Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg4"><tr><td colspan="2">(1) <b>procedure </b><svg height="12.2245pt" id="M394" style="vertical-align:-2.268109pt" version="1.1" viewbox="-0.0498162 -9.95639 41.5408 12.2245" width="41.5408pt" 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="M74 662V0H314C362 0 406 9 441 26C505 59 547 124 547 193C547 273 510 337 419 366C483 395 511 443 511 499C511 611 434 662 279 662H74ZM161 394V588H291C383 588 422 562 422 499C422 427 370 394 251 394H161ZM161 74V317H240C308 317 350 315 385 304C430 289 458 250 458 202C458 131 410 74 287 74H161Z" id="g202-13"></path><glyph.data ascent="684" descent="-216" horiz-adv-x="604" vert-adv-y="604" xpluscharwidth="7.8814752"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.881,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" 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460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" vert-adv-y="693" xpluscharwidth="21.027"></glyph.data></g></svg> is a <svg height="10.2959pt" id="M396" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -7.0048 32.9313 10.2959" width="32.9313pt" 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="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 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vert-adv-y="346" xpluscharwidth="75.962"></glyph.data></g></svg></td></tr><tr><td colspan="2">(4)<span style="margin-left:1em"></span><b>return</b>  <svg height="9.49473pt" id="M399" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="469" vert-adv-y="469" xpluscharwidth="6.097"></glyph.data></g></svg></td></tr><tr><td colspan="2">(5) <b>end procedure</b></td></tr></table></td></tr></table>

Security and Communication Networks

alg4

Algorithm 4

Algorithm 4: Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage 