Nonlinear Multi-Image Encryption Scheme with the Reality-Preserving Discrete Fractional Angular Transform and DNA Sequences

<div>Decrypted images with deviated keys: (a) <span class="nowrap"><svg height="14.7729pt" id="M226" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -11.5914 100.558 14.7729" width="100.558pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.304,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g 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272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z"></path></g></svg>,</span> (b) <span class="nowrap"><svg height="14.7729pt" id="M227" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -11.5914 100.558 14.7729" width="100.558pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M430 689C430 695 425 700 413 700C377 700 332 667 290 635C232 640 213 677 213 696C213 713 220 724 226 732L209 744C166 731 135 700 135 674C135 636 184 601 255 599C144 503 23 345 23 181C23 82 68 44 135 20C156 12 177 7 202 2C238 -5 252 -25 252 -53C252 -98 211 -144 192 -164L214 -187C257 -152 328 -92 328 -19C328 31 298 58 251 70C230 75 208 81 189 88C142 105 108 134 108 208C108 346 202 512 303 595C352 599 430 626 430 689Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.304,3.132)"><path d="M414 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602Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.589,0)"><path d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z"></path></g><g transform="matrix(.013,0,0,-0.013,46.831,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.071,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,62.217,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,72.754,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,78.994,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,85.28,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,90.84,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,95.272,-5.741)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z"></path></g></svg>,</span> and (c) <span class="nowrap"><svg height="11.9413pt" id="M228" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5914 74.4613 11.9413" width="74.4613pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.28,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 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Security and Communication Networks

fig7

Figure 7

Figure 7: Nonlinear Multi-Image Encryption Scheme with the Reality-Preserving Discrete Fractional Angular Transform and DNA Sequences 