## 4 Proposed Key Management Infrastructure Design for IACS
### Key Establishment Phase
The following abbreviations are used in this manuscript: \begin{tabular}{l l} ASKMA & Advanced SCADA Key Management Architecture \\ BC & Broadcasting \\ CGK & Control Level Group Key \\ CKMI & Comprehensive Key Management Infrastructure \\ CN & Control Level Network \\ ECC & Elliptic Curve Cryptography \\ ECDH & Elliptic Curve Die Hellman \\ FGK & Field Level Group Key \\ FN & Field Level Network \\ HMI & Human Machine Interface \\ IACS & Industrial Automation and Control Systems \\ ICS & Industrial Control Systems \\ IEC & Intelligent Electronic Device \\ KMI & Key Management Infrastructure \\ KDC & Key Distribution Center \\ MC & Multicasting \\ NIST & National Institute of Standards and Technology \\ OPC & Open Platform Controller \\ PK & Pairwise Key \\ \end{tabular} \begin{table}
\begin{tabular}{c c c} \hline
**Finite Field (\(F_{p}\))** & **Number of Points on the Curve (Cardinality)** & **Computation Time (in \(\mu\)s)** \\ \hline \(F_{5}\) & 9 & 1.36 \\ \(F_{509}\) & 520 & 10,000 \\ \(F_{2113}\) & 2173 & 210,000 \\ \(F_{4021}\) & 4012 & 740,000 \\ \hline \end{tabular}
\end{table} 
Table 11: Elliptic curve point generation for the curve \(y^{2}=x^{3}+x+1\) (where a = 1, b = 1). \begin{table}
\begin{tabular}{c c c} \hline
**Scalar Value** & **Point** & **Computation Time (in \(\mu\)s)** \\ \hline
100 & (0,4,1) & 0.54 \\
500 & (0,4,1) & 0.82 \\
1000 & (0,4,1) & 0.89 \\ \hline \end{tabular}
\end{table} 
Table 12: Scalar multiplication operation in ECDH method. PN Plant Level Network

PGK Plant Level Group Key

PLC Programmable Logic Controller

RR RTU-RTU

RTU Remote Terminal Units

SCADA Supervisory Control and Data Acquisition

SK Session Key

VPN Virtual Private Networks

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