Two-Party Attribute-Based Key Agreement Protocol with Constant-Size Ciphertext and Key

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:6.54em"/><col style="width:9.94em"/></colgroup><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Protocol</td><td class="align_center">Communication cost</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Protocol [<a href="/journals/scn/2018/8738960/#B4" target="_blank">4</a>]</td><td class="align_center"><span style="width: 112.198ptpx;"><svg height="25.8198pt" id="M602" style="vertical-align:-6.468399pt" version="1.1" viewbox="-0.0498162 -19.3514 112.198 25.8198" width="112.198pt" 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="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 transform="matrix(.013,0,0,-0.013,6.24,0)"><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(.0091,0,0,-0.0091,11.67,-12.181)"><path d="M770 27H140L0 -163H35C42 -152 67 -128 110 -90C159 -48 191 -27 206 -27H704C719 -27 751 -48 800 -90C843 -128 868 -152 875 -163H910L770 27Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.738,0)"><path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"></path></g><rect height="0.484101" width="6.99246" x="13.91" y="-4.0673"></rect><rect height="0.484101" width="6.49432" x="13.91" y="-1.64679"></rect><g transform="matrix(.0091,0,0,-0.0091,13.91,6.419)"><path d="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.546,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.177,0)"><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,-0.013,38.417,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.915,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,46.334,0)"><path d="M664 534L634 568C565 641 475 676 375 676C172 676 45 530 45 333C45 141 176 -13 374 -13C478 -13 572 30 655 90V329H358V285H489V56C462 37 413 31 380 31C319 31 256 44 213 91V579C254 614 326 632 379 632C490 632 563 586 632 502L664 534ZM611 118C584 102 562 78 533 66V285H611V118ZM169 119C118 180 89 253 89 333C89 410 118 492 169 551V119Z"></path></g><g transform="matrix(.013,0,0,-0.013,55.512,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,61.837,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,72.373,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,76.792,-9.698)"><path d="M2350 683L2337 714C2213 634 2080 595 1900 595C1667 595 1473 615 1188 648C857 691 698 706 481 706C337 706 150 673 0 563L13 532C157 608 291 651 473 651C739 651 912 628 1162 598C1442 564 1661 540 1889 540C2041 540 2226 570 2350 683Z"></path></g><rect height="0.65243" width="32.6639" x="75.7922" y="-14.7346"></rect><rect height="0.65243" width="32.6639" x="75.7922" y="-11.4724"></rect><g transform="matrix(.013,0,0,-0.013,75.792,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,84.927,-4.551)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,86.036,4.041)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,92.151,6.142)"><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><g transform="matrix(.0091,0,0,-0.0091,95.873,4.041)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,98.029,4.041)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,104.144,6.142)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.013,0,0,-0.013,108.456,0)"><path d="M162 -163V703H101V-163H162Z"></path></g></svg></span></td></tr><tr><td class="align_left">Our protocol</td><td class="align_center"><span style="width: 75.4372ptpx;"><svg height="25.5432pt" id="M603" style="vertical-align:-6.191799pt" version="1.1" viewbox="-0.0498162 -19.3514 75.4372 25.5432" width="75.4372pt" 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="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.659,0)"><path d="M664 534L634 568C565 641 475 676 375 676C172 676 45 530 45 333C45 141 176 -13 374 -13C478 -13 572 30 655 90V329H358V285H489V56C462 37 413 31 380 31C319 31 256 44 213 91V579C254 614 326 632 379 632C490 632 563 586 632 502L664 534ZM611 118C584 102 562 78 533 66V285H611V118ZM169 119C118 180 89 253 89 333C89 410 118 492 169 551V119Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.837,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.162,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.698,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.117,-9.698)"><path d="M2350 683L2337 714C2213 634 2080 595 1900 595C1667 595 1473 615 1188 648C857 691 698 706 481 706C337 706 150 673 0 563L13 532C157 608 291 651 473 651C739 651 912 628 1162 598C1442 564 1661 540 1889 540C2041 540 2226 570 2350 683Z"></path></g><rect height="0.65243" width="32.6639" x="39.1172" y="-14.7346"></rect><rect height="0.65243" width="32.6639" x="39.1172" y="-11.4724"></rect><g transform="matrix(.013,0,0,-0.013,39.117,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.252,-4.551)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,49.361,4.041)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,55.476,6.142)"><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><g transform="matrix(.0091,0,0,-0.0091,59.198,4.041)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,61.354,4.041)"><path d="M757 650H506L497 618C579 615 596 608 596 570S591 477 571 380L560 327C516 117 435 41 309 41C199 41 108 114 144 303L187 529C202 609 208 612 291 618L296 650H30L24 618C109 612 113 606 99 529L58 299C33 161 62 83 113 41C161 0 222 -17 283 -17C348 -17 417 3 470 48C546 111 584 203 603 311L615 380C631 474 647 531 658 567C667 599 672 616 750 618L757 650Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,67.47,6.142)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.013,0,0,-0.013,71.781,0)"><path d="M162 -163V703H101V-163H162Z"></path></g></svg></span></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The comparison of communication cost.</div>

Security and Communication Networks

tab2

Table 2

Table 2: Two-Party Attribute-Based Key Agreement Protocol with Constant-Size Ciphertext and Key 