# 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}{c c c c c} \hline \hline  & **Target Scenario** & **Security Goals** & \begin{tabular}{c} **Mechanism for** \\ **Anonymity** \\ \end{tabular} & **Cryptographic Alg.** \\ \hline \multirow{2}{*}{Ours} & D2S authentication/D2D authentication & D2S authentication/D2D authentication/anonymity/unlinkability & 2 LCH anonymous identification & Hash/DH\({}_{\text{ECC}}\)/Sym. \\ \hline \multirow{2}{*}{[PERSON] [11, 25]} & D2S authentication [11, 25]/D2S group authentication [25] & D2S authentication/D2S group authentication & \multirow{2}{*}{Not consider} & Hash/ECC/pairing [25] \\ \hline \multirow{2}{*}{[PERSON] et al. [12]\({}^{1}\)} & D2S authentication/D2S group authentication & D2S authentication/unlinkability of the level-1 device & \multirow{2}{*}{Level-1 IoT:} & \multirow{2}{*}{Level-1 IoT:} & \multirow{2}{*}{\begin{tabular}{c} Hash/Sym./ECC- \\ CLPK. \\ \end{tabular} } \\  & & authentication/anonymity/unlinkability & Level-2 IoT:} & \multirow{2}{*}{\begin{tabular}{c} Hash/Sym. \\ \end{tabular} } \\  & & level-2 devices & & pseudonyms \\ \hline \multirow{2}{*}{[PERSON] [13]} & D2D group authentication & D2D authentication/D2D group authentication/anonymity & \multirow{2}{*}{\begin{tabular}{c} Pseudonym-bound \\ PKC \\ \end{tabular} } & \multirow{2}{*}{Hash/pairing-based PKC/Sym.} \\  & & authentication/non-repudiation/ & & \\ \hline \multirow{2}{*}{SeDS [15]} & D2D authentication/data sharing & D2D authentication/non-repudiation/ & \multirow{2}{*}{\begin{tabular}{c} Pseudonym-bound \\ PKC \\ \end{tabular} } & \multirow{2}{*}{Hash/sym./pairing-PKC} \\  & & anonymity & & \\ \hline \multirow{2}{*}{AAKA-D2D [16]} & D2D authentication & D2D authentication/anonymity & \multirow{2}{*}{\begin{tabular}{c} Pseudonym-bound \\ PKC \\ \end{tabular} } & \multirow{2}{*}{Hash/sym./pairing-PKC} \\ \hline \multirow{2}{*}{Sec-D2D [18]} & Near field D2D authentication & D2D authentication & Not consider & Hash/Physical Layer Security (acceleration \\  & authentication & & & sensor/speaker/microphone) \\ \hline \multirow{2}{*}{[PERSON] et al. [20]} & D2D group authentication & D2D group/anonymity & \multirow{2}{*}{\begin{tabular}{c} Pseudonym-bound \\ CLPK \\ \end{tabular} } & \multirow{2}{*}{Hash/Sym./ECC-CLPK} \\ \hline \multirow{2}{*}{[PERSON] et al. [22]} & D2S authentication/D2D & D2S authentication/D2D group authentication & \multirow{2}{*}{\
\begin{tabular}{c} Pairing-based IDPE \\ [26] \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} Hash/Sym./signature/batch \\ signature/pairing-based IDPE \\ \end{tabular} } \\  & & & \\ \hline \multirow{2}{*}{Authentication: authentication; alg.: algorithm; PKC: Public-Key Cryptography; ECC: Elliptic Curve Cryptography; DH\({}_{\text{ECC}}\): Diffie-Hellman key using ECC; Sym.: symmetric key cryptography; pairing-PKC: PKC using pairing operations; pseudonym-bound PKC: PKC bound to entities’ pseudonym; ECC-CLPK: Certificate Less Public Key system using ECC; pairing-based IDPE: identity-based prefix encryption using pairing. \({}^{1}\) In the D2S group authentication [12], one compromised level-2 device impersonate any other devices in the group as the session key computation only use public values and one single group common secret.} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Brief summary of the targeted scenarios and the security goals of D2S/D2D authentication schemes. Regarding the communication cost, we concerned two metrics: the message bit length and the number of message rounds. Let \(L_{ID}\) and \(L_{h}\) respectively denote the bit length of one identity and one hash, and \(L_{SIG}\) denote the bit length of one ordinary digital signature. We let the bit length of one random challenge be the same as one hash. We also let the bit length of one encryption be the bit length of its plaintext; for example, the bit length of \(Enc_{K_{i}}(D_{i}^{*},PN)\) be \(1L_{ID}+1L_{h}\).