<table><caption>Sensitivity on γ<sub>0</sub><sup>(2)</sup></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><th>Channel</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Baboon</th><td>33.378</td><td>33.502</td><td>33.427</td><td>33.487</td><td>33.428</td><td>33.368</td><td>33.427</td><td>33.487</td><td>33.476</td><td>33.395</td><td>33.451</td><td>33.473</td><td>33.454</td><td>33.498</td><td>33.452</td></tr><tr><th>Flowers</th><td>33.514</td><td>33.456</td><td>33.465</td><td>33.461</td><td>33.462</td><td>33.519</td><td>33.469</td><td>33.518</td><td>33.406</td><td>33.461</td><td>33.552</td><td>33.519</td><td>33.383</td><td>33.424</td><td>33.529</td></tr><tr><th>Peppers</th><td>33.441</td><td>33.497</td><td>33.463</td><td>33.527</td><td>33.551</td><td>33.447</td><td>33.420</td><td>33.439</td><td>33.401</td><td>33.417</td><td>33.434</td><td>33.407</td><td>33.424</td><td>33.433</td><td>33.547</td></tr><tr><th>Goldhill</th><td>33.449</td><td>33.475</td><td>33.422</td><td>33.460</td><td>33.439</td><td>33.473</td><td>33.437</td><td>33.512</td><td>33.468</td><td>33.420</td><td>33.435</td><td>33.452</td><td>33.499</td><td>33.440</td><td>33.470</td></tr><tr><th>Black</th><td>33.492</td><td></td><td></td><td>33.457</td><td></td><td></td><td>33.446</td><td></td><td></td><td>33.532</td><td></td><td></td><td>33.511</td><td></td><td></td></tr><tr><th>Boats</th><td>33.443</td><td></td><td></td><td>33.485</td><td></td><td></td><td>33.510</td><td></td><td></td><td>33.480</td><td></td><td></td><td>33.460</td><td></td><td></td></tr><tr><th>Clock</th><td>33.580</td><td></td><td></td><td>33.568</td><td></td><td></td><td>33.447</td><td></td><td></td><td>33.474</td><td></td><td></td><td>33.360</td><td></td><td></td></tr><tr><th>White</th><td>33.490</td><td></td><td></td><td>33.401</td><td></td><td></td><td>33.525</td><td></td><td></td><td>33.505</td><td></td><td></td><td>33.468</td><td></td><td></td></tr><tr><th>Average</th><td>33.468</td><td>Pass</td><td></td><td>33.471</td><td>Pass</td><td></td><td>33.462</td><td>Pass</td><td></td><td>33.463</td><td>Pass</td><td></td><td>33.460</td><td>Pass</td><td></td></tr></tbody></table>

<table><caption>Sensitivity on γ<sub>0</sub><sup>(1)</sup></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><th>Channel</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Baboon</th><td>33.485</td><td>33.417</td><td>33.565</td><td>33.533</td><td>33.441</td><td>33.486</td><td>33.526</td><td>33.505</td><td>33.466</td><td>33.395</td><td>33.477</td><td>33.537</td><td>33.466</td><td>33.353</td><td>33.495</td></tr><tr><th>Flowers</th><td>33.419</td><td>33.503</td><td>33.422</td><td>33.531</td><td>33.471</td><td>33.470</td><td>33.458</td><td>33.539</td><td>33.435</td><td>33.474</td><td>33.491</td><td>33.509</td><td>33.428</td><td>33.606</td><td>33.337</td></tr><tr><th>Peppers</th><td>33.469</td><td>33.441</td><td>33.507</td><td>33.430</td><td>33.483</td><td>33.420</td><td>33.431</td><td>33.514</td><td>33.452</td><td>33.467</td><td>33.527</td><td>33.488</td><td>33.526</td><td>33.417</td><td>33.430</td></tr><tr><th>Goldhill</th><td>33.492</td><td>33.448</td><td>33.422</td><td>33.467</td><td>33.507</td><td>33.532</td><td>33.495</td><td>33.448</td><td>33.453</td><td>33.459</td><td>33.436</td><td>33.466</td><td>33.450</td><td>33.487</td><td>33.424</td></tr><tr><th>Black</th><td>33.493</td><td></td><td></td><td>33.477</td><td></td><td></td><td>33.463</td><td></td><td></td><td>33.451</td><td></td><td></td><td>33.441</td><td></td><td></td></tr><tr><th>Boats</th><td>33.490</td><td></td><td></td><td>33.494</td><td></td><td></td><td>33.483</td><td></td><td></td><td>33.489</td><td></td><td></td><td>33.465</td><td></td><td></td></tr><tr><th>Clock</th><td>33.643</td><td></td><td></td><td>33.481</td><td></td><td></td><td>33.398</td><td></td><td></td><td>33.564</td><td></td><td></td><td>33.425</td><td></td><td></td></tr><tr><th>White</th><td>33.476</td><td></td><td></td><td>33.454</td><td></td><td></td><td>33.438</td><td></td><td></td><td>33.446</td><td></td><td></td><td>33.469</td><td></td><td></td></tr><tr><th>Average</th><td>33.481</td><td>Pass</td><td></td><td>33.480</td><td>Pass</td><td></td><td>33.469</td><td>Pass</td><td></td><td>33.480</td><td>Pass</td><td></td><td>33.451</td><td>Pass</td><td></td></tr></tbody></table>

