{"id":91423,"date":"2024-04-01T18:24:24","date_gmt":"2024-04-01T18:24:24","guid":{"rendered":"https:\/\/science-hub.click\/%E6%A5%95%E5%86%86%E6%9B%B2%E7%B7%9A%E6%9A%97%E5%8F%B7%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-04-01T18:24:24","modified_gmt":"2024-04-01T18:24:24","slug":"%E6%A5%95%E5%86%86%E6%9B%B2%E7%B7%9A%E6%9A%97%E5%8F%B7%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=91423","title":{"rendered":"\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><p>\u6697\u53f7\u5316\u3067\u306f\u3001\u6570\u5b66\u7684\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3042\u308b\u6955\u5186\u66f2\u7dda\u306f\u3001\u5b89\u5168\u3067\u306a\u3044\u30c1\u30e3\u30cd\u30eb\u3067\u306e\u9375\u4ea4\u63db\u3084\u975e\u5bfe\u79f0\u6697\u53f7\u5316\u306a\u3069\u306e\u975e\u5bfe\u79f0\u64cd\u4f5c\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5834\u5408\u3001<strong>\u6955\u5186\u66f2\u7dda<span><a href=\"https:\/\/science-hub.click\/?p=20956\">\u6697\u53f7<\/a><\/span><\/strong>\u307e\u305f\u306f<strong>ECC<\/strong> (\u82f1\u8a9e\u306e<i>\u6955\u5186\u66f2\u7dda\u6697\u53f7<\/i>\u306e\u982d\u5b57\u8a9e\u304b\u3089) \u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002\u6697\u53f7\u5316\u306b\u304a\u3051\u308b\u6955\u5186\u66f2\u7dda\u306e<span><a href=\"https:\/\/science-hub.click\/?p=61221\">\u4f7f\u7528\u306f<\/a><\/span>\u30011985 \u5e74\u306b Neal Koblitz \u3068 Victor Miller \u306b\u3088\u3063\u3066\u72ec\u7acb\u3057\u3066\u63d0\u6848\u3055\u308c\u307e\u3057\u305f\u3002<\/p><p><span><a href=\"https:\/\/science-hub.click\/?p=9830\">\u6955\u5186\u66f2\u7dda<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=94973\">\u6697\u53f7\u5316<\/a><\/span>\u306b\u4f7f\u7528\u3055\u308c\u308b\u9375\u306f\u3001RSA \u306e\u3088\u3046\u306a\u56e0\u6570\u5206\u89e3\u554f\u984c\u306b\u57fa\u3065\u304f\u30b7\u30b9\u30c6\u30e0\u3088\u308a\u3082\u77ed\u304f\u306a\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001ECC \u306f\u4ed6\u306e\u65b9\u5f0f\u3068\u540c\u7b49\u4ee5\u4e0a\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3 \u30ec\u30d9\u30eb\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 ECC \u306e\u3082\u3046 1 \u3064\u306e\u9b45\u529b\u306f\u3001\u30b0\u30eb\u30fc\u30d7\u9593\u3067<span><a href=\"https:\/\/science-hub.click\/?p=35122\">\u53cc\u4e00\u6b21<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=21882\">\u6f14\u7b97\u5b50<\/a><\/span>\u3092\u5b9a\u7fa9\u3067\u304d\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u6f14\u7b97\u5b50\u306f\u3001Weil \u30ab\u30c3\u30d7\u30ea\u30f3\u30b0\u307e\u305f\u306fTate \u30ab\u30c3\u30d7\u30ea\u30f3\u30b0\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u53cc\u4e00\u6b21\u6f14\u7b97\u5b50\u306f\u3001\u6700\u8fd1\u3001ID \u30d9\u30fc\u30b9\u306e\u6697\u53f7\u5316\u306a\u3069\u3001\u6697\u53f7\u5316\u306b\u304a\u3044\u3066\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3067\u9069\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30de\u30a4\u30ca\u30b9<span><a href=\"https:\/\/science-hub.click\/?p=43578\">\u70b9<\/a><\/span>\u306f\u3001\u6697\u53f7\u5316\u3068\u5fa9\u53f7\u5316\u306e\u64cd\u4f5c\u304c\u4ed6\u306e\u65b9\u6cd5\u3088\u308a\u3082<span><a href=\"https:\/\/science-hub.click\/?p=38628\">\u8907\u96d1<\/a><\/span>\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002<\/p><p>\u6955\u5186\u66f2\u7dda\u306b\u57fa\u3065\u304f\u30b7\u30b9\u30c6\u30e0\u306e\u5f37\u307f\u306f\u3001\u6955\u5186<span><a href=\"https:\/\/science-hub.click\/?p=78293\">\u66f2\u7dda<\/a><\/span>\u306b\u5bfe\u5fdc\u3059\u308b\u7fa4\u306e\u96e2\u6563<span>\u5bfe\u6570<\/span>\u306e\u554f\u984c\u306b\u3042\u308a\u307e\u3059\u3002\u66f2\u7dda\u306b\u95a2\u3059\u308b\u7406\u8ad6\u7684\u958b\u767a\u306f\u6bd4\u8f03\u7684\u6700\u8fd1\u306e\u3082\u306e\u3067\u3059\u304c\u3001\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306f\u3042\u307e\u308a\u77e5\u3089\u308c\u3066\u304a\u3089\u305a\u3001\u305d\u306e\u958b\u767a\u3092\u59a8\u3052\u308b<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u591a\u6570<\/a><\/span>\u306e\u7279\u8a31\u306b\u60a9\u307e\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><h2><span>\u9375\u4ea4\u63db<\/span><\/h2><p><span><a href=\"https:\/\/science-hub.click\/?p=18710\">\u30a2\u30ea\u30b9\u3068\u30dc\u30d6\u306f<\/a><\/span>\u6955\u5186\u66f2\u7dda\u306b\u3064\u3044\u3066\uff08\u516c\u7684\u306b\uff09\u5408\u610f\u3057\u3066\u3044\u308b<div class=\"math-formual notranslate\">$$ {E(a,b,p)~} $$<\/div>\u3064\u307e\u308a\u3001\u6955\u5186\u66f2\u7dda\u3092\u9078\u629e\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {y^2~mod~p = (x^3+ax+b)~mod~p~} $$<\/div> \u3002\u5f7c\u3089\u306f\u307e\u305f\u3001\u3042\u308b\u70b9\u306b\u3064\u3044\u3066\u306f\u516c\u306b\u540c\u610f\u3057\u3066\u3044\u308b<div class=\"math-formual notranslate\">$$ {P~} $$<\/div>\u30ab\u30fc\u30d6\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002<\/p><p>\u30a2\u30ea\u30b9\u306f\u3053\u3063\u305d\u308a\u6574\u6570\u3092\u9078\u3073\u307e\u3059<div class=\"math-formual notranslate\">$$ {d_A~} $$<\/div> \u3001\u30dc\u30d6\u306f\u6574\u6570<div class=\"math-formual notranslate\">$$ {d_B~} $$<\/div> \u3002\u30a2\u30ea\u30b9\u306f\u30dc\u30d6\u306b\u30dd\u30a4\u30f3\u30c8\u3092\u9001\u4fe1\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {d_A P~} $$<\/div> \u3001\u30dc\u30d6\u306f\u30a2\u30ea\u30b9\u306b\u9001\u4fe1\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {d_B P~} $$<\/div> \u3002\u305d\u308c\u305e\u308c\u72ec\u7acb\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {d_A(d_B P)=(d_A d_B) P~} $$<\/div>\u3053\u308c\u306f\u66f2\u7dda\u306e\u70b9\u3067\u3042\u308a\u3001\u5171\u901a\u306e\u79d8\u5bc6\u9375\u3092\u69cb\u6210\u3057\u307e\u3059\u3002<\/p><p>\u3082\u3057\u30a4\u30d6\u304c\u5f7c\u3089\u306e\u3084\u308a\u3068\u308a\u3092\u76d7\u307f\u898b\u3066\u3044\u305f\u306a\u3089\u3001\u5f7c\u5973\u306f\u77e5\u3063\u3066\u3044\u308b<div class=\"math-formual notranslate\">$$ {E(a,b,p), P, d_A P, d_B P~} $$<\/div> \u3002\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u306b\u306f<div class=\"math-formual notranslate\">$$ {d_A d_B P~} $$<\/div> \u3001\u8a08\u7b97\u3067\u304d\u308b\u3053\u3068\u304c\u5fc5\u8981\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {d_A~} $$<\/div>\u77e5\u3063\u3066\u3044\u308b<div class=\"math-formual notranslate\">$$ {P~} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {d_A P~} $$<\/div> \u3002\u3053\u308c\u3092\u6955\u5186\u66f2\u7dda\u4e0a\u306e\u96e2\u6563\u5bfe\u6570\u3092\u89e3\u304f\u3068\u3044\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u73fe\u6642\u70b9\u3067\u306f\u3001\u6570\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u5834\u5408\u3001\u3053\u306e\u554f\u984c\u3092\u9069\u5207\u306a\u6642\u9593\u5185\u306b\u89e3\u6c7a\u3059\u308b\u52b9\u679c\u7684\u306a\u65b9\u6cd5\u304c\u308f\u304b\u308a\u307e\u305b\u3093\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/jxmN8LqyTR4\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2><span><span><a