# An Optimized Flexible Accelerator for Elliptic Curve Point Multiplication over NIST Binary Fields
## 2 Lopez-Dahab Projective Form of ECC over \(GF(2^{m})\)
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Ref. \#** & **Algorithm (on)** & **Device** & **Slices** & **LUTs** & **Clock** & **Freq** & **Latency** & **Thrypt** & **T/Area** & **m** \\  & **PM Method** & & & & **Cycles** & **MHz** & **(ios)** & **(Kyps)** & & \\ \hline Area-optimized PM accelerators & & & & & & & & & & \\ \hline
[12] & Montgomery Ladder & Virtex-5 & 473 & – & – & 359 & 110 & 9.09 & 19.21 & 163 \\
[12] & Binary & Virtex-5 & 420 & – & – & 362 & 830 & 1.20 & 2.85 & 163 \\
[12] & Frobenius Map & Virtex-5 & 710 & – & – & 165 & 300 & 3.33 & 4.69 & 163 \\
[13] & Lopez-Dahab & Virtex-7 & 3657 & 10,128 & 3426 & 135 & 25 & 40 & 10.93 & 163 \\
[15] & Montgomery Ladder & Artix-7 & 442 & – & 1,553,782 & 190 & 8177 & 0.12 & 0.27 & 233 \\
[16] & Frobenius Map & Artix-7 & – & 8577 & 550,068 & 150 & 367 & 2.72 & 0.31 & 163 \\ \hline Throughput and area-optimized PM architectures & & & & & & & & & \\ \hline
[17] & Montgomery Ladder & Virtex-7 & 2207 & 9965 & 3960 & 369 & 10 & 100 & 45.31 & 163 \\
[17] & Montgomery Ladder & Virtex-7 & 5120 & 189,53 & 5634 & 357 & 15 & 66.66 & 13.01 & 233 \\
[17] & Montgomery Ladder & Virtex-7 & 5207 & 20,202 & 6850 & 337 & 20 & 50 & 9.60 & 283 \\
[18] & Montgomery Ladder & Virtex-7 & 1529 & 4162 & 3798 & 383 & 9 & 111.11 & 72.66 & 163 \\
[18] & Montgomery Ladder & Virtex-7 & 2048 & 6407 & 5402 & 379 & 14 & 71.42 & 34.87 & 233 \\
[18] & Montgomery Ladder & Virtex-7 & 2623 & 6753 & 6568 & 377 & 17 & 58.82 & 22.42 & 283 \\
[18] & Montgomery Ladder & Virtex-7 & 3373 & 10,083 & 9454 & 342 & 27 & 37.03 & 10.97 & 409 \\
[19] & Montgomery Ladder & Virtex-7 & 4560 & 12,691 & 12,329 & 340 & 36 & 27.77 & 6.08 & 571 \\ \hline Throughput/speed-optimized PM designs & & & & & & & & & \\ \hline
[14] & Montgomery Ladder & Virtex-5 & 6150 & 22,936 & 1571 & 250 & 5 & 200 & 32.52 & 163 \\
[14] & Montgomery Ladder & Virtex-5 & 8134 & 28,683 & 2898 & 145 & 20 & 50 & 6.14 & 233 \\
[14] & Montgomery Ladder & Virtex-5 & 7069 & 25,030 & 647 & 189 & 33 & 30.30 & 3.28 & 283 \\
[14] & Montgomery Ladder & Virtex-5 & 10,236 & 28,503 & 16,541 & 161 & 102 & 9.80 & 0.95 & 409 \\
[14] & Montgomery Ladder & Virtex-5 & 11,640 & 32,432 & 44,007 & 127 & 348 & 2.87 & 0.24 & 571 \\
[19] & Double and Add & Virtex-7 & – & 50,789 & 65,783 & 91 & 722 & 1.38 & 0.02 & 256 \\
[20] & Montgomery Ladder & Virtex-7 & 2234 & 5478 & – & 170 & 352 & 2.84 & 1.27 & 225919 \\
[21] & NAF & Virtex-7 & – & 46,638 & 7,955k & 40 & 200 & 5 & 0.10 & 256 \\
[22] & Double and Add & Virtex-7 & 6543 & 25,998 & 198,715 & 104 & 1903 & 0.52 & 0.07 & 256 \\
[23] & Montgomery Ladder & Virtex-7 & 6099 & – & 32,3k & 232 & 139 & 7.19 & 1.04 & 256 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison to most recent state-of-the-art PM hardware accelerators. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Ref. \#** & **Algorithm (or)** & **Device** & **Slices** & **LUPs** & \begin{tabular}{c} **Clock** \\ **Cycles** \\ \end{tabular} & \begin{tabular}{c} **Freq** \\ **MHz** \\ \end{tabular} & \begin{tabular}{c} **Latency** \\ **(as)** \\ \end{tabular} & \begin{tabular}{c} **Thript** \\ **(Kyps)** \\ \end{tabular} & \begin{tabular}{c} **T/Area** \\ \end{tabular} & \
\begin{tabular}{c} **m** \\ \end{tabular} \\ \hline \multirow{6}{*}{TW} & \multirow{6}{*}{Montgomery Ladder} & \multirow{6}{*}{
\begin{tabular}{c} 173 \\ 2291 \\ 3543 \\ 4758 \\ \end{tabular} } & 1479 & 3862 & 2653 & 339 & 7.82 & 127.87 & 72.12 & 163 \\  & & 2291 & 6681 & 3775 & 321 & 11.76 & 58.03 & 37.11 & 233 \\  & & 2291 & 6896 & 4575 & 303 & 15.09 & 66.26 & 23.09 & 283 \\  & & 3543 & 10,081 & 6773 & 287 & 23.59 & 42.39 & 11.96 & 409 \\  & & 4758 & 12.269 & 9187 & 269 & 34.15 & 29.82 & 4.31 & 571 \\ \cline{2-11}  & & 1479 & 3862 & 2653 & 371 & 7.15 & 139.86 & 94.56 & 163 \\  & & 1998 & 6079 & 3775 & 356 & 10.60 & 94.33 & 47.21 & 233 \\  & & 2573 & 6341 & 4575 & 345 & 13.26 & 75.41 & 29.20 & 283 \\  & & 3271 & 9983 & 6773 & 323 & 20.96 & 47.70 & 14.58 & 409 \\  & & 4469 & 11.871 & 9187 & 302 & 30.42 & 32.87 & 7.35 & 571 \\ \hline \end{tabular}
\end{table}