Privacy-Preserving Outsourced Logistic Regression on Encrypted Data from Homomorphic Encryption

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg7"><tr><td> </td><td><b>Input</b>: <svg height="12.7178pt" id="M142" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 45.2614 12.7178" width="45.2614pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.533,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.799,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,24.942,0)"><path d="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.208,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.738,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg></td></tr><tr><td> </td><td><b>Output</b>: <svg height="12.7178pt" id="M143" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 40.9987 12.7178" width="40.9987pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.439,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.975,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.504,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg></td></tr><tr><td>(1)</td><td>mod_switch_to_inplace (<span class="nowrap"><svg height="12.7178pt" id="M144" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 20.2339 12.7178" width="20.2339pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.795,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg>,</span> <span class="nowrap"><svg height="11.439pt" id="M145" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 19.9729 11.439" width="19.9729pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.533,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg>.</span>parms_id())</td></tr><tr><td>(2)</td><td>sub (<span class="nowrap"><svg height="11.439pt" id="M146" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 19.9729 11.439" width="19.9729pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.533,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg>,</span> <span class="nowrap"><svg height="12.7178pt" id="M147" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 20.2339 12.7178" width="20.2339pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.795,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg>,</span> <span class="nowrap"><svg height="12.7178pt" id="M148" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 40.9987 12.7178" width="40.9987pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.439,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.975,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.504,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg>)</span></td></tr><tr><td>(3)</td><td><b>return</b>: <svg height="12.7178pt" id="M149" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 40.9987 12.7178" width="40.9987pt" 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="M427 -163V-135C320 -126 318 -122 318 -44V583C318 662 321 666 427 675V703H120V-163H427ZM268 -126C183 -117 181 -99 181 -44V583C181 638 184 657 268 666V-126Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.266,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.439,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.975,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.504,0)"><path d="M363 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H363ZM302 -43C302 -98 299 -117 215 -126V667C299 657 302 639 302 584V-43Z"></path></g></svg></td></tr></table></td></tr></table>

Security and Communication Networks

alg7

Algorithm 7

Algorithm 7: Privacy-Preserving Outsourced Logistic Regression on Encrypted Data from Homomorphic Encryption 