<table><caption>Sensitivity on ω<sub>0</sub><sup>(2)</sup></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><th>Channel</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Baboon</th><td>33.443</td><td>33.405</td><td>33.436</td><td>33.426</td><td>33.391</td><td>33.423</td><td>33.515</td><td>33.496</td><td>33.520</td><td>33.519</td><td>33.483</td><td>33.371</td><td>33.411</td><td>33.475</td><td>33.512</td></tr><tr><th>Flowers</th><td>33.462</td><td>33.555</td><td>33.549</td><td>33.460</td><td>33.421</td><td>33.405</td><td>33.503</td><td>33.488</td><td>33.467</td><td>33.445</td><td>33.475</td><td>33.531</td><td>33.476</td><td>33.531</td><td>33.429</td></tr><tr><th>Peppers</th><td>33.525</td><td>33.531</td><td>33.469</td><td>33.411</td><td>33.543</td><td>33.459</td><td>33.434</td><td>33.500</td><td>33.471</td><td>33.436</td><td>33.448</td><td>33.455</td><td>33.409</td><td>33.424</td><td>33.432</td></tr><tr><th>Goldhill</th><td>33.469</td><td>33.463</td><td>33.445</td><td>33.453</td><td>33.448</td><td>33.392</td><td>33.497</td><td>33.512</td><td>33.444</td><td>33.489</td><td>33.504</td><td>33.450</td><td>33.420</td><td>33.437</td><td>33.449</td></tr><tr><th>Black</th><td>33.461</td><td></td><td></td><td>33.492</td><td></td><td></td><td>33.464</td><td></td><td></td><td>33.489</td><td></td><td></td><td>33.465</td><td></td><td></td></tr><tr><th>Boats</th><td>33.458</td><td></td><td></td><td>33.396</td><td></td><td></td><td>33.449</td><td></td><td></td><td>33.472</td><td></td><td></td><td>33.465</td><td></td><td></td></tr><tr><th>Clock</th><td>33.515</td><td></td><td></td><td>33.541</td><td></td><td></td><td>33.386</td><td></td><td></td><td>33.385</td><td></td><td></td><td>33.519</td><td></td><td></td></tr><tr><th>White</th><td>33.484</td><td></td><td></td><td>33.485</td><td></td><td></td><td>33.468</td><td></td><td></td><td>33.449</td><td></td><td></td><td>33.449</td><td></td><td></td></tr><tr><th>Average</th><td>33.479</td><td>Pass</td><td></td><td>33.447</td><td>Pass</td><td></td><td>33.476</td><td>Pass</td><td></td><td>33.463</td><td>Pass</td><td></td><td>33.456</td><td>Pass</td><td></td></tr></tbody></table>

