ECC decryption experiment result by invalid point attack 192-bit ECC ======================================================== Test NO.1 (ECC-192) Rho method to solve n from R=n*Q by python ----- Input information --------------- p=4781668983906166242955001894344923773259119655253013193367 r=4781668983906166242955001894240948913609282999764344030467 a=2613009377683017747869391908421543348309181741502784219375 b=1000000000000000000000000000000000000000000000000000004770 Qx=1593889661302055414318333964781641257753039885084337731116 Qy=2322259340285307797472465934945297741490702626769473687901 Rx=274295121425475481660992619112795295648554719881531659846 Ry=1346714342144372110238567270386186938492768320192133999599 ----- Solving information ------------- Search pointer size=8388608 r=9 sol=3 loop=3 r=193 sol=127 loop=6 r=227 sol=198 loop=19 r=132263 sol=7838 loop=163 r=3137623 sol=762940 loop=2161 r=16683221 sol=11202507 loop=11962 r=52859731 sol=27345700 loop=6268 r=61875179 sol=42724137 loop=19800 r=111947219 sol=98743528 loop=15112 r=4783877767 sol=1368670346 loop=74594 ----- Decoding result n for R=n*Q -------- solve n=2204629002711795220677648393099340358400938802723270527589 solve total loop=130088 used time=5.59 sec ======================================================== Test NO.2 (ECC-192) Rho method to solve n from R=n*Q by python ----- Input information --------------- p=4781668983906166242955001894344923773259119655253013193367 r=4781668983906166242955001894240948913609282999764344030467 a=2613009377683017747869391908421543348309181741502784219375 b=1000000000000000000000000000000000000000000000000000004770 Qx=1593889661302055414318333964781641257753039885084337731116 Qy=2322259340285307797472465934945297741490702626769473687901 Rx=711931662815895270745723599382141266451391903169428730231 Ry=572273548191286785937488687543123465749667143002901182411 ----- Solving information ------------- Search pointer size=8388608 r=9 sol=7 loop=7 r=193 sol=56 loop=11 r=227 sol=192 loop=18 r=132263 sol=24321 loop=603 r=3137623 sol=1180409 loop=1522 r=16683221 sol=12621036 loop=2685 r=52859731 sol=448330 loop=7309 r=61875179 sol=47265186 loop=8699 r=111947219 sol=45534599 loop=9547 r=4783877767 sol=3703932583 loop=42735 ----- Decoding result n for R=n*Q -------- solve n=3336136916755101551994061033769301642375433385069417496982 solve total loop=73136 used time=3.22 sec ======================================================== Test NO.3 (ECC-192) Rho method to solve n from R=n*Q by python ----- Input information --------------- p=4781668983906166242955001894344923773259119655253013193367 r=4781668983906166242955001894240948913609282999764344030467 a=2613009377683017747869391908421543348309181741502784219375 b=1000000000000000000000000000000000000000000000000000004770 Qx=1593889661302055414318333964781641257753039885084337731116 Qy=2322259340285307797472465934945297741490702626769473687901 Rx=1751104685028327544851356565843296599234246635840081118022 Ry=43753114151081180150497903434252735799452346348859018041 ----- Solving information ------------- Search pointer size=8388608 r=9 sol=0 loop=9 r=193 sol=114 loop=23 r=227 sol=74 loop=16 r=132263 sol=28922 loop=245 r=3137623 sol=2201332 loop=862 r=16683221 sol=2150977 loop=2146 r=52859731 sol=28220828 loop=6957 r=61875179 sol=57369669 loop=6490 r=111947219 sol=24837681 loop=9917 r=4783877767 sol=3777444367 loop=168327 ----- Decoding result n for R=n*Q -------- solve n=2860485488918686169467371249894140894969936447623948541964 solve total loop=194992 used time=8.43 sec