Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg2"><tr><td colspan="2"><span class="sans-serif">Enc</span>:<span style="margin-left:12.222222222222221em"></span><svg height="16.0921pt" id="M189" style="vertical-align:-3.8339pt" version="1.1" viewbox="-0.0498162 -12.2582 37.7992 16.0921" width="37.7992pt" 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="M823 0V32C771 40 767 43 767 100V293C767 395 719 454 632 454C603 454 576 441 554 426C530 409 507 394 482 376C464 421 424 454 368 454C339 454 312 442 281 422C259 409 240 395 218 379V456C157 439 89 425 42 418V389C89 382 93 373 93 315V105C93 42 88 39 30 32V0H265V32C227 38 220 43 220 100V344C248 366 273 376 297 376C334 376 366 354 366 282V100C366 41 362 38 315 32V0H546V32C501 38 494 43 494 100V302C494 317 493 331 492 342C524 369 549 376 569 376C601 376 639 359 639 277V105C639 42 632 38 588 32V0H823Z" id="g13-107"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="843" vert-adv-y="843" xpluscharwidth="10.959"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.591,0)"><path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528" xpluscharwidth="21.455"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.087,0)"><path d="M567 618V662H70V0H236V304H501V348H236V618H567ZM192 44H114V618H192V44Z" id="g197-17"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="469" vert-adv-y="469" xpluscharwidth="31.2068872"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,32.462,-5.741)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509" xpluscharwidth="37.093884730000006"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,31.184,3.784)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="35.61568539"></glyph.data></g></svg></td></tr><tr><td colspan="2"><span style="margin-left:2.2222222222222223em"></span>Generate a random<span style="margin-left:5em"></span><svg height="12.0262pt" id="M190" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" 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="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="504" vert-adv-y="504" xpluscharwidth="6.552"></glyph.data></g></svg></td></tr><tr><td colspan="2"><span style="margin-left:4.4444444444444446em"></span>suffix<span style="margin-left:7.5555555555555554em"></span><svg height="13.7903pt" id="M191" style="vertical-align:-3.83391pt" version="1.1" viewbox="-0.0498162 -9.95639 31.8568 13.7903" width="31.8568pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z" id="g13-120"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="445" vert-adv-y="445" xpluscharwidth="5.785"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.417,0)"><path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528" xpluscharwidth="16.281"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.913,0)"><path d="M567 618V662H70V0H236V304H501V348H236V618H567ZM192 44H114V618H192V44Z" id="g197-17"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="469" vert-adv-y="469" xpluscharwidth="26.0328872"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,27.288,-5.741)"><path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z" id="g50-115"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="427" vert-adv-y="427" xpluscharwidth="31.173687190000003"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,26.01,3.784)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="30.441685390000004"></glyph.data></g></svg></td></tr><tr><td colspan="2"><span style="margin-left:15em"></span><svg height="12.0262pt" id="M192" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" 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="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="504" vert-adv-y="504" xpluscharwidth="6.552"></glyph.data></g></svg></td></tr><tr><td colspan="2"><span style="margin-left:3.3333333333333335em"></span>Add suffix<span style="margin-left:5.5555555555555554em"></span><svg height="16.8803pt" id="M193" style="vertical-align:-3.834001pt" version="1.1" viewbox="-0.0498162 -13.0463 62.444 16.8803" width="62.444pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" xpluscharwidth="4.498"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M823 0V32C771 40 767 43 767 100V293C767 395 719 454 632 454C603 454 576 441 554 426C530 409 507 394 482 376C464 421 424 454 368 454C339 454 312 442 281 422C259 409 240 395 218 379V456C157 439 89 425 42 418V389C89 382 93 373 93 315V105C93 42 88 39 30 32V0H265V32C227 38 220 43 220 100V344C248 366 273 376 297 376C334 376 366 354 366 282V100C366 41 362 38 315 32V0H546V32C501 38 494 43 494 100V302C494 317 493 331 492 342C524 369 549 376 569 376C601 376 639 359 639 277V105C639 42 632 38 588 32V0H823Z" id="g13-107"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="843" vert-adv-y="843" xpluscharwidth="15.457"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.457,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228" xpluscharwidth="18.421"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.6,0)"><path d="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z" id="g13-120"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="445" vert-adv-y="445" xpluscharwidth="26.385"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.385,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 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-5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509" xpluscharwidth="57.01888473"></glyph.data></g><g transform="matrix(.0065,0,0,-0.0065,57.019,-9.852)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 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style="margin-left:3.8888888888888888em"></span>Encode<span style="margin-left:6.666666666666667em"></span><svg height="13.7903pt" id="M195" style="vertical-align:-3.83391pt" version="1.1" viewbox="-0.0498162 -9.95639 32.3331 13.7903" width="32.3331pt" 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="M399 120C363 89 334 79 292 79S154 123 154 256C154 363 199 401 238 401C266 401 298 385 339 349C348 341 354 338 361 338C378 338 404 364 404 393C405 407 401 419 386 429C369 443 336 454 300 454H299C261 454 196 440 130 392C67 345 29 274 29 201C29 92 109 -12 246 -12C307 -12 372 31 418 96L399 120Z" id="g13-97"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="422" vert-adv-y="422" xpluscharwidth="5.486"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.118,0)"><path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528" xpluscharwidth="15.982"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.614,0)"><path d="M567 618V662H70V0H236V304H501V348H236V618H567ZM192 44H114V618H192V44Z" id="g197-17"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="469" vert-adv-y="469" xpluscharwidth="25.7338872"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,26.99,-5.741)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512" xpluscharwidth="31.649184639999998"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,25.711,3.784)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="30.142685389999997"></glyph.data></g></svg></td></tr></table></td></tr></table>

<div><span class="sans-serif">AddHomSE</span> encryption.</div>

Security and Communication Networks

alg2

Algorithm 2

Algorithm 2: Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage 