SEMDA: Secure and Efficient Multidimensional Data Aggregation in Smart Grid without a Trusted Third Party

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Scheme</td><td class="align_center"><svg height="8.98583pt" id="M280" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 74.6948 8.98583" width="74.6948pt" 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="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.875,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.588,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.124,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.558,0)"><path d="M445 282C445 390 384 448 297 448C266 448 231 437 189 418C96 376 23 279 23 151C23 65 66 -12 169 -12C233 -12 294 18 337 53C411 113 445 201 445 282ZM355 280C355 161 302 62 243 36C231 31 219 30 207 30C147 30 111 78 111 154C111 302 180 380 220 399C231 404 246 407 264 407C311 407 355 367 355 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.547,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,56.084,0)"><path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,63.457,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z"></path></g></svg> (n)</td><td class="align_center"><svg height="8.98583pt" id="M281" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.6359 73.3769 8.98583" width="73.3769pt" 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="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.373,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.189,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.725,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.159,0)"><path d="M445 282C445 390 384 448 297 448C266 448 231 437 189 418C96 376 23 279 23 151C23 65 66 -12 169 -12C233 -12 294 18 337 53C411 113 445 201 445 282ZM355 280C355 161 302 62 243 36C231 31 219 30 207 30C147 30 111 78 111 154C111 302 180 380 220 399C231 404 246 407 264 407C311 407 355 367 355 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.148,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,55.685,0)"><path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.369,0)"><path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g></svg> (k)</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">MSDA [<a href="/journals/scn/2023/6693296/#B31" target="_blank">31</a>]</td><td class="align_center">2048</td><td class="align_center">2048</td></tr><tr><td class="align_left">EPMDA-FED [<a href="/journals/scn/2023/6693296/#B18" target="_blank">18</a>]</td><td class="align_center">3200</td><td class="align_center">3200</td></tr><tr><td class="align_left">FPDA [<a href="/journals/scn/2023/6693296/#B11" target="_blank">11</a>]</td><td class="align_center">2048</td><td class="align_center">2048</td></tr><tr><td class="align_left">Our</td><td class="align_center">3168</td><td class="align_center">3168</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of communication overhead.</div>

Security and Communication Networks

tab7

Table 7

Table 7: SEMDA: Secure and Efficient Multidimensional Data Aggregation in Smart Grid without a Trusted Third Party 