Privacy-Protection Scheme Based on Sanitizable Signature for Smart Mobile Medical Scenarios

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Notations</td><td class="align_center">Operations</td><td class="align_center">Time</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left"><span style="width: 21.0451ptpx;"><svg height="14.2627pt" id="M220" style="vertical-align:-5.30058pt" version="1.1" viewbox="-0.0498162 -8.96212 21.0451 14.2627" width="21.0451pt" 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(.0091,0,0,-0.0091,7.176,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.125,3.132)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.512,3.132)"><path d="M173 382V461C125 442 68 425 25 418V390C88 382 92 382 92 317V-127C92 -191 84 -199 18 -204V-235H259V-204C180 -196 173 -192 173 -120V7C188 -1 212 -11 243 -12C375 12 495 109 495 261C495 361 427 451 316 451C303 451 283 446 266 435L173 382ZM173 345C200 365 243 388 274 388C346 388 409 329 409 222C409 111 353 40 266 40C231 40 196 56 173 79V345Z"></path></g></svg></span></td><td class="align_center">A modular exponentiation operation</td><td class="align_center"><span style="width: 34.3917ptpx;"><svg height="8.55521pt" id="M221" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 34.3917 8.55521" width="34.3917pt" 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="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><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 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120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g></svg></span></td></tr><tr><td class="align_left"><span style="width: 16.6425ptpx;"><svg height="14.3267pt" id="M222" style="vertical-align:-5.36458pt" version="1.1" viewbox="-0.0498162 -8.96212 16.6425 14.3267" width="16.6425pt" 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(.0091,0,0,-0.0091,7.176,3.132)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.99,3.132)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z"></path></g></svg></span></td><td class="align_center">A point addition operation</td><td class="align_center"><span style="width: 34.3917ptpx;"><svg height="8.55521pt" id="M223" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 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22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.684,0)"><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,-0.013,27.924,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g></svg></span></td></tr><tr><td class="align_left"><span style="width: 19.9581ptpx;"><svg height="14.3267pt" id="M224" style="vertical-align:-5.36458pt" version="1.1" viewbox="-0.0498162 -8.96212 19.9581 14.3267" width="19.9581pt" 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(.0091,0,0,-0.0091,7.176,3.132)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.835,3.132)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"></path></g></svg></span></td><td class="align_center">A point multiplication operation</td><td class="align_center"><span style="width: 34.3917ptpx;"><svg height="8.55521pt" id="M225" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 34.3917 8.55521" width="34.3917pt" 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="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 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642 73 579V24C128 -2 179 -12 220 -12C353 -12 471 92 471 238C471 357 381 449 274 449C262 449 249 446 233 439L152 404ZM152 374C170 384 202 393 230 393C313 393 382 326 382 213C382 97 330 26 246 26C194 26 165 62 158 81C154 91 152 101 152 116V374Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.698,3.132)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g></svg></span></td><td class="align_center">A bilinear pair operation</td><td class="align_center"><span style="width: 34.3917ptpx;"><svg height="8.55521pt" id="M227" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 34.3917 8.55521" width="34.3917pt" xmlns="http://www.w3.org/2000/svg" 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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,-0.013,27.924,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg></span></td></tr><tr><td class="align_left"><span style="width: 22.5888ptpx;"><svg height="14.3267pt" id="M228" style="vertical-align:-5.36458pt" version="1.1" viewbox="-0.0498162 -8.96212 22.5888 14.3267" width="22.5888pt" 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 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<div>Running time of different operations (ms).</div>

Wireless Communications and Mobile Computing

tab2

Table 2

Table 2: Privacy-Protection Scheme Based on Sanitizable Signature for Smart Mobile Medical Scenarios 