Algorithm 1: The algorithm of integrity verification

Let $CS={\cup }_{s_i\in \Psi }\left\{{\Im }_i\right\}$ be an encrypted dataset that Sink receives from M. Sink verifies the integrity of QR as follows.  Sink performs the following three steps to verify each ${\Im }_i$ contributed by si $\in$ ψ.  (1) If ${\Im }_i$ = Ø, it could not satisfy Definition 2. Thus the integrity of QR is violated. Quit the algorithm.  (2) If ${\Im }_i$ ≠ Ø, Sink decrypts all factors in ${\Im }_i$ using ki,t only shared with si, and checks whether both of following two conditions are satisfied. If so, add all the data within [low, high] into QR, and then turn to Step (3). Otherwise, the integrity of QR is violated so quit the algorithm.   1) Each factor Fi,v in ${\Im }_i$ satisfies following condition: low ≤ LB(Fi,v) ≤ high ∨ low ≤ UB(Fi,v) ≤ high ∨ LB(Fi,v) ≤ low ∧ high ≤ UB(Fi,v)   2) Fi,k and Fi,v+1 satisfy the following formula, where Fi,v and Fi,v+1 are two adjacent factors in ${\Im }_i$. UB(Fi,v) = LB(Fi,v+1) (3) If all factors contributed by si $\in$ ψ are processed through Steps (1) and (2), and all of them satisfy the query, then the QR satisfies the query, thus return the QR. Otherwise, continue to process the next ${\Im }_i$ contributed by unprocessed sensor node, and turn to Step (1).