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Using the multiple BFcodes scheme, each master node needs O(m �� w) time to test the membership of each datum, while false positives are reduced. The partition of w groups affects the performance of eliminating false positive. Here, we give two schemes. The first scheme separates [a, b] uniformly into w consecutive sub-ranges, which is called consecutive multiple BFcodes (CMB). The second one inserts data into a certain group with a probability 1/w, which is called random multiple BFcodes (RMB). The two schemes are evaluated in Section 9. 8.?Theoretical Analysis Section 3 describes the requirements for a good privacy-preserving range query protocol. selleck inhibitor Result accuracy is affected by the probability of false positives, which is discussed in Sections 5 and 6. In this section, we analyze efficiency and privacy. 8.1. Efficiency Analysis In WSNs, communication cost is the main factor to influence the efficiency of a protocol. As in [2�C9], we analyze the proposed protocol in terms of communication cost, which is defined as the communication consumption in find more bits during query processing. It is generated during data submission from sensor nodes to master nodes and result submission from master nodes to the sink, i.e., communication cost of sensor nodes and communication cost of master nodes. The lower the communication cost, the higher the efficiency. Assume N denotes the number of sensor nodes, le denotes the average length of an encrypted part, m denotes the size of a BFcode, �� denotes the average number of data collected by a sensor node and p denotes the probability that data are considered to be in the query range. 8.1.1. Communication Cost of Sensor Nodes In any protocol, sensor nodes transmit encrypted data and associated BFcodes to the nearest master nodes, so the communication cost of sensor nodes is: N*(le+m)*(��+2) (10) 8.1.2. Adenylyl cyclase Communication Cost of Master Nodes The rules of membership testing influence the accuracy of ?��, ��?, and thus, the accuracy of ?��, ��? affects the communication cost of master nodes. Three cases should be considered: (1) if �� > ��, the expectation of communication cost is N �� 2 �� (le + m) �� (1 ? p)��; (2) if �� = ��, the expectation of communication cost is N �� 2 �� (le + m) �� (1 ? p)��?1 �� p; and (3) if ��