<table><caption>Sensitivity on ω<sub>0</sub><sup>(1)</sup></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><th>Channel</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Baboon</th><td>33.520</td><td>33.447</td><td>33.503</td><td>33.472</td><td>33.469</td><td>33.395</td><td>33.428</td><td>33.500</td><td>33.526</td><td>33.484</td><td>33.541</td><td>33.491</td><td>33.430</td><td>33.395</td><td>33.450</td></tr><tr><th>Flowers</th><td>33.429</td><td>33.483</td><td>33.398</td><td>33.396</td><td>33.450</td><td>33.453</td><td>33.456</td><td>33.415</td><td>33.544</td><td>33.583</td><td>33.418</td><td>33.517</td><td>33.411</td><td>33.405</td><td>33.288</td></tr><tr><th>Peppers</th><td>33.469</td><td>33.517</td><td>33.442</td><td>33.436</td><td>33.418</td><td>33.465</td><td>33.517</td><td>33.393</td><td>33.500</td><td>33.425</td><td>33.439</td><td>33.441</td><td>33.469</td><td>33.427</td><td>33.435</td></tr><tr><th>Goldhill</th><td>33.517</td><td>33.447</td><td>33.444</td><td>33.455</td><td>33.476</td><td>33.489</td><td>33.423</td><td>33.452</td><td>33.406</td><td>33.420</td><td>33.476</td><td>33.451</td><td>33.414</td><td>33.461</td><td>33.440</td></tr><tr><th>Black</th><td>33.516</td><td></td><td></td><td>33.490</td><td></td><td></td><td>33.441</td><td></td><td></td><td>33.485</td><td></td><td></td><td>33.532</td><td></td><td></td></tr><tr><th>Boats</th><td>33.454</td><td></td><td></td><td>33.390</td><td></td><td></td><td>33.505</td><td></td><td></td><td>33.530</td><td></td><td></td><td>33.457</td><td></td><td></td></tr><tr><th>Clock</th><td>33.532</td><td></td><td></td><td>33.471</td><td></td><td></td><td>33.494</td><td></td><td></td><td>33.548</td><td></td><td></td><td>33.258</td><td></td><td></td></tr><tr><th>White</th><td>33.496</td><td></td><td></td><td>33.492</td><td></td><td></td><td>33.416</td><td></td><td></td><td>33.451</td><td></td><td></td><td>33.532</td><td></td><td></td></tr><tr><th>Average</th><td>33.476</td><td>Pass</td><td></td><td>33.451</td><td>Pass</td><td></td><td>33.464</td><td>Pass</td><td></td><td>33.481</td><td>Pass</td><td></td><td>33.425</td><td>Pass</td><td></td></tr></tbody></table>

<table><caption>Sensitivity on S<sub>0</sub></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><th>Channel</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Baboon</th><td>33.466</td><td>33.523</td><td>33.434</td><td>33.520</td><td>33.432</td><td>33.502</td><td>33.528</td><td>33.487</td><td>33.525</td><td>33.458</td><td>33.445</td><td>33.446</td><td>33.498</td><td>33.473</td><td>33.435</td></tr><tr><th>Flowers</th><td>33.450</td><td>33.456</td><td>33.519</td><td>33.409</td><td>33.457</td><td>33.484</td><td>33.462</td><td>33.487</td><td>33.525</td><td>33.478</td><td>33.388</td><td>33.551</td><td>33.441</td><td>33.579</td><td>33.440</td></tr><tr><th>Peppers</th><td>33.469</td><td>33.457</td><td>33.371</td><td>33.435</td><td>33.417</td><td>33.434</td><td>33.422</td><td>33.439</td><td>33.441</td><td>33.520</td><td>33.514</td><td>33.426</td><td>33.438</td><td>33.529</td><td>33.541</td></tr><tr><th>Continued</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>Goldhill</th><td>33.527</td><td>33.423</td><td>33.525</td><td>33.469</td><td>33.419</td><td>33.474</td><td>33.501</td><td>33.483</td><td>33.474</td><td>33.422</td><td>33.478</td><td>33.442</td><td>33.478</td><td>33.453</td><td>33.512</td></tr></tbody></table>
<table><caption>**Table 21.** Exemplar simulation for Structure 3 in Fig. 1c: Sensitivity of secret key by UACI.</caption><caption>Sensitivity on S<sub>0</sub></caption><thead><tr><th rowspan="2">N<sub>e</sub></th><th colspan="3">1</th><th colspan="3">2</th><th colspan="3">3</th><th colspan="3">4</th><th colspan="3">5</th></tr><tr><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th><th>R</th><th>G</th><th>B</th></tr></thead><tbody><tr><td>Black</td><td>33.426</td><td></td><td></td><td>33.551</td><td></td><td></td><td>33.431</td><td></td><td></td><td>33.446</td><td></td><td></td><td>33.526</td><td></td><td></td></tr><tr><td>Boats</td><td>33.497</td><td></td><td></td><td>33.449</td><td></td><td></td><td>33.436</td><td></td><td></td><td>33.465</td><td></td><td></td><td>33.446</td><td></td><td></td></tr><tr><td>Clock</td><td>33.501</td><td></td><td></td><td>33.633</td><td></td><td></td><td>33.383</td><td></td><td></td><td>33.573</td><td></td><td></td><td>33.471</td><td></td><td></td></tr><tr><td>White</td><td>33.494</td><td></td><td></td><td>33.492</td><td></td><td></td><td>33.518</td><td></td><td></td><td>33.496</td><td></td><td></td><td>33.433</td><td></td><td></td></tr><tr><td>Average</td><td>33.471 (Pass)</td><td></td><td></td><td>33.474 (Pass)</td><td></td><td></td><td>33.471 (Pass)</td><td></td><td></td><td>33.472 (Pass)</td><td></td><td></td><td>33.481 (Pass)</td><td></td><td></td></tr></tbody></table>

