Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left"><span style="width: 35.6575ptpx;"><svg height="9.48819pt" id="M685" style="vertical-align:-0.1802893pt" version="1.1" viewbox="-0.0498162 -9.3079 35.6575 9.48819" width="35.6575pt" 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="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g 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104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.56,0)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"></path></g></svg></span></td><td class="align_center">1</td><td class="align_center">2</td><td class="align_center">3</td><td class="align_center">4</td><td class="align_center">5</td><td class="align_center">Reference</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Correlation</td><td class="align_center"><span style="width: 16.8904ptpx;"><svg height="11.6412pt" id="M686" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5914 16.8904 11.6412" 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class="align_center">[<a href="/journals/scn/2020/4898612/#B18" target="_blank">18</a>]</td></tr><tr><td class="align_left">Correlation</td><td class="align_center">1</td><td class="align_center"><span style="width: 16.8904ptpx;"><svg height="11.6412pt" id="M689" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5914 16.8904 11.6412" width="16.8904pt" 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="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.24,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.8,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 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height="12.7112pt" id="M692" style="vertical-align:-1.1198pt" version="1.1" viewbox="-0.0498162 -11.5914 32.6302 12.7112" width="32.6302pt" 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="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.503,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.063,-5.741)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.495,-5.741)"><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"></path></g></svg></span></td><td class="align_center">This paper</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Correlation of the linear trails for Chaskey.</div>

Security and Communication Networks

tab7

Table 7

Table 7: Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64 