# Optimized Implementation and Analysis of CHAM in Quantum Computing
## 3 Quantum Implementation of CHAM
### Fse'20
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CHAM**} & \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Total Gates**} & \multicolumn{2}{c}{**Total**} & \multirow{2}{*}{**Cost**} & \multirow{2}{*}{**Security** [12]} \\  & & & & **Depth** & & [12] \\ \hline \multirow{4}{*}{64/128} & PLU & \(1.456\times 2^{81}\) & \(1.025\times 2^{76}\) & \(1.462\times 2^{157}\) & \\  & FSE’20 & \(1.226\times 2^{81}\) & \(1.002\times 2^{76}\) & \(1.228\times 2^{157}\) & \(2^{170}\) \\  & PLU (revision) & \(1.568\times 2^{81}\) & \(1.119\times 2^{76}\) & \(1.755\times 2^{157}\) & (Level 1) \\  & FSE’20 (revision) & \(1.345\times 2^{81}\) & \(1.094\times 2^{76}\) & \(1.471\times 2^{157}\) & \\ \hline \multirow{4}{*}{128/128} & PLU & \(1.583\times 2^{81}\) & \(1.233\times 2^{77}\) & \(1.952\times 2^{158}\) & \\  & FSE’20 & \(1.305\times 2^{81}\) & \(1.005\times 2^{77}\) & \(1.311\times 2^{158}\) & \(2^{170}\) \\  & PLU (revision) & \(1.103\times 2^{82}\) & \(1.716\times 2^{77}\) & \(1.894\times 2^{159}\) & (Level 1) \\  & FSE’20 (revision) & \(1.818\times 2^{81}\) & \(1.400\times 2^{77}\) & \(1.273\times 2^{159}\) & \\ \hline \multirow{4}{*}{128/256} & PLU & \(1.895\times 2^{146}\) & \(1.219\times 2^{141}\) & \(1.155\times 2^{288}\) & \\  & FSE’20 & \(1.562\times 2^{146}\) & \(1.198\times 2^{141}\) & \(1.871\times 2^{287}\) & \(2^{333}\) \\ \cline{1-1}  & PLU (revision) & \(1.179\times 2^{147}\) & \(1.511\times 2^{141}\) & \(1.781\times 2^{288}\) & (Level 3) \\ \cline{1-1}  & FSE’20 (revision) & \(1.946\times 2^{146}\) & \(1.491\times 2^{141}\) & \(1.450\times 2^{288}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of cost of [PERSON]’s key search by methods applied to key-schedule for CHAM. In future studies, in addition to PLU factorization and FSE'20, we will find a way to optimize the circuit, apply it to lightweight block ciphers such as CHAM, and compare these and then try to find an optimal method. In addition, if the two techniques applied in the thesis are applied to other ciphers (e.g., SPECK, SIMON, and LEA block ciphers), a new optimization study will be able to proceed. Software, Y.Y., K.J. and A.B. ; Writing--original draft, Y.Y. ; Supervision, H.S. All authors have read and agreed to the published version of the manuscript. This research was financially supported by Hansung University. We thank [PERSON] (Indian Institute of Technology Madras, India) and [PERSON] (Hubei University, Wuhan, China) for the kind help. The authors declare no conflict of interest. ## References

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