# Two-Level-Composite-Hashing Facilitating Highly Efficient Anonymous IoT and D2D Authentication
## 5 Security Analysis and Performance Evaluation
### The Performance Evaluation
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline \multicolumn{2}{c}{**Schemes**} & **Computation** & **Communication** \\ \hline \multirow{8}{*}{Ours} & \multirow{2}{*}{D2S authentication} & \(D_{i}\); \(6\times T_{h}+2T_{ECCM}\) (0.597 ms); & \(9L_{h}+3L_{ID}\); 3 msg. steps \\  & & S: \(6\times T_{h}+2T_{ECCM}\) (0.597 ms); & \\ \cline{2-3}  & \multirow{2}{*}{S-assist-always D2S2D authentication} & \(D_{i}\); \(7\times T_{h}+2T_{enc}+2T_{ECCM}\) (0.597 ms); & \\  & & \(D_{i}^{*}\); \(6\times T_{h}+1T_{enc}+2T_{ECCM}\) & \(18L_{h}+7L_{ID}\); msg. steps \\  & & S: \(6\times T_{h}+3T_{enc}\) & \\ \cline{2-3}  & \multirow{2}{*}{S-assisted-once-a-while D2S2D authentication} & \(D_{i}\); \(8\times T_{h}+2T_{enc}+2T_{ECCM}\) (0.597 ms); & \\  & & \(D_{i}^{*}\); \(6\times T_{h}+T_{enc}+2T_{ECCM}\) & \(22L_{h}+7L_{ID}\); 4 msg. steps \\  & & S: \(9\times T_{h}+3T_{enc}\) & \\ \cline{2-3}  & \multirow{2}{*}{Direct D2D} & \(D_{i}\); \(7\times T_{h}+2T_{ECCM}\) ((0.597 ms));\(D_{i}^{*}\); \(7\times T_{h}+2T_{ECCM}\) & \\ \hline \multirow{8}{*}{Fang} & Level-1 IoT: D2S authentication & \(D_{i}:5\times T_{h}+6T_{ECCM}\) (1.79 ms) & \(12L_{h}\); 3 msg. steps \\  & \multirow{2}{*}{Level-2 IoT: D2S authentication 3 [FOOTNOTE:3]Footnote 3: \(m\) denotes the number of services one device access within the specified time-zone; for example, \(|m=40\) with time zone = 1 day) means “a device issues 40 requests per day”, which represents those cases of which a device seldom issues requests; \(|m=1200\) with time zone = 1 day \\  & & \(2 nL_{\text{ENC}}\), where \(n\) is the number of the group; \(7\) msg. steps \\ \hline \multirow{2}{*}{SeDS [15] 2 [FOOTNOTE:2]Footnote 2: \(m\) denotes the number of services one device access within the specified time-zone; for example, \(|m=40\) with time zone = 1 day) means “a device issues 40 requests per day”, which represents those cases of which a device seldom issues requests; \(|m=1200\) with time zone = 1 day \\  & & \(2 nL_{\text{ENC}}\), where \(n\) is the number of the group; \(7\) msg. steps \\ \hline \multirow{2}{*}{SeDS [15] 2 [FOOTNOTE:2]Footnote 2: \(m\) denotes the number of services one device access within the specified time-zone; for example, \(|m=40\) with time zone = 1 day) means “a device issues 40 requests per day”, which represents those cases of which a device seldom issues requests; \(|m=1200\) with time zone = 1 day \\  & & \(16L_{h}+21L_{ID}\) (\(2L_{\text{ENC}}\) + \(2T_{\text{ENC}}\) (1.709 ms); & \(2L_{\text{sig}}\)); 8 msg. steps \\  & & \(D_{i}(request)\): \(4\times T_{h}+1T_{exp}+4T_{pair}\) (55.036 ms) & \\ \hline \multirow{2}{*}{AAKA-D2D [16] & D2S2D authentication & \(D_{i}\);\(3\times T_{h}+5T_{exp}+3T_{ENC}+2T_{pair}\) (29.056 ms); & \(10L_{h}+12L_{ID}\); 7 msg. steps \\ \hline \multirow{2}{*}{[PERSON] et al. [22] & Direct D2D group authentication & \(D_{i}(initiator):(n+3)\times T_{h}+nT_{exp}+nT_{mlp}+(n+3)L_{h}+(5n+5)L_{ID}+(2n+1)T_{ECCM}+(2n+2)T_{ECCA}+T_{SIG}+T_{PE}\) & \((n+3)L_{h}+(5n+5)L_{ID}+(n+2)\) msg. steps \\  & & \(+nT_{ENC}\) & \(+nT_{ENC}\) \\ \hline \multirow{2}{*}{Chien [25] & D2S authentication & \((6+2/m)\)\(T_{h}+2/m\)\(T_{ECCM}\)\({}^{1}\) (0.64 ms for \(m=40\); \(0.31\) & \(4L_{h}+1L_{ID}\) (\(4L_{h}+3L_{ID}\))/\(m\); 3 msg. steps \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the computational cost and the communication cost per session. so the amortized cost of a device per session is \((6+2/m)T_{h}+1T_{ECCM}+1/m\ T_{pair}\); when \(m\) (the number of requests within one time zone) is large enough, the amortized pairing computation \(1/m\ T_{pair}\) could be greatly reduced. To our knowledge, there is no one single experiment covering all the execution times of all the operations our schemes use. Therefore, to further compare the computation cost, we refer to the figures from the two implementations (24,44), where the bit length of Galois field is 1024 bits, the ECC group \(G\) is of order \(\mid q\mid=160\), the hash is SHA-256, and the symmetric encryption is AES-CCM.