<table><caption>**Table 22.** Comparison with existing algorithms of chaos-based MIE.</caption><thead><tr><th rowspan="3">Algorithms</th><th colspan="4">Statistical analysis</th><th colspan="2">Security analysis</th><th colspan="2">Sensitivity of secret key</th></tr><tr><th rowspan="2">IE</th><th colspan="3">Corr. coeff. (worse cases on average)</th><th rowspan="2">χ<sup>2</sup></th><th rowspan="2">Key Space</th><th rowspan="2">by NCPR</th><th rowspan="2">by UACI</th></tr><tr><th>Horizontal</th><th>Vertical</th><th>Diagonal</th></tr></thead><tbody><tr><td>Structure 1</td><td>7.9992</td><td>0.0001</td><td>-0.0003</td><td>-0.0004</td><td>Pass</td><td>2<sup>486</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Structure 2</td><td>7.9992</td><td>0.0003</td><td>0.0002</td><td>-0.0003</td><td>Pass</td><td>2<sup>486</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Structure 3</td><td>7.9993</td><td>-0.0001</td><td>0.0003</td><td>0.0001</td><td>Pass</td><td>2<sup>486</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Karawia<sup>23</sup></td><td>7.9989</td><td>0.0002</td><td>0.0008</td><td>0.0008</td><td>-</td><td>10<sup>210</sup> ≈ 1.5209 × 2<sup>697</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Zarebnia<sup>25</sup></td><td>7.9995</td><td>-0.0036</td><td>0.00262</td><td>0.001239</td><td>-</td><td>10<sup>195</sup> ≈ 1.7124 × 2<sup>647</sup></td><td>-</td><td>-</td></tr><tr><td>Patro<sup>49</sup></td><td>7.9993</td><td>-0.0003</td><td>-0.0001</td><td>-0.0002</td><td>Pass</td><td>1.2446 × 2<sup>327</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Zhang<sup>6</sup></td><td>7.9993</td><td>-0.0003</td><td>0.0003</td><td>-0.0002</td><td>-</td><td>10<sup>56</sup> ≈ 1.0195 × 2<sup>186</sup></td><td>-</td><td>-</td></tr><tr><td>Malik<sup>24</sup></td><td>7.9993</td><td>0.0000</td><td>0.0008</td><td>0.0005</td><td>-</td><td>10<sup>165</sup> ≈ 1.3653 × 2<sup>548</sup></td><td>-</td><td>-</td></tr><tr><td>Patro<sup>26</sup></td><td>7.9993</td><td>-0.0006</td><td>-0.0001</td><td>-0.0020</td><td>-</td><td>1.964 × 2<sup>426</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Patro<sup>27</sup></td><td>7.9974</td><td>-0.0012</td><td>-0.0015</td><td>0.0005</td><td>-</td><td>1.964 × 2<sup>426</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Hoang<sup>38</sup></td><td>7.9972</td><td>0.0031</td><td>0.0018</td><td>0.0002</td><td>Pass</td><td>2<sup>332</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Hoang<sup>79</sup></td><td>7.9971</td><td>-0.0019</td><td>0.0018</td><td>-0.0010</td><td>Pass</td><td>2<sup>230</sup> (Logistic map) and 2<sup>230</sup> (Standard map)</td><td>Pass</td><td>Pass</td></tr><tr><td>Sahasrabuddhe<sup>30</sup></td><td>7.9999</td><td>-0.0036</td><td>0.0016</td><td>-0.0058</td><td>-</td><td>9.4599 × 10<sup>76</sup> ≈ 1.634 × 2<sup>255</sup></td><td>-</td><td>-</td></tr><tr><td>Jahangir<sup>31</sup></td><td>7.9979</td><td>-0.0002</td><td>0.0000</td><td>-0.0036</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Zhou<sup>33</sup></td><td>7.9999</td><td>-0.0017</td><td>-0.0006</td><td>0.0007</td><td>-</td><td>10<sup>15 × 8</sup> ≈ 1.5491 × 2<sup>398</sup></td><td>-</td><td>-</td></tr><tr><td>Tanveer<sup>34</sup></td><td>7.9963</td><td>0.0016</td><td>-0.0056</td><td>0.0015</td><td>-</td><td>10<sup>105</sup> ≈ 2<sup>348</sup></td><td>-</td><td>-</td></tr><tr><td>Liu<sup>39</sup></td><td>7.9897</td><td>-0.0119</td><td>-0.0087</td><td>-0.0045</td><td>-</td><td>10<sup>15</sup> × 16 ≈ 1.1997 × 2<sup>797</sup></td><td>-</td><td>-</td></tr><tr><td>Chen<sup>40</sup></td><td>7.9973</td><td>-0.0023</td><td>0.0024</td><td>0.0011</td><td>-</td><td>10<sup>103</sup> × 2<sup>108</sup> ≈ 1.1162 × 2<sup>450</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Qiu<sup>42</sup></td><td>7.9991</td><td>0.0008</td><td>0.0007</td><td>-0.0003</td><td>-</td><td>2<sup>512</sup></td><td>-</td><td>-</td></tr><tr><td>Joshi<sup>46</sup></td><td>7.9959</td><td>-0.0223</td><td>-0.0056</td><td>-0.0274</td><td>-</td><td>10<sup>75</sup> ≈ 2<sup>250</sup></td><td>-</td><td>-</td></tr><tr><td>Tang<sup>47</sup></td><td>-</td><td>0.0705</td><td>-0.1504</td><td>-0.0491</td><td>-</td><td>8 × 10<sup>63</sup> ≈ 1.2155 × 2<sup>212</sup></td><td>-</td><td>-</td></tr><tr><td>Kaur<sup>35</sup></td><td>7.9952</td><td>0.0013</td><td>0.0020</td><td>0.0042</td><td>-</td><td>10<sup>247</sup> ≈ 1.4302 × 2<sup>820</sup></td><td>-</td><td>-</td></tr><tr><td>Gao<sup>50</sup></td><td>7.9993</td><td>0.0021</td><td>0.0029</td><td>0.0023</td><td>Pass</td><td>10<sup>249</sup> ≈ 2<sup>827</sup></td><td>Pass</td><td>Pass</td></tr><tr><td>Haq<sup>7</sup></td><td>7.9994</td><td>0.0072</td><td>-0.0002</td><td>0.0006</td><td>-</td><td>2<sup>245</sup></td><td>-</td><td>-</td></tr><tr><td>Zhang<sup>36</sup></td><td>7.9992</td><td>0.0018</td><td>-0.0021</td><td>0.0018</td><td>-</td><td>10<sup>135</sup> × (8k)! ≈ 1.3712 × 2<sup>744</sup> (8 images)</td><td>-</td><td>-</td></tr><tr><td>Zhang<sup>32</sup></td><td>7.9936</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<figure><img src="image_18.png" /><figcaption>Fig. 9. The hardware architecture.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 10. Blocks of pixels.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 11. Timing diagram of the scheme of two consecutive read commands with the DDR4 SDRAM<sup>76</sup>.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 12. Operation phases of MIE-IP.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. 13. The abstract architecture of the MIE-IP.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 14. Timing diagram of PCM pipelining computing.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>**Fig. 15.** The method of organizing image data in the DDR4 SDRAM for images ①, ②, ③, and ④.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>**Fig. 16.** The FSM of Global Controller for a single cohort of pixels.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Fig. 17.** The FSMs of AXI4 Controller for reading and writing operations between the SRAM and the DDR4 SDRAM.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>(a) Setting up for testing</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 18. Testing model for the system.</figcaption></figure>

<table><caption>Table 23. Resource utilization and power consumption of the MIE-IP and MIE system.</caption><thead><tr><td>Metrics</td><td>MIE-IP</td><td>MIE system</td></tr></thead><tbody><tr><td>ALMs</td><td>20,222/251,680 (8.03%)</td><td>55,599/251,680 (22.09%)</td></tr><tr><td>Registers</td><td>25,866/503,360 (5.14%)</td><td>85,787/503,360 (17.04%)</td></tr><tr><td>Block memory bits</td><td>1,152/43,642,880 (0.26%)</td><td>32,397,108/43,642,880 (74.23%)</td></tr><tr><td>RAM blocks</td><td>11/2,131 (0.516%)</td><td>2,048/2,131 (96.1%)</td></tr><tr><td>DSP blocks</td><td>140/1,687 (8.29%)</td><td>143/1,687 (8.47%)</td></tr><tr><td>Power consumption (W)</td><td>1.423</td><td>6.828</td></tr></tbody></table>
<table><caption>**Table 24.** Speed and efficiency of the MIE-IP.</caption><tr><td>Speed</td><td>Maximum frequency (MHz)</td><td>51.99</td></tr><tr><td></td><td>Throughput (Mbps)</td><td>998.2</td></tr><tr><td colspan="2">Efficiency (Mbps/ALMs)</td><td>0.018</td></tr></table>

