## 5 Comparative Study of PPDA Protocols  
In this section, we present a comparison result of the existing PPDA protocols for WSNs. The comparison result is based on the following metrics. _(a) Communication cost (CMC):_ This is the number of messages generated in the given WSN. To evaluate CMC, we use _High, Medium and Low_. The communication costs of protocols belong to _High, Medium and Low_ when the numbers of message generated (m) per sensor node is \(m\geq 3\), \(3>m>1\), \(m=1\), respectively. For example, iPDA, CPDA and CDA protocols belong to _High, Medium and Low_ because they generates 5, 2 and 1 message(s) per sensor node, respectively. _(b) Computation cost (CPC):_ This is a processing overhead to achieve privacy-preserving data aggregation. The CPC can be divided into three types; _High, Medium and Low_. A protocol has a high cost if its sensor node performs many encryption/decryption, arithmetic operations and other computation like matrix operations. A protocol has a medium cost if its sensor node performs a couple of encryptions/ decryptions and some arithmetic operations. If a sensor node performs a few arithmetic operations and just encrypts its data, a protocol has a low cost. For example, because a sensor node in the AH scheme just encrypt data, the AH scheme has a low cost. The CPC of the PHA is medium because its sensor node performs two encryption and a few addition operations. Lastly, the CPC of the DADDP is high because its sensor node performs about four pairs of encryption/decryption and many addition/multiplication operations. _(c) Data pollution (DP):_ This is a logical operator for detecting the malicious modification of sensor data. If the malicious modification is detected, the metric gives _Yes_, otherwise it gives _No_. because all of the current PPDA protocols do not support DP feature, they are labeled _No_. _(d) Privacy support type (PST):_ There are two types of privacy support. The first one is used to preserve the privacy of raw sensor data from other trusted sensor nodes in the same network whereas the second one is used to preserve their privacy from adversaries/outsiders. _Both_ and _Outsider_ are two labeling for this metric. If a protocol supports data privacy against the trusted sensor nodes and outsiders, it is labeled _Both_. The CPDA belongs to _Both_. On the other hand, when the privacy of data is protected only from adversaries not being in the same network, it is labeled _Outsider_. The Sheng & Li's scheme belongs to _Outsider_. _(e) Delay (DLY):_ This is the time lag which takes for the aggregated data to reach the sink from the source nodes, due to the overhead of protocol execution. To evaluate DLY, we use _High, Medium and Low_. For example, [PERSON] _et al._'s scheme has high transmission delay because its data rotate two rounds in the Hamiltonian circuit of cluster members before being sent to the aggregation tree. The SMART has medium transmission delay because its data are encrypted/decrypted before they are aggregated. The transmission delay of CDA is low because its data are aggregated in cipher texts form. (f) Memory consumption (MC):This is the amount of main memory space required for storing keys, variables and integer ranges in a sensor node. The MC has three values; _High_, _Medium_ and _Low_. For example, the PHA requires high memory consumption because it needs about 1 Kbytes to store 200 keys, random numbers and data mapping ranges. The SMART requires medium memory consumption because it needs a few hundreds of bytes to store many keys and some variables. Lastly, the memory consumption of CDA is low because only about 10 bytes are needed to store some keys and variables. (g) Data integrity (DI):This is a metric used to check whether a protocol supports data integrity or not. If a protocol supports this feature (the DI value is _Yes_), we can assure that sensor data have been correctly aggregated. Otherwise, the DI value is _No_. For example, because the iPDA supports data integrity, its DI value is _Yes_.