Dynamic Outsourced Proofs of Retrievability Enabling Auditing Migration for Remote Storage Security

<div>An example of bv23Tree. Besides the verified ordered leaves set <span class="nowrap"><svg height="12.5794pt" id="M145" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 140.266 12.5794" width="140.266pt" 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="M608 643C551 682 486 687 443 687C299 687 188 608 188 504C188 361 341 312 465 312C483 312 501 313 518 315C454 195 366 93 314 59C255 82 201 109 141 109C73 109 33 83 33 52C33 13 76 -9 159 -9C218 -9 267 -1 314 15C354 0 402 -15 478 -15C575 -15 671 36 759 141L740 155C657 63 571 16 475 16C448 16 411 26 372 39C458 74 565 199 627 333C806 381 931 499 931 587C931 634 908 669 848 669C767 669 671 582 620 506C591 462 569 411 534 347C503 343 490 342 471 342C330 342 229 399 229 500C229 603 346 657 451 657C486 657 540 657 596 624L608 643ZM890 588C890 519 822 457 747 414C712 395 678 378 643 369C683 484 760 632 841 632C873 632 890 615 890 588ZM266 35C235 24 200 21 161 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62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path></g><g transform="matrix(.0091,0,0,-0.0091,85.307,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,89.739,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path></g><g transform="matrix(.013,0,0,-0.013,94.702,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g113-45"></path></g><g transform="matrix(.013,0,0,-0.013,99.845,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path></g><g transform="matrix(.0091,0,0,-0.0091,105.656,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,110.088,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,115.051,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g113-45"></path></g><g transform="matrix(.013,0,0,-0.013,120.194,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path></g><g transform="matrix(.0091,0,0,-0.0091,126.005,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,130.437,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path></g><g transform="matrix(.013,0,0,-0.013,135.4,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path></g></svg>,</span> the verifier only needs to retrieve the necessary auxiliary tree nodes (colored in red), which are organized into a special table structure as will be shown later. Then, the verifier can batch-verify the indices and values of these leaves in <svg height="9.25986pt" id="M146" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 12.4438 9.25986" width="12.4438pt" 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="M608 643C551 682 486 687 443 687C299 687 188 608 188 504C188 361 341 312 465 312C483 312 501 313 518 315C454 195 366 93 314 59C255 82 201 109 141 109C73 109 33 83 33 52C33 13 76 -9 159 -9C218 -9 267 -1 314 15C354 0 402 -15 478 -15C575 -15 671 36 759 141L740 155C657 63 571 16 475 16C448 16 411 26 372 39C458 74 565 199 627 333C806 381 931 499 931 587C931 634 908 669 848 669C767 669 671 582 620 506C591 462 569 411 534 347C503 343 490 342 471 342C330 342 229 399 229 500C229 603 346 657 451 657C486 657 540 657 596 624L608 643ZM890 588C890 519 822 457 747 414C712 395 678 378 643 369C683 484 760 632 841 632C873 632 890 615 890 588ZM266 35C235 24 200 21 161 21C103 21 74 32 74 54C74 75 122 79 141 79C172 79 209 69 266 36V35Z" id="g198-13"></path></g></svg> all together.</div>

Wireless Communications and Mobile Computing

fig2

Figure 2

Figure 2: Dynamic Outsourced Proofs of Retrievability Enabling Auditing Migration for Remote Storage Security 