href=\"https:\/\/science-hub.click\/?p=62923\">\u5b9f\u88c5<\/a><\/span><\/span><\/h2><h3><span>\u30c9\u30e1\u30a4\u30f3\u8a2d\u5b9a<\/span><\/h3><ul><li>\u30b7\u30e5\u30fc\u30d5\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/li><\/ul><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/RFWsbW3tPDw\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u30ad\u30fc\u306e\u9577\u3055<\/span><\/h3><p>128\u30d3\u30c3\u30c8\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u306e\u305f\u3081\u3001\u672c\u4f53\u306b\u66f2\u7dda\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathbb{F}_q} $$<\/div> \u3001 \u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {q \\approx 2^{256}} $$<\/div> \u3002<\/p><\/div><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/HZ_Y5iQWL0I\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%AA%D8%B9%D9%85%D9%8A%D8%A9_%D8%A8%D8%A7%D9%84%D9%85%D9%86%D8%AD%D9%86%D9%8A%D8%A7%D8%AA_%D8%A7%D9%84%D8%A5%D9%87%D9%84%D9%8A%D9%84%D8%AC%D9%8A%D8%A9\">\u00ff\u2122\u00ff\u03c0\u0178\u00d6\u0178\u00e4\u00ff\u00a9 \u00ff\u00ae\u00ff\u00df\u0178\u00d1\u0178\u00d6\u0178\u00dc\u00ff\u2260\u0178\u00dc\u0178\u00e4\u00ff\u00df\u00ff\u2122 \u00ff\u00df\u0178\u00d1\u00ff\u2022\u0178\u00e1\u0178\u00d1\u0178\u00e4\u0178\u00d1\u00ff\u00a8\u0178\u00e4\u00ff\u00a9\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Criptografia_de_corba_el%C2%B7l%C3%ADptica\">Criptografia de corba el\u00ac\u2211l\u221a\u2260ptica\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cs.wikipedia.org\/wiki\/Kryptografie_nad_eliptick%C3%BDmi_k%C5%99ivkami\">Kryptografie nad eliptick\u221a\u03a9mi k\u2248\u00f4ivkami\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020tch\u221a\u00aeque<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Elliptic_Curve_Cryptography\">Elliptic Curve Cryptography\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/el.wikipedia.org\/wiki\/%CE%9A%CF%81%CF%85%CF%80%CF%84%CE%BF%CE%B3%CF%81%CE%B1%CF%86%CE%AF%CE%B1_%CE%B5%CE%BB%CE%BB%CE%B5%CE%B9%CF%80%CF%84%CE%B9%CE%BA%CF%8E%CE%BD_%CE%BA%CE%B1%CE%BC%CF%80%CF%85%CE%BB%CF%8E%CE%BD\">\u0152\u00f6\u0153\u00c5\u0153\u00d6\u0153\u00c4\u0153\u00d1\u0152\u00f8\u0152\u2265\u0153\u00c5\u0152\u00b1\u0153\u00dc\u0152\u00d8\u0152\u00b1 \u0152\u00b5\u0152\u00aa\u0152\u00aa\u0152\u00b5\u0152\u03c0\u0153\u00c4\u0153\u00d1\u0152\u03c0\u0152\u222b\u0153\u00e9\u0152\u03a9 \u0152\u222b\u0152\u00b1\u0152\u00ba\u0153\u00c4\u0153\u00d6\u0152\u00aa\u0153\u00e9\u0152\u03a9\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020grec<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Elliptic-curve_cryptography\">Elliptic-curve cryptography\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020anglais<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u6955\u5186\u66f2\u7dda\u6697\u53f7\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u6955\u5186\u66f2\u7dda\u6697\u53f7 (ECC) \u306e\u4ed5\u7d44\u307f\u3092\u7d76\u5bfe\u306b\u7406\u89e3\u3059\u308b\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/kTgvsDxeNuc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u6697\u53f7\u5316\u3067\u306f\u3001\u6570\u5b66\u7684\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3042\u308b\u6955\u5186\u66f2\u7dda\u306f\u3001\u5b89\u5168\u3067\u306a\u3044\u30c1\u30e3\u30cd\u30eb\u3067\u306e\u9375\u4ea4\u63db\u3084\u975e\u5bfe\u79f0\u6697\u53f7\u5316\u306a\u3069\u306e\u975e\u5bfe\u79f0\u64cd\u4f5c\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5834\u5408\u3001\u6955\u5186\u66f2\u7dda\u6697\u53f7\u307e\u305f\u306fECC (\u82f1\u8a9e\u306e\u6955\u5186\u66f2\u7dda\u6697\u53f7\u306e\u982d\u5b57\u8a9e\u304b\u3089) \u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002\u6697\u53f7\u5316\u306b 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