed matching”

1: $I n_{P_{i}, V_{i}} = \emptyset$

2: if $| T_{3} - T_{S M_{V_{i}}} | < ψ_{t}$ then

3: $R_{i}$ verifies the reputation certificate and signature of $V_{i}$

4: if equation (11) and (12) hold then

5: $R_{i}$ matches the starting position and destination of the $V_{i}$ and $P_{i}$

6: if equation (13) holds then

7: $R_{i}$ verifies whether $V_{i}$ meets $P_{i}$ ’s multi-faceted trust needs

8: if all the $T V_{V_{i} (I_{1})} ~ T V_{V_{i} (I_{7})} > χ_{m - n}$ then

9: $V_{i}$ meets $P_{i}$ ’s multi-faceted trust needs

10: end if

11: end if

12: end if

13: end if

14: for $\forall p \in {m, \dots, n}$ then

15: if mem_test ${B f_{V_{i}}, r_{2}, x_{p}}$ then

16: $I n_{P_{i}, V_{i}} = I n_{P_{i}, V_{i}} \cup {x_{p}}$

17: end if

18: end for

19: if $I n_{P_{i}, V_{i}}$ and $P S_{P_{i}}$ are the same then

20: Result = “successful matching”

21: else

22: Result = “failed matching”

23: end if