## 4 Proposed Key Management Infrastructure Design for IACS
### Key Establishment Phase
The secure property of the schemes depend on the parameters shown in Table 5. Table 6 gives the comparison between the key management designs. The design is resistant to the following attacks:

* **Replay attack:** In the proposed scheme, this attack is eliminated using nonce values during key establishment. * **Key exposure attack:** In the proposed scheme, the secret key is never transmitted over the network during the key establishment phase. Alternatively, devices self-compute the keys using the pre-shared crypto parameters. Thus, the chances of exposure of secret keys are reduced. * **Man in middle attack:** If the adversary is able to capture all the communication data between the devices, he will not be able to either compromise the devices or compute the secret key used for encrypting the messages. Use of digital signatures for ECDH prevents man-in-the-middle attack. ### Test Setup and Implementation Results

The prototype was developed and tested for the proposed key management infrastructure for IACS. Figure 8 shows the setup of an industrial automation network with key establishment schemes. The bottom level is the field level, the middle level is the control level, and the plant level is at the top. The communication medium was Ethernet with IP based network. Each device had a unique IP address. It was assumed that the key server had loaded the crypto parameters of the key establishment schemes in the devices using a secure channel. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & \multicolumn{8}{c}{**Key Management States Supported**} \\ \cline{2-11}  & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** \\ \hline SKE [20] & ✓ & & ✓ & ✓ & & & ✓ & & \\ SKMA [21] & ✓ & & ✓ & & & ✓ & ✓ & & \\ ASKMA+ [23] & ✓ & & ✓ & ✓ & ✓ & ✓ & ✓ & & \\ Versatile KMS [25] & ✓ & & ✓ & & ✓ & & ✓ & & \\ Advanced metering infrastructure [26] & ✓ & & ✓ & & ✓ & & ✓ & & \\ KMI with Join/leave [8] & ✓ & ✓ & ✓ & & ✓ & ✓ & ✓ & & \\ Proposed Scheme & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular} Note: S, State; S1, Key Generation; S2, Device Registration; S3, Key Establishment; S4, Key Storage; S5, Device Addition; S6, Key Revocation; S7, Key Update; S8, Key Recovery; S9, Key Archival; S10, Key Destruction.

\end{table} 
Table 6: Comparison between the previous works and proposed work in terms of key management states supported. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Key Establishment Schemes**} & **Secure Property of the Schemes** \\ \hline Polynomial Key establishment scheme & \(\lambda\) collision resistance property \\ Matrix Key establishment scheme & \(\lambda\) collision resistance property \\ ECDH & Discrete logarithmic problem \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Secure property of the key establishment schemes. ## 7 Conclusions

We have proposed an elegant key management design for IACS to handle the key management operations. The design considers all the key management operations by considering the constraints of IACS devices. The proposed design can be applied for major IACS by using suitable crypto methods such as ECDH, matrix and polynomial method. The choice of these schemes is justified. Although these crypto methods are meant for key establishment, the same methods are extended to support other key management operations. Changes made at one level of devices to incorporate key management operations does not affect the other level of devices. The impact of attack confines only to that level of devices, thus reducing the recovery time of devices. The test setup and implementation results show that the design is efficient. The proposed design is scalable and supports to secure the communications of IACS devices. All authors have equally contributed to this work. This research was supported by Florida International University Graduate School Dissertation Year Fellowship award recieved by the author [PERSON]. The authors declare no conflict of interest.