A Hierarchical Matrix Decomposition-Based Signcryption without Key-Recovery in Large-Scale WSN

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:3.83em"/><col style="width:3.95em"/><col style="width:6.50em"/><col style="width:6.50em"/><col style="width:1.96em"/><col style="width:10.34em"/><col style="width:7.69em"/></colgroup><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Factor</td><td class="align_center">r<sub>11</sub></td><td class="align_center">r<sub>22</sub></td><td class="align_center">r<sub>33</sub></td><td class="align_center">...</td><td class="align_center"><span style="width: 44.0943ptpx;"><svg height="10.6534pt" id="M125" style="vertical-align:-4.679451pt" version="1.1" viewbox="-0.0498162 -5.97395 44.0943 10.6534" width="44.0943pt" 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="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.823,3.132)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.081,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.15,3.132)"><path d="M300 253H71L57 198H286L300 253Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.401,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 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0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.892,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Y/<svg height="8.72483pt" id="M127" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -5.54333 9.26865 8.72483" width="9.26865pt" 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="M474 0V26C414 34 401 43 364 100L267 248C300 297 324 332 345 358C381 400 394 405 455 411V437H272V411C316 406 323 401 305 370C287 337 267 306 247 276L188 369C169 397 173 405 215 411V437H16V411C71 404 83 396 114 348L201 212C171 167 144 127 116 92C77 42 66 34 4 26V0H190V26C139 34 136 43 156 77C175 113 198 150 220 183L294 66C311 39 302 31 260 26V0H474Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.136,3.132)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z"></path></g></svg></td><td class="align_center">Y<sub>1</sub>=r<sub>11</sub></td><td class="align_center">Y<sub>2</sub>=<svg height="8.72483pt" id="M128" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -5.54333 9.26865 8.72483" width="9.26865pt" 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class="tbody-hr"/></td></tr></table></td></tr></table>

Wireless Communications and Mobile Computing

tab2

Table 2

Table 2: A Hierarchical Matrix Decomposition-Based Signcryption without Key-Recovery in Large-Scale WSN 