Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Initial key</td><td class="align_center"><span style="width: 17.8674ptpx;"><svg height="13.9182pt" id="M104" style="vertical-align:-5.2823pt" version="1.1" viewbox="-0.0498162 -8.6359 17.8674 13.9182" width="17.8674pt" 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="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.23,3.132)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,13.498,5.233)"><path d="M394 0V37C301 42 295 50 295 122V635C236 613 178 596 109 583V553L165 551C205 549 209 544 209 495V122C209 50 203 42 111 37V0H394Z"></path></g></svg></span></td><td class="align_center"><span style="width: 18.7352ptpx;"><svg height="13.9769pt" id="M105" style="vertical-align:-5.341001pt" version="1.1" viewbox="-0.0498162 -8.6359 18.7352 13.9769" width="18.7352pt" 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="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.23,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.362,5.233)"><path d="M455 312C455 472 400 635 248 635C95 635 39 458 39 312C39 144 93 -12 248 -12C400 -12 455 166 455 312ZM361 314C361 173 337 30 249 30C163 30 131 174 131 313C131 451 155 594 248 594C334 594 361 454 361 314Z"></path></g></svg></span></td></tr><tr><td class="align_left" colspan="2"><hr/></td></tr><tr><td class="align_left"><span style="width: 23.6526ptpx;"><svg height="11.439pt" id="M106" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 23.6526 11.439" width="23.6526pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.285,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.646,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g></svg></span></td><td class="align_center">49.911</td><td class="align_center">49.796</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Sensitivity analysis of initial value.</div>

Complexity

tab5

Table 5

Table 5: Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption 