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

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Initial key</td><td class="align_center" colspan="3">Correlation coefficient</td></tr><tr class="thead"><td class="align_center"><span style="width: 18.7352ptpx;"><svg height="13.9769pt" id="M120" 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><td class="align_center"><span style="width: 17.8674ptpx;"><svg height="13.9182pt" id="M121" 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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: 17.1732ptpx;"><svg height="13.9182pt" id="M122" style="vertical-align:-5.2823pt" version="1.1" viewbox="-0.0498162 -8.6359 17.1732 13.9182" width="17.1732pt" 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="M460 334C460 396 434 451 378 451C330 451 241 408 148 300H146L237 679C241 697 241 710 232 710C213 710 153 684 67 675L66 646H95C141 646 145 642 134 595L39 170C23 97 31 54 46 33C64 8 100 -12 137 -12C178 -12 234 3 298 43C391 101 460 222 460 334ZM371 320C371 204 316 89 248 51C230 41 208 37 192 37C143 37 102 72 119 166C124 194 129 215 135 235C202 323 298 392 335 392C353 392 371 372 371 320Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.806,5.233)"><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></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">—</td><td class="align_center">0.0041</td><td class="align_center">0.0018</td><td class="align_center">−0.0022</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Correlation coefficient of different initial keys.</div>

Complexity

tab6

Table 6

Table 6: Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption 