# Maintaining Secure Level on Symmetric Encryption under Quantum Attack
## 3 System Architecture
### AES-384, AES-512 Concept and Software Implementation  
In order to maintain the security level of AES in a quantum computer environment, it is necessary to extend the length of the original key, and this paper proposes two versions of AES-384 and AES-512 with an extended key. The proposed new schedule must conform to the security framework of the Rijndael algorithm, so we extend it based on the original framework [16]. The differences between the two new key schedules and the original architecture are only the number of cryptographic rounds and the key expansion steps, except for the key length.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Key Length** & \begin{tabular}{c} **Number of** \\ **Encrypted Segments** \\ **(Nb)** \\ \end{tabular} & \
\begin{tabular}{c} **Number of Key** \\ **Segments** \\ **(Nk)** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Encrypted Rounds** \\ **(Nr)** \\ \end{tabular} \\ \hline
128 & 4 & 4 & 10 \\
192 & 4 & 6 & 12 \\
256 & 4 & 8 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Important AES parameters.  
Both AES-384 and AES-512 execute only AddRoundKey in the first round, and execute SubBytes, ShiftRows, MixColumns and AddroundKey in the second round to the \(Nr-1\) round In the final round, it executes SubBytes, ShiftRows and AddRoundKey. We then calculate the number of needed rounds by the formula: \(Nr=6+\text{bits of key}/32\). The results are shown in Table 2.  
Turning now to the key expansion, the first step is calculating the needed words by using the formula \(i=Nb*(Nr+1)\). Note whether the number of subkeys is correct. The results of the calculations are presented in Table 3 sketch pictures of key expansions according to calculations. The figures make it easy to understand the work. Figures 1 and 2 illustrate the process of key expansion for AES-384 and AES-512.  
From Tables 4 and 5, we know that AES-384/512 is extended by the original architecture, so the original encryption standard will not be changed, thus affecting security. The benefit of designing AES-384 and AES-512 by extending from the original standard is that the use of this method can reduce the risk posed to AES-192 and AES-256.  
\begin{table}
\begin{tabular}{c c} \hline
**Version** & **Round** \\ \hline
384 & 18 \\ \hline
512 & 22 \\ \hline \end{tabular}
\end{table}
Table 2: Number of rounds for AES 384/512.  
Figure 1: AES 384 key expansion.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Block Number** & **Rule** \\ \hline \(i\ mod\ 12=0\) & \(Wi=Sub(Rot(Wi-1))\) \\ \hline \(i\ mod\ 12\
eq 0\) & \(Wi=Wi-1+Wi-12\) \\ \hline \(i\ mod\ 12\
eq 0\) \& \(i\ mod\ 8\
eq 0\) \& \(i\ mod\ 4=0\) \\ \hline \(i\ mod\ 12\
eq 0\) \& \(i\ mod\ 8=0\) & \(Wi=Sub(Wi-1)+Wi-12\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: AES 384 key expansion rule.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Block Number** & **Rule** \\ \hline \(i\ mod\ 16=0\) & \(Wi=Sub(Rot(Wi-1))+Remm\left[\frac{i}{16}\right]+Wi-16\) \\ \hline \(i\ mod\ 16\
eq 0\) & \(Wi=Wi-1+Wi-16\) \\ \hline \(i\ mod\ 16\
eq\emptyset\ \&\ i\ mod\ 12\
eq 0\ \&\) \\ \hline \(i\ mod\ 8\
eq 0\ \&\ i\ mod\ 4=0\) & \(Wi=Sub(Wi-1)+Wi-16\) \\ \hline \(i\ mod\ 16\
eq 0\ \&\ i\ mod\ 12\
eq 0\ \&\) \(i\ mod\ 8=0\) & \(Wi=Sub(Wi-1)+Wi-16\) \\ \hline \(i\ mod\ 16\
eq 0\ \&\ i\ mod\ 12=0\) & \(Wi=Sub(Wi-1)+Wi-16\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Key expansion of AES 512.  
Figure 2: AES 512 key expansion.