Hierarchical Key Management Scheme with Probabilistic Security in a Wireless Sensor Network (WSN)

<p>Key establishment between sensor with <svg height="12.4633pt" id="M38" style="vertical-align:-3.22715pt" version="1.1" viewbox="-0.0498162 -9.23615 15.7617 12.4633" width="15.7617pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.484,0)"><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><g transform="matrix(.0091,0,0,-0.0091,10.348,3.132)"><path d="M523 0V30C483 33 455 48 422 83C390 115 285 234 266 263C309 314 327 333 351 357C388 392 414 404 483 415V444L273 435V405C320 400 321 392 302 364C285 339 256 300 233 277C218 262 201 250 170 243V710C130 697 73 680 22 675V647C85 642 89 637 89 570V107C89 44 83 35 14 30V0H244V30C179 35 170 41 170 107V214C176 216 181 217 186 217C194 217 203 212 216 196C273 129 333 54 384 -1L523 0Z"></path></g></svg> and sensor with <svg height="14.724pt" id="M39" style="vertical-align:-5.48785pt" version="1.1" viewbox="-0.0498162 -9.23615 13.3868 14.724" width="13.3868pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.484,0)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 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560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.484,0)"><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><g transform="matrix(.0091,0,0,-0.0091,10.348,3.132)"><path d="M523 0V30C483 33 455 48 422 83C390 115 285 234 266 263C309 314 327 333 351 357C388 392 414 404 483 415V444L273 435V405C320 400 321 392 302 364C285 339 256 300 233 277C218 262 201 250 170 243V710C130 697 73 680 22 675V647C85 642 89 637 89 570V107C89 44 83 35 14 30V0H244V30C179 35 170 41 170 107V214C176 216 181 217 186 217C194 217 203 212 216 196C273 129 333 54 384 -1L523 0Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.255,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.518,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.002,0)"><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><g transform="matrix(.0091,0,0,-0.0091,40.866,3.132)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z"></path></g></svg>).</span></p>

Security and Communication Networks

fig2

Figure 2

Figure 2: Hierarchical Key Management Scheme with Probabilistic Security in a Wireless Sensor Network (WSN) 