## 6 Conclusions  
Many studies have been conducted to speed up the cipher algorithm using various optimization methods. Currently, high-speed research is being conducted not only in CPU, but also in the GPU environment, and such research is essential for data encryption technology that is continuously evolving.  
In this paper, we present various optimization techniques in Maxwell, Pascal, and Turing GPU architecture in order to encrypt a large amount of data. Our optimization studies were conducted for AES, CHAM, and LEA. AES is a well-known block cipher algorithm, but the lightweight block cipher algorithms CHAM and LEA have not been actively researched in the GPU environment. In particular, this is the first GPU optimization study for CHAM to the best of our knowledge.  
First, it was implemented to reduce the time to copy from the first CPU to the GPU by using the characteristics of the CTR mode. Next, an optimization implementation was attempted to reduce the number of accesses to global memory with slow access latency by actively using shared memory and registers inside the GPU. In addition, we tried to prevent and reduce various problems that can occur while implementing in the GPU environment. Additionally, by implementing inline PTX that is performed inside the GPU, an optimization implementation method that simplifies heavy-duty computation or reduces unnecessary computation is applied.  
As the proposed optimization methods, in the case of AES, a performance improvement of up to 4.18 times in RTX 2070, and throughput of 310 Gbps was obtained excluding the memory copy time. In our implementation, CHAM shows 3.03 Tbps throughput when applying all of the proposed optimization methods. This implementation is 6.98 times faster than a basic implementation without optimization. In particular, CHAM, which consists of simple operations that do not use tables, can significantly reduce kernel operating time through inline PTX. CHAM performance increased by 3.09 times when only the inline PTX optimization implementation method was applied. Since LEA is composed of simple operations like CHAM, it is possible to have an effective performance improvement through the inline PTX optimization method. When LEA applied only the inline PTX optimization implementation, the performance increased by 97%. LEA was able to obtain up to 6.48 times faster speed through all of the proposed optimization methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Platform** & **AES** & **CHAM** & **LEA** \\ \hline [PERSON] et al. [6] & GTX 680 & 63.9 & - & - \\ \hline [PERSON] et al. [8] & GTX 480 & 78.6 & - & - \\ \hline [PERSON] et al. [9] & GTX TITAN X & 207.25 & - & - \\  & GTX 1080 & 279.86 & - & - \\ \hline [PERSON] et al. [12] & GTX 980 & 154 & - & 678 \\  & GTX 1080 & 256 & - & 1478 \\ \hline [PERSON] et al. [13] & i5 [EMAIL_ADDRESS] GHz (CPU) & - & 1.33 & - \\ \hline [PERSON] et al. [10] & GTX 680 & - & - & 138.8 \\ \hline Our work & GTX 970 & 123 & 936 & 868 \\  & GTX 1070 & 214 & 1601 & 1505 \\  & RTX 2070 & 310 & 3033 & 2472 \\ \hline \end{tabular}
\end{table}
Table 8: Throughput comparison with existing implementations (Gbps).  
We studied the optimization of block cipher algorithms on various GPU platforms. In the future, we will conduct optimization research on public-key algorithms in the GPU environment. Through the results of this paper, it can be considered to be useful in environments such as cloud computing services and IoT edge computing services.  
Writing-original draft, S.A. and S.C.S.; Writing-review and editing, S.A. and S.C.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1058494).  
The authors declare no conflict of interest.