<table><caption>**Table 25.** Comparison of hardware metrics between the proposed system and other reported non-chaos-based and chaos-based ciphers.</caption><thead><tr><td>Cipher</td><td>Year</td><td>Implementation target</td><td>Throughput (Mbps)</td><td>Efficiency</td></tr></thead><tbody><tr><td>LED (64-bit key)<sup>78</sup></td><td>2020</td><td>ASIC</td><td>680.3</td><td>0.191</td></tr><tr><td>LED (128-bit key)<sup>78</sup></td><td>2020</td><td>ASIC</td><td>1010.1</td><td>0.284</td></tr><tr><td>RC4<sup>80</sup></td><td>2000</td><td>FPGA</td><td>135.52</td><td>0.013</td></tr><tr><td>A5/1<sup>81</sup></td><td>2004</td><td>FPGA</td><td>90.85</td><td></td></tr><tr><td>E0<sup>81</sup></td><td>2004</td><td>FPGA</td><td>93.36</td><td></td></tr><tr><td>Moustique<sup>82</sup></td><td>2008</td><td>FPGA</td><td>369</td><td></td></tr><tr><td>Chaos-based stream cipher<sup>83</sup></td><td>2014</td><td>FPGA</td><td>3682.87</td><td>0.411</td></tr><tr><td>Chaos-ring<sup>84</sup></td><td>2020</td><td>FPGA</td><td>464.688</td><td>-</td></tr><tr><td>LSPT-SC<sup>77</sup></td><td>2020</td><td>FPGA</td><td>992.21</td><td>0.29</td></tr><tr><td>LSP-SC<sup>77</sup></td><td>2020</td><td>FPGA</td><td>1037.27</td><td>0.32</td></tr><tr><td>LST-SC<sup>77</sup></td><td>2020</td><td>FPGA</td><td>1179.07</td><td>1.12</td></tr><tr><td>AES-128 (FSM Architecture)<sup>79</sup></td><td>2020</td><td>FPGA</td><td>3485</td><td>2.591</td></tr><tr><td>AES-128 (Loop Unrolled)<sup>79</sup></td><td>2020</td><td>FPGA</td><td>4342</td><td>0.488</td></tr><tr><td>AES-256<sup>85</sup></td><td>2021</td><td>FPGA</td><td>278</td><td>-</td></tr><tr><td>CLEFIA (three configurations)<sup>86</sup></td><td>2021</td><td>FPGA</td><td>990/818/696</td><td>-</td></tr><tr><td>4D memristive hyperchaos cipher<sup>87</sup></td><td>2024</td><td>FPGA</td><td>163.84</td><td>-</td></tr><tr><td>This exemplar design</td><td><strong>2024</strong></td><td>FPGA</td><td><strong>998.2</strong></td><td><strong>0.018</strong></td></tr></tbody></table>

## Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

## Code availability

The code used for simulation, design, and analysis during the current study is available from the corresponding author on reasonable request.

Received: 7 March 2025; Accepted: 25 November 2025

Published online: 14 December 2025

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## Acknowledgements

This research is funded by Hanoi University of Science and Technology (HUST) under project number T2023-TĐ-013.

## Author contributions

T.M.H.: conceptualization, methodology, visualization, writing original draft, review and editing, funding acquisition. P.Q.A.: visualization, original draft writing, hardware design, test and verification. M.-H.H.: software design for simulation, review, and editing. D.Q.T.: software design for analysis. S.E.A.: conceptualization, methodology.
**Declarations**

**Competing interests**

The authors declare no competing interests.

**Additional information**

Correspondence and requests for materials should be addressed to T.M.H.

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