## 4 Classification of PPDA Protocols
### Homogenous protocols
#### 4.2.1 Perturbation
In the twin-key establishment step, it is assumed that each node contains a pre-deployed ring of \(K\) symmetric key [28], randomly chosen from a larger common key pool of size \(P\). Each node establishes a number of twin keys with the other nodes. In particular, a node \(n_{i}\) establishes a twin key with another node (twin-node) in the cluster when \(n_{i}\) is aware there is a node sharing a key with it. The twin keys are only known to the owners and they are established anonymously. In the data aggregation step, each cluster first computes the aggregated value of its nodes during which an aggregate is routed twice along the Hamiltonian circuit. Each node adds its own sensed value to the aggregate. For each live twin key, it adds (or removes) a corresponding shadow value. The cluster head obtains the correct aggregate for the cluster, because it is guaranteed that any shadow value added during aggregation by one node will be removed by another node that shares the same twin key. Then, by using a tree-aggregation hierarchical structure, the cluster head nodes contribute to the aggregate with the cluster aggregate. Finally, the base station (BS) receives the sum of the values owned by all of the cluster heads. Figures 3 and 4 illustrate data aggregation with shadow values and aggregation of the cluster aggregates of the proposed scheme, respectively. Although this scheme preserves the privacy of the data contributed by a sensor to the aggregate value, it has limited applications, since the information about the key pool is only known to the nodes manufacturer. In addition, this scheme incurs higher communication cost because not only an aggregate is routed twice along the Hamiltonian circuit, but also all nodes are involved while routing individual cluster aggregates to the BS. Furthermore, this scheme decreases the lifetime of the WSN, because all sensor nodes need longer idle times until the BS receives the aggregated value from the cluster heads. **DADPP:** Data Aggregation Different Privacy-levels Protection (DADPP) [29] offers different levels of data aggregation privacy based on different node numbers for pre-treating the data. This protocol is inspired by the work of [PERSON] _et al._[30] in terms of different levels of privacy as well as the CPDA in terms of the privacy achieving method. In DADPP, a hierarchical wireless sensor network is first constructed in such that sensor nodes form several clusters each of which has a fixed cluster head below the energy efficient BS. According to the desired privacy level, all nodes within the same cluster are partitioned into multiple groups belonging to the same privacy level. Data are pretreated only in the same group and privacy levels are defined by the size of groups. The lowest privacy level consists of partitioned groups that have at least 3-sensor-nodes. The upper privacy level corresponds to portioned groups with 4-sensor-nodes. By analogy, if all sensor nodes of a cluster belong to a single group, they consider this case as the highest privacy level. The data aggregation process is similar to the one described in the previous section. Figure 4: Aggregation of four-cluster aggregates. Figure 3: Data aggregation with shadow values. that of the CPDA. First, original data are pretreated in each group. Secondly, the cluster head aggregates all pretreated data. Finally, data are aggregated on the plane of the cluster head up to the BS. The hierarchical wireless sensor network is illustrated in Figure 5. Although DADPP reduces traffic by partitioning a cluster with \(n\) sensor nodes into multiple in-networks with pretreatment of groups according to the desired privacy-levels, it suffers from the inherent high communication and computation overheads. Furthermore, these overheads increase with increasing privacy level. **PHA:** [PERSON] _et al._[31] proposed the Perturbed Histogram-based Aggregation (PHA) to preserve privacy for queries targeted at special sensor data or sensor data distribution.