## 4 Proposed Key Management Infrastructure Design for IACS
### Key Establishment Phase
## 6 Performance Analysis

### Justification of Key Establishment Mechanisms Employed for Establishing the Shared Secret Keys

Based on the constraints of IACS devices, the proposed design makes use of the polynomial method, matrix method and ECDH method to establish the shared secret keys between the devices. The selected key establishment mechanisms are well supported to handle all the key management operations effectively. * Justification for choosing Elliptic Curve Diffie-Hellman key establishment scheme
* **Fewer bits:*
* The security level of a 160-bit ECC, 1024-bit RSA, and 1024-bit DSA is similar. ECC requires fewer bits. Table 3 shows a comparison between ECC and other crypto techniques. Figure 7: Proposed CKMI design for IACS. * **Power consumption:*
* ECC crypto mechanism consumes less power for its functioning when compared to other asymmetric crypto schemes (Table 4). * **Computational efficiency*
* Use of scalar multiplication enables fast computation. ECC based scheme has a wide selection of finite fields and curves. As per crypto++ 5.6.0 benchmarks [39], the run time of ECDH key-pair generation over GF(p) 256 is 0.00287 s and the run time of ECDH key agreement over GF(p) 256 is 0.00282 s.
* **Discrete logarithmic problem:*
* ECDH works on the discrete logarithm problem. It is hard to crack the private keys of the devices. Over the past few years, elliptic curve cryptography has gained popularity and has become a standard around the world. In IACS hierarchy, when compared to control and field level devices, the plant level devices have sufficient storage and computational capabilities. From the above analysis, it can be observed that the ECDH approach is more suitable than any other public key schemes for key establishment in plant level devices. * Justification for choosing the matrix method and polynomial method key establishment schemes. * Any pair of devices of the same level in IACS can communicate directly. * **High resilience:*
* Both polynomial and matrix-based system are \(\lambda\) collision resistance methods, meaning that, as long as \(\lambda\) number of devices are compromised, the communication between the non-compromised devices is secure. * **Less communication overhead:*
* The number of messages exchanged to compute the shared secret key is less. In the polynomial method, the device ID is exchanged. In the matrix method, a seed value is exchanged. * Both methods are scalable. * **Less storage overhead:*
* In the case of a polynomial method, field devices are required to store only one \(\lambda\)-degree polynomial share. Based on the degree of the polynomial, it utilizes memory and provides security. In the case of a matrix method, control devices are required to store only one secret row and a seed value. By choosing the appropriate value for \(\lambda\), both storage and computation overhead can be optimized. The novelty of our work resides in the fact that originally, the basic polynomial method, matrix method and ECDH method handled only key establishment, but our proposed scheme handles \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Key Size (bits)** & **Key Generation (\(\mu\)s)** & **Sign (mJ)** & **Verify (mJ)** \\ \hline RSA & 1024 & 270.13 & 546.5 & 15.97 \\ DSA & 1024 & 293.20 & 313.6 & 338.02 \\ ECDSA & 163 & 226.65 & 134.2 & 196.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analyzing the energy consumption of security protocols [38]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symmetric Key Size (bits)** & **ECC-Based Scheme (bits)** & **RSA/DSA (bits)** \\ \hline
56 & 112 & 512 \\
80 & 160 & 1024 \\
112 & 224 & 2048 \\
128 & 256 & 3072 \\
192 & 384 & 7680 \\
256 & 512 & 15,360 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparing the key size in terms of computation effort [37]. device addition, key storage, key revocation, key update, and key recovery in addition to the original behavior. ### Security Analysis and Comparison

The key establishment schemes used in the proposed design is resilient in nature.