CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '9136cb151d5b5ff7',cH: 'L97S8gm_jGZlbVlPL3KJwTZmhLrtShn2oGIdwmB1Euc-1739805960-1.2.1.1-qnSPVCSAT8h1FNL_CavKId.LpQ7zdS..40emtGjVBJAbjj7cr_kHi4KiwNyBYcwD',cUPMDTk: "\/abstracts\/search?q=elliptic%20curves&__cf_chl_tk=uOPwQdOlJGgtHNULvdxfB8N3F.L32gXzij9pdHjvHVc-1739805960-1.0.1.1-asTE01PCfddP4LlvzbJxeyd._3QwQaKfCjWyNnsuhXw",cFPWv: 'g',cITimeS: '1739805960',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=elliptic%20curves&__cf_chl_f_tk=uOPwQdOlJGgtHNULvdxfB8N3F.L32gXzij9pdHjvHVc-1739805960-1.0.1.1-asTE01PCfddP4LlvzbJxeyd._3QwQaKfCjWyNnsuhXw",md: "avc89MoF7ucQMrjRMkmJGSPzGgvST_.SUymTOjGZGmc-1739805960-1.2.1.1-t73fCz8rRTPyniyG9bcqJyDV0U4AQ2DJP2iePHuQ2wOVO17IRKOkAjgvmRzpziTOR9QJBreiBiSOa64yPo1Jw1LnFvjEnyOfglgRaJTBcbvw69Gy5twq7G19gSMU7QaIY25uJEr1XSbPur82lXM0Nd2WqIDNthBenHVJrQdZ0OXal1.o4HWWDaob0vUrsmOkofU.t4bB2DN.30Sh1MujRLU58kt_.O.dH0Wo.YBAN1lGacHE57rmKEkurKv5NjzzpgygE.EE0p1f0.Iqpm01nEfTspmLYmV89_Ivs8OrF7hKfE2e43INWx_xyLphvG5fkVr9ioAoYRquqs6MUjjXLshYP5.csoCLMVsgCx0zsNQLNQCaU2tzmDaEDHMMWj3cxGCKmpQmlbJjVxirqSaDt0b7CeWPbXrWZStZklWnyamHlXLHel7BCC2TgDBZJo8Cr_PRwQUIV7Oj_UpBcVyXZwuFBWuCtzS2ma2l_vL49roOiVY_2M4da7oJWG4hyoYox7o2HNJPqL4oGfz9RGlefzjdxmGLR.95bz2aE_PyCtoNrFIAUNAGNJ0pATC4E8iYD_.QzMDlDNhaEG41na5Z3wLEWaeuhdNmYIOXp.6LcBL9R7oeutAF1wTpDBfkYnIth5dQXISznz7hfic7ZGOHp4InWADhYP18ERpfIvZ9w19At_zzbCxboSukBEdtPx3sY_pciZq3wHIWhyUBRaeJbO3zBnMpVGbJ4iJjb7k7XykYhpRAqKyt75TRlUGrKg4sszHTmKPNx1l5IdPRQIJ3kb9HJ.zWPUcrkUM4m0uJ51UYOP04kxfsJaufTapoh8rg5id1wnDILYkLPeesxxLZPQYeO2kFJNcOfvdHdPfxxIIXf9c3J1OwdUoVH2Xd6G7mTOLDqMUAgdGORIHCraPcycBoCgGWYgoCS2alHk02kWRbT_exZhjwMRHsX1GqQ1Ubus3LUySiRgl2OdD0GSp1JzDTGD06Tx74D1TrSO6isq1AlUZbqyyLNWZlM0n8.gPAhaVKYSNcjutE6MAoJQv_bkz05XTDu3xLLHFZAISDlYJI8M8M07Ybl_RBZtuxext6Pjb2FGEr_s621du47CAbkkqydrteNA_hUPvpoCZ7dGb6lapYj4DqrPji1zjWqQ.F6_Yvp.OAaNUd.rP79yOmmbE7Exq0LRxxdRkM1iYKuMxeAVuyjgnNOPCTW_8eax0YbrPVwv376WLYX0ecKQtUw5x0BxKw5AmX5.vCWOgpUMu5XjbYy6RIne8Zt6DtfKg9jlLIDjNUndM3fbKqqGMf0.CPiUVwXVRSikQPhW_eac3ThBWHSq1YiaslasqjW6aR1sLOtMC3chkNO2JyCOHvJz21ZmHzJup42yNosLtK6pC9eUq3wtlMP43DPvL55bi75ZzQ011zFpjS4fNzbHlsEjf1GmzWY0dzbQ0e7PWKs.Up5qyf8vujbTCVABeN2EQYjcbujKi8vcQIPJxvhfc1b6ixphbaFheUiTVMoQYRi5gFcx2BUSqbFjDV_GZPrL7VEQhJnqhsok7uaDrciOtdH9qpKDacNW5p2fnZA8yEEB9kKGJ76ZkKZBryRFKpy3BzlZEziI7Lyo9wBsYAoC7tZiV0K.tf9tAUFnnszKa08oW7Hglo05qd7d5nFurP3IAhFseuPK6NtaTV1oMvCaBAegj78QZ8AvxjgXqMu3H3jsPWSJrKOAp.1L1YnC_X7MnxEM_g5czphl48O8k2ci22B3v9HZHr_ARBA8Vb1UDa_EXC4QmplGevSZvR6yt9eOaSsGOQ5QYtn_EUR6niHfamC6WJ16q79h.BECBhxAHsKJRJcAmuHLArZCdLA8bRHHmkjZs0RC1RJDYYKsWqNr3P8IIKIhJxgNmkCA7Wc9F_KQZYu_Bg0r184_w5o_JkCxdGOAQs5eHg.lUrbZzNLmfrcfgqWkJwC80J83GwA_0hJUM",mdrd: "Mp0rgukJclCHo3acQULYtMslMx_ts6osy7JOA2TrHs4-1739805960-1.2.1.1-LSG21Xw7fsRsnFHrt6_Gp0xJPI94MIzVGKPoclKrm84XvTBcMxpq9P.2u_AUx7zqQtYGve4753DAUtE1o6gZEPRlt0xhAu2D3s5aFzTwNF7V7v6HlNE8XXmq10xdEElcoGZsOEytmXPvfR4p9H.vhGUJMnB5KHDljjZQnD6LlLyU_B3Ja_ekUWhfLhGYAyAzRvNZEqEokj9lqeVaNcVHjEbqlw81n_Oa1sAjKzQPy8mRf5dQCqHguQVRLPZn6BEMjN.BsLrti9tSy40eHoAmih8xgGPtE9plboTr2aWPdWRDq1UTrIBdkBCT3_9vmUpLJpbMcvYn9rxK35LbYFUtbJw99VhJt25SHydRzZiKB3ZvBIgsyW36S7j1vnqv.9.fE7v27mwSjc.mBZB85IknOvv8sbJzhhbutLLSMYMHc4ZtnOgL.Tz2G27iJvoHDfks9wLErv4LRiZccnW9RvQoumIgnxIMSt4pgnjKxszPEMyx2U0Bm8FjT8KLul0CR.PQB3_PEUagBAGQ6wINx6jKDdkg3O9EFQK_XaP8NAVOYP.PQNlxfweSc2lNbsrarWcMKmX1uOX4wh7oeOrsdZGLzyFN6TUUY8Wydo5bmxm2S2CxFm_5CNWyqDayVn6y5NBwOsb0WlfwKaxN5CQEC3otuL8yRTohmR5YOklorM2ICyYp1hYjztIwXTz_oGquXtAIykQYEd1y4oaciIgDaz0JvWcrAq8XynvoZUTR3Zqji4b2plISQDLzRK_aMICNoDaSFXv0ays3dR7h4apoz1m1oPOAD5wXa0dg_FGtQAXu8mdIIY0g_bJub60G55MNyAxITSiYrTLzeU3lrr.9k.ZXbzon4LggP6OM1jqaNEwp3lbO.2cKVEnsXEKY80dgfvHvSKDingJyGzGFBRMemMAJ7CXeF4TNqux9B8xbgBrMAPB3EQtNqoJwUZYAh7KYGVbtVmU9KoC7893.RygkguRk_VOqxwzaVFlEYjDqcApUoDcQnujuIhj_AKM1UR2kiAxw1H9cMJxTXfDKSwD6qYS9TBN9PXHfuBeauddy3F1g5URj66xqmfXYDg0e51HJDCFb_0pmIZW75HRzSNbfyt5py2x1.w1QMVFiLh4iJ3WICrXjGgQ33eGGMDFPXzLQ2rYaktk6RjGYlDSN8IcnfeIR8rIupWblctjmSA7dO0Ldvqj0czOfo7sVBrx7EOas8GkwdSpTwIJq.ytk7kBPLgjzkU_VwXCWih6v6N4eq69dPLkqEYqfpgo_C6DEr2YnUUoKgdK2Ox2tim6aooJEl6h6LEdYhPBbuh_SF_5Qz6AWMxiAKeqV6wEKXLdaMsbnP.p6w2XHSsy5VggoVSnQAksyion13QekB4M1Atl8vZcFVAhwIThGOoShEVdHxYykYkgIscdVR3kqV7YvCBeK.PpbcFNJu1Zic1TYOPvSAG9NB_ETlcevHgMGdmxl45_swXVIyEoxeIJD2AkU9OssgQjbYRpZ25yhTIGe8clOuD_3D4IhkzP8N.GzbX1q6dZl17F3M7Hj9jrIyDC.zQcb9kEbD1hehoPWby8bSyRMP9FOyYCucI77r9UrboFgay8291R2gc6WYLp8WDxsKCVwL5MLvkHGWyR24CQIUtqJp4escbDy0upeUlXnmByI9i0JQ2dxTGKUm6WS.BfpZsHU0phdIqHt6TQ5gKJrHc8wFOIm8BW5EtkFcgYWGzO2HDv8P8tUWX6JqABm558KLEhe2QO9j.A8ro3WRKrN7_IISadbKmT0ZtG7IXPz.y9bVX0SxXzXo_9LZ3zi7KwTrl.wfuLLNCB4GUk1fO1el.ZjKjPr52gwfDVbKLYn0knusMXJJ12MsmBt43fW0bPvr4bb8v44z8K0OOAsRAQ.gNWw492oDoNgiLQLODSNWRaUajn7mRO6nZt8ftBX0o8_BpwXxlQLVT5MepwcpF4LxGQW4v1cGiI"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=9136cb151d5b5ff7';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=elliptic%20curves&__cf_chl_rt_tk=uOPwQdOlJGgtHNULvdxfB8N3F.L32gXzij9pdHjvHVc-1739805960-1.0.1.1-asTE01PCfddP4LlvzbJxeyd._3QwQaKfCjWyNnsuhXw" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>