# Side Channel Leakages Against Financial IC Card of the Republic of Korea +
## 3 Evaluation Methodology for the Financial IC Card Protocol
### Security Evaluation Methodology of Side Channel Analysis Under Black Box Model
#### 3.2.3 Recovering the Master Key via Some Round Keys
Two possible criteria for obtaining some leakages in order to perform side channel analysis are the back and forth of S-box operations. In other words, there are two alignment points. The result of the alignment to the back of S-box operations is shown in Figure 7.

The aim of alignment to the front of the S-box operations is to analyze the plaintext and S-box operations. Furthermore, the purpose of the other alignment is to analyze the output of G-function and S-box operations. This is directly related to the suggestion of [19]. To sum up, the notations are defined as below, according to the following alignment criteria:

* Alignment 1: front of S-box operations. * Alignment 2: rear of S-box operations (refer to Figure 7). #### 4.2.1 Result of Performing Side Channel Analysis Defined in Enumeration

This section describes the side channel analysis performed using the defined scheme in Section 3.2.1. As a result, we cannot identify any secret information for Alignment 1. Therefore, it is represented to all results for Alignment 2 in this section. None of the first-order leakage on the collect traces was revealed, and the second-order leakage of the combination between each of the S-boxes was also not exposed. However, by performing item 2b, two round keys can be retrieved as shown in Table 1.

Figure 8 represents the result for the first G-function of 1 round based on all combinations in Appendix A. Additionally, the \(x\)-axis and \(y\)-axis indicate the absolute correlation and key candidates, respectively. In general, the key candidate with the highest value is considered to be the correct key. When considering all combinations, there are 20 results. As shown in Figure 8, the result is only represented if the correct key is retrieved. As described in Appendix A, the performance is superior to that of the previous proposal [19], owing to the fact that results Figure 8a-d have higher correlation. In order to analyze all combinations, 1,000,000 traces were collected. However, only 20,000 traces were required to recover the correct key in results Figure 8a-d.

By analyzing the first G-function of 1 round, the scored key \(K_{1,0}\oplus K_{1,1}\) can be acquired. Therefore, it is necessary to analyze the second G-function of 1 round, the first G-function of 2 round, and the second G-function of 2 round to obtain two round keys. All results are analogous to Figure 8.

Figure 5.0 Five behaviors when operating \(DEA\) algorithm. ### Recovering the Master Key via Two Round Keys

Two round keys were already retrieved to recover the master key. At first, the G-function in 1 round, the \(K_{1,0}\oplus K_{1,1}\), is used for the G-function. Therefore, it was necessary to perform side channel analysis for the second G-function in order to recover each \(K_{1,0}\) and \(K_{1,1}\). By the same logic, the second round key can be recovered. To calculate the master key, a correct single pair \((R_{C},R_{T},UP_{C}^{*},CT*_{C})\) should be acquired in the financial IC card protocol. Afterwards, Algorithm 1 is operated to recover a correct master key. As mentioned earlier, \(R_{T}\) and \(UP_{C}^{*}\) were controlled by the adversary, utilizing a fake ATM. Therefore, we set to the fixed zero value. The result of performing Algorithm 1 is as follows. \begin{table}
\begin{tabular}{c c} \hline \hline
**Round Key** & **Value** \\ \hline \(K_{1,0}\) & 0 xD555B112 \\ \(K_{1,1}\) & 0 xA476A39F \\ \(K_{2,0}\) & 0x15043F29 \\ \(K_{2,1}\) & 0x1886A9 FA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analyzed two round keys. Figure 8: When performing combinations defined in item 1(b), the result is only represented if the correct key is revealed. As shown in Figure 9, the number of filtering temporary keys is 16. Finally, the analyzed master key (0 xE73A67 FFE48 EF10 DD542 EC7 BE57A9 FBE) could be recovered by utilizing a correct pair defined in Table 2.

## 5 Conclusions

A specific payment system is one that is only applied to its domestic market.