Cryptanalysis of Compact-LWE and Related Lightweight Public Key Encryption

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:5.40em"/><col style="width:7.75em"/><col style="width:7.75em"/><col style="width:7.39em"/><col style="width:6.02em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Parameter</td><td class="align_center">Time for Step <a href="https://static.hindawi.com/articles/scn/volume-2018/4957045/figures/#step1" target="_blank">1</a></td><td class="align_center">Time for Step <a href="https://static.hindawi.com/articles/scn/volume-2018/4957045/figures/#step2" target="_blank">2</a></td><td class="align_center">Time for attack</td><td class="align_center">Success rate</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"> <svg height="8.97279pt" id="M451" style="vertical-align:-0.2324896pt" version="1.1" viewbox="-0.0498162 -8.7403 34.3135 8.97279" width="34.3135pt" 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="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z" id="g13-78"></path></g><g transform="matrix(.013,0,0,-0.013,7.5,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z" id="g13-95"></path></g><g transform="matrix(.013,0,0,-0.013,13.493,0)"><path d="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z" id="g13-112"></path></g><g transform="matrix(.013,0,0,-0.013,18.849,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z" id="g13-95"></path></g><g transform="matrix(.013,0,0,-0.013,24.907,0)"><path d="M687 0V35C623 43 611 56 577 144C512 316 450 490 386 665L335 652L130 138C97 54 84 43 18 35V0H242V35C169 44 166 58 181 106C193 146 206 182 217 213H409C424 173 439 130 449 100C465 56 460 44 401 35V0H687ZM390 266H234C260 337 285 410 313 483H316L390 266Z" id="g13-63"></path></g></svg></td><td class="align_center"> 0.57 s</td><td class="align_center"> 1.14 s</td><td class="align_center"> 1.71 s</td><td class="align_center"> 100%</td></tr><tr><td class="align_left"> <svg height="8.97279pt" id="M452" style="vertical-align:-0.2324896pt" version="1.1" viewbox="-0.0498162 -8.7403 33.4131 8.97279" width="33.4131pt" 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="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z" id="g13-78"></path></g><g transform="matrix(.013,0,0,-0.013,7.5,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z" id="g13-95"></path></g><g transform="matrix(.013,0,0,-0.013,13.493,0)"><path d="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z" id="g13-112"></path></g><g transform="matrix(.013,0,0,-0.013,18.849,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z" id="g13-95"></path></g><g transform="matrix(.013,0,0,-0.013,24.907,0)"><path d="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z" id="g13-64"></path></g></svg></td><td class="align_center"> 0.57 s</td><td class="align_center"> 1.14 s</td><td class="align_center"> 1.71 s</td><td class="align_center"> 100%</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Experimental results for optimized attack.</div>

Security and Communication Networks

tab2

Table 2

Table 2: Cryptanalysis of Compact-LWE and Related Lightweight Public Key Encryption 