# [PERSON] on Korean Block Ciphers
## 2 Related Works
### Target Block Ciphers  
Hight  
In CHES'06, ultra lightweight block cipher HIGHT was presented [11]. HIGHT is a 64-bit block cipher with 128-bit keys. Eight whitening keys and 128 subkeys, 8-bit respectively,are generated from the 128-bit key. HIGHT block cipher performs 8-bit wise ARX operations and the encryption/decryption operation consists of 32 rounds. In each round, a 64-bit round key is required, and, in total, 2048-bit of round keys are needed to process a 64-bit block. The parameters for the HIGHT block cipher are shown in Table 2.  
The key schedule of HIGHT uses the initial key words \(K\) to generate whitening keys \(WK\) and round keys \(RK\). The whitening key is used for initial conversion of plain text and final conversion for cipher text. The whitening key is generated as follows:  
\[ \begin{split} WK[i]&=K[i+12],\ 0\leq i\leq 3\\ WK[i]&=K[i-4],\ \ 4\leq i\leq 7\end{split}  \tag{1}\]  
The connection polynomial of LFSR \(h\) is \(x^{7}+x^{3}+1\). The initial internal state value of \(h\) is \(\delta_{0}=(s_{6},s_{5},s_{4},s_{3},s_{2},s_{1},s_{0})=(1,0,1,1,0,1,0)\). For \(1\leq i\leq 127\), \(\delta_{i}\) is generated as follows and used for round key generation:  
\[ \begin{split} s_{i+6}&=s_{i+2}\oplus s_{i-1}\\ \delta_{i}&=(s_{i+6},s_{i+5},s_{i+4},s_{i+3},s_{i+2},s_{i+1},s_{i})\end{split}  \tag{2}\]  
Round key RK is generated as follows:  
\[ \begin{split}\text{for }i=0\text{ to }7:\\ \text{for }j=0\text{ to }7:\\ RK[16\cdot i+j]&=K[j-i\text{ mod }8]\boxplus\delta_{16 +i+j}\\ \text{for }j=0\text{ to }7:\\ RK[16\cdot i+j+8]&=K[(j-i\text{ mod }8)+8]\boxplus\delta_{16 +i+j+8}\end{split}  \tag{3}\]  
Before performing the round function, the initial conversion of plaintext \(T\) using four whitening keys \(WK\) is performed in the encryption process, as follows:  
\[ \begin{split} X_{0}[i]&=T[i],i=1,3,5,7\\ X_{0}[0]&=T[0]\boxplus WK[0]\\ X_{0}[2]&=T[2]\boxplus WK[1]\\ X_{0}[4]&=T[4]\boxplus WK[2]\\ X_{0}[6]&=T[6]\boxplus WK[3]\end{split}  \tag{4}\]  
In the round function of HIGHT, auxiliary functions \(F_{0}(X)\) and \(F_{1}(X)\) using left rotation operation are used, and, for \(1\leq i<32\), the round function is shown in Equation (6): \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Meaning** \\ \hline \(K\) & Initial keywords \\ \hline \(RK\) & Round key \\ \hline \(\oplus\) & XOR operation \\ \hline \(\boxplus\) & Modular addition operation \\ \hline \(\text{ROL}_{i}\) & Rotation left operation (\(i\)-bit) \\ \hline \(\text{ROR}_{i}\) & Rotation right operation (\(i\)-bit) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cipher** & **Block Size (bits)** & **Key Size (bits)** & **Word Size (bits)** & **Keywords** & **Rounds** \\ \hline HIGHT & 64 & 128 & 8 & 16 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of HIGHT. \[ \begin{array}{l}F_{0}(X)=\text{ROL}_{1}(X)\oplus\text{ROL}_{2}(X)\oplus\text{ROL} _{7}(X)\\ F_{1}(X)=\text{ROL}_{3}(X)\oplus\text{ROL}_{4}(X)\oplus\text{ROL}_{6}(X)\end{array}  \tag{5}\]  
\[ \begin{array}{l}X_{i}[j]=X_{i-1}[j-1],\quad j=1,3,5,7\\ X_{i}[0]=X_{i-1}[7]\oplus(F_{0}(X_{i-1}[6])\boxplus RK[4i-1])\\ X_{i}[2]=X_{i-1}[1]\boxplus(F_{0}(X_{i-1}[0])\oplus RK[4i-4])\\ X_{i}[4]=X_{i-1}[3]\oplus(F_{0}(X_{i-1}[2])\boxplus RK[4i-3])\\ X_{i}[6]=X_{i-1}[5]\boxplus(F_{0}(X_{i-1}[4])\oplus RK[4i-2])\end{array}  \tag{6}\]  
In the last round \(i=32\), the \(F_{1}(X)\) is also used, and the output positions of the input values are not changed as follows:  
\[ \begin{array}{l}X_{32}[i]=X_{31}[i],\quad i=0,2,4,6\\ X_{32}[1]=X_{31}[1]\boxplus(F_{1}(X_{31}[0])\oplus RK[124])\\ X_{32}[3]=X_{31}[3]\oplus(F_{0}(X_{31}[2])\boxplus RK[125])\\ X_{32}[5]=X_{31}[5]\boxplus(F_{1}(X_{31}[4])\oplus RK[126])\\ X_{32}[7]=X_{31}[7]\oplus(F_{0}(X_{31}[6])\boxplus RK[127])\end{array}  \tag{7}\]  
After executing all round functions, the ciphertext \(C\) is generated by the final conversion using the whitening key, and the final conversion is shown in Equation (8):  
\[