Multidivisible Online/Offline Cryptography and Its Application to Signcryptions

<div>Description of adversary <svg height="9.25986pt" id="M524" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 12.496 9.25986" width="12.496pt" 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="M895 660C863 648 835 636 808 620C736 668 639 687 564 687C395 687 153 589 153 403C153 307 221 260 300 260C447 260 534 401 534 561H514C506 396 415 290 305 290C234 290 194 335 194 396C194 555 383 657 566 657C626 657 716 643 776 601C669 531 592 432 501 271C389 71 313 16 189 16C118 16 69 60 69 95H71C78 84 93 83 101 83C129 83 144 106 144 131C144 160 121 179 93 179C60 179 34 150 34 107C34 41 100 -15 207 -15C365 -15 509 76 621 311C626 300 647 292 668 292C675 292 701 294 717 298C752 278 763 243 763 203C763 140 734 78 685 49C666 38 647 34 624 34C596 34 574 55 574 82C574 127 623 171 679 176L675 199C586 184 537 132 537 67C537 32 567 -11 631 -11C672 -11 710 0 743 22C804 63 839 127 839 186C839 234 813 289 749 316V318C837 329 902 398 902 463C902 524 873 566 830 601C850 615 874 628 902 641L895 660ZM841 485C841 420 802 346 717 338C697 349 675 352 662 352C655 352 644 351 639 348C691 449 736 524 801 580C825 555 841 524 841 485Z"></path></g></svg> attacking <svg height="11.5564pt" id="M525" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 86.7172 11.5564" width="86.7172pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g 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262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.036,0)"><path d="M716 650H478V622C549 617 570 605 575 566C579 535 582 493 582 401V326C582 161 537 40 393 40C269 40 205 133 205 294V521C205 611 213 617 291 622V650H33V622C111 615 120 611 120 521V272C120 154 148 80 208 34C252 0 309 -14 368 -14C434 -14 501 7 548 55C605 116 623 201 623 319V401C623 493 626 536 629 563C633 605 656 618 716 622V650Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.604,0)"><path d="M493 503C489 551 484 614 483 650H43V622C120 616 128 611 128 525V126C128 40 120 34 40 28V0H312V28C221 34 213 40 213 126V307H316C407 307 412 296 424 227H453V420H424C412 355 407 346 316 346H213V584C213 613 216 616 246 616H322C398 616 419 607 436 579C449 559 455 539 464 499L493 503Z"></path></g><g transform="matrix(.013,0,0,-0.013,52.56,0)"><path d="M300 253H71L57 198H286L300 253Z"></path></g><g transform="matrix(.013,0,0,-0.013,57.205,0)"><path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z"></path></g><g transform="matrix(.013,0,0,-0.013,65.85,0)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.013,0,0,-0.013,77.433,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z"></path></g></svg> security of <span class="nowrap"><svg height="8.98583pt" id="M526" style="vertical-align:-0.2324905pt" version="1.1" viewbox="-0.0498162 -8.75334 25.8579 8.98583" width="25.8579pt" 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="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.79,0)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.501,0)"><path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z"></path></g></svg>.</span></div>

Security and Communication Networks

fig11

Figure 11

Figure 11: Multidivisible Online/Offline Cryptography and Its Application to Signcryptions 