{"id":5944,"date":"2025-03-05T11:50:44","date_gmt":"2025-03-05T02:50:44","guid":{"rendered":"https:\/\/jfs.or.jp\/jfs-cs\/?p=5944"},"modified":"2025-03-08T18:00:10","modified_gmt":"2025-03-08T09:00:10","slug":"crypt-rsa01","status":"publish","type":"post","link":"https:\/\/jfs.or.jp\/jfs-cs\/crypt-rsa01\/","title":{"rendered":"IT\u306b\u5229\u7528\u3055\u308c\u308b\u6697\u53f7\u5316\u6280\u8853\u3000RSA\u6697\u53f7\u306e\u89e3\u8aac"},"content":{"rendered":"<p>\u30cd\u30c3\u30c8\u4e0a\u3067\u306f\u3001\u81a8\u5927\u306a\u901a\u4fe1\u304c\u884c\u308f\u308c\u3066\u3044\u307e\u3059\u3002<br \/>\n\u901a\u4fe1\u306f\u30d0\u30b1\u30c4\u30ea\u30ec\u30fc\u65b9\u5f0f\u3067\u3001\u30d1\u30b1\u30c3\u30c8\u3068\u3044\u3046\u5c0f\u5206\u3051\u3057\u305f\u6587\u304c\u884c\u304d\u6765\u3057\u307e\u3059\u3002\u9014\u4e2d\u3067\u76d7\u307f\u898b\u3089\u308c\u305f\u3089\u56f0\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\u30cd\u30c3\u30c8\u901a\u4fe1\u3067\u306f\u6697\u53f7\u30b7\u30b9\u30c6\u30e0\u304c\u5229\u7528\u3055\u308c\u307e\u3059\u3002Web\u3067\u306f\u300chttps\u300d\u304b\u3089\u306f\u3058\u307e\u308bURL\u306f\u901a\u4fe1\u5185\u5bb9\u3092\u6697\u53f7\u5316\u3057\u3001\u3088\u308a\u5b89\u5168\u6027\u304c\u9ad8\u304f\u306a\u3063\u3066\u3044\u308b\u3068\u3002<br \/>\n\u3067\u306f\u3001\u6697\u53f7\u5316\u3068\u306f\uff1f<\/p>\n<p>\u30cd\u30c3\u30c8\u3067\u89e3\u308a\u3084\u3059\u304f\u7d39\u4ecb\u3057\u3066\u3044\u308b\u30b5\u30a4\u30c8\u304c\u6848\u5916\u5c11\u306a\u304b\u3063\u305f\u306e\u3067\u3001\u6700\u3082\u7c21\u6f54\u304b\u3064\u5206\u304b\u308a\u3084\u3059\u3044\u30b5\u30a4\u30c8\u304b\u3089\u4e00\u90e8\u3092\u5f15\u7528\u3054\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>IT\u30c8\u30ec\u30f3\u30c9\u793e\u306e\u3000<a href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056\">https:\/\/it-trend.jp\/encryption\/article\/64-0056<\/a><\/p>\n<h2 class=\"text-3xl font-bold my-4\">RSA\u6697\u53f7\u3068\u306f\uff1f\u4ed5\u7d44\u307f\u3084\u5fdc\u7528\u4e8b\u4f8b\u3092\u521d\u5fc3\u8005\u306b\u3082\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff01<\/h2>\n<p>2024\u5e7412\u670804\u65e5 \u6700\u7d42\u66f4\u65b0<\/p>\n<p>\u6697\u53f7\u5316\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u6d3b\u7528\u3055\u308c\u308bRSA\u6697\u53f7\u3067\u3059\u304c\u3001\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u5bfe\u7b56\u3092\u8003\u3048\u308b\u4e2d\u3067\u6697\u53f7\u5316\u306e\u4ed5\u7d44\u307f\u304c\u6c17\u306b\u306a\u3063\u3066\u3044\u308b\u4eba\u306f\u591a\u3044\u3067\u3057\u3087\u3046\u3002<br \/>\n\u3053\u306e\u8a18\u4e8b\u3067\u306fRSA\u6697\u53f7\u306e\u6982\u8981\u304b\u3089\u6697\u53f7\u5316\u3068\u5fa9\u53f7\u306e\u6d41\u308c\u3001\u305d\u3057\u3066\u5fdc\u7528\u4f8b\u307e\u3067\u89e3\u8aac\u3057\u307e\u3059\u3002\u305c\u3072\u53c2\u8003\u306b\u3057\u3066\u3001\u6697\u53f7\u5316\u6280\u8853\u3078\u306e\u7406\u89e3\u3092\u6df1\u3081\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<div class=\"pb-4 text-2xl font-bold\">\u76ee\u6b21<\/div>\n<ul>\n<li class=\"py-2 border-b\"><a class=\"text-blue-500 hover:underline text-sm\" href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056#chapter-1\">RSA\u6697\u53f7\u3068\u306f<\/a><\/li>\n<li class=\"py-2 border-b\"><a class=\"text-blue-500 hover:underline text-sm\" href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056#chapter-2\">RSA\u6697\u53f7\u3092\u4f7f\u3063\u305f\u3084\u308a\u53d6\u308a\u306e\u4ed5\u7d44\u307f<\/a><\/li>\n<li class=\"py-2 border-b\"><a class=\"text-blue-500 hover:underline text-sm\" href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056#chapter-3\">RSA\u6697\u53f7\u306e\u5fdc\u7528\u4e8b\u4f8b<\/a><\/li>\n<li class=\"py-2 border-b\"><a class=\"text-blue-500 hover:underline text-sm\" href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056#chapter-4\">RSA\u6697\u53f7\u3092\u6d3b\u7528\u3057\u305f\u30bd\u30d5\u30c8<\/a><\/li>\n<li class=\"py-2 \"><a class=\"text-blue-500 hover:underline text-sm\" href=\"https:\/\/it-trend.jp\/encryption\/article\/64-0056#chapter-5\">RSA\u6697\u53f7\u306b\u3064\u3044\u3066\u7406\u89e3\u3057\u3001\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u306e\u77e5\u8b58\u3092\u6df1\u3081\u3088\u3046<\/a><\/li>\n<\/ul>\n<p>\u304b\u3089\u4e00\u90e8\u3092\u5f15\u7528\u3054\u7d39\u4ecb<\/p>\n<h3>RSA\u6697\u53f7\u3068\u306f<\/h3>\n<p>RSA\u6697\u53f7\u3068\u306f\u3001\u7d20\u6570\u3092\u639b\u3051\u3042\u308f\u305b\u305f\u6570\u5b57\u306e\u7d20\u56e0\u6570\u5206\u89e3\u306e\u4ed5\u7d44\u307f\u3092\u5229\u7528\u3057\u305f\u6697\u53f7\u6280\u8853\u306e\u4e00\u3064\u3067\u3059\u3002\u3053\u3053\u3067\u306fRSA\u6697\u53f7\u306e\u6982\u8981\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u7d20\u56e0\u6570\u5206\u89e3\u304c\u56f0\u96e3\u3067\u3042\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong><\/span><\/p>\n<p>\u3000\u5927\u304d\u306a\u6570\u5b57\u3092\u7d20\u56e0\u6570\u5206\u89e3\u3059\u308b\u306e\u306f\u56f0\u96e3\u3067\u3059\u3002\u7dcf\u5f53\u305f\u308a\u3059\u308b\u4ee5\u5916\u306b\u7d20\u56e0\u6570\u3092\u898b\u3064\u3051\u51fa\u3059\u65b9\u6cd5\u304c\u306a\u3044\u305f\u3081\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u7d20\u56e0\u6570\u5206\u89e3\u3057\u3088\u3046\u3068\u3057\u3066\u3082\u3001\u5927\u304d\u306a\u6570\u3067\u3042\u308c\u3070\u81a8\u5927\u306a\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u3000\u3053\u306e\u7d20\u56e0\u6570\u5206\u89e3\u306e\u56f0\u96e3\u3055\u3092\u4ed5\u7d44\u307f\u3068\u3057\u3066\u5229\u7528\u3057\u305f\u306e\u304cRSA\u6697\u53f7\u3067\u3059\u3002RSA\u306f\u767a\u660e\u3057\u305f\uff13\u4eba\u306e\u540d\u524d\u300cR. L. Rivest\u3001A. Shamir\u3001L. Adleman\u300d\u306b\u7531\u6765\u3057\u307e\u3059\u3002<\/p>\n<p>\u3000\u7d20\u56e0\u6570\u5206\u89e3\u306e\u96e3\u3057\u3055\u3092\u5b89\u5168\u6027\u306e\u6839\u62e0\u306b\u3059\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u9006\u306b\u3044\u3048\u3070\u7d20\u56e0\u6570\u5206\u89e3\u3055\u308c\u3066\u3057\u307e\u3046\u3068\u89e3\u8aad\u3055\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u81a8\u5927\u306a\u6642\u9593\u3092\u639b\u3051\u3066\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u8a08\u7b97\u3057\u305f\u308a\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3092\u6d3b\u7528\u3057\u305f\u308a\u3059\u308c\u3070\u7d20\u56e0\u6570\u5206\u89e3\u3055\u308c\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n<p>\u3000\u3057\u304b\u3057\u3001\u305d\u308c\u307e\u3067\u306b\u306f\u60c5\u5831\u304c\u53e4\u304f\u306a\u308a\u4fa1\u5024\u304c\u5931\u308f\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u6697\u53f7\u3068\u3057\u3066\u6a5f\u80fd\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<h3>\u516c\u958b\u9375\u6697\u53f7\u65b9\u5f0f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u7a2e<\/h3>\n<p>\u3000\u6697\u53f7\u5316\u65b9\u5f0f\u306b\u306f\u516c\u958b\u9375\u6697\u53f7\u65b9\u5f0f\u3068\u5171\u901a\u9375\u6697\u53f7\u65b9\u5f0f\u306e\uff12\u3064\u304c\u3042\u308a\u3001RSA\u6697\u53f7\u306f\u516c\u958b\u9375\u6697\u53f7\u306b\u8a72\u5f53\u3057\u307e\u3059\u3002<span class=\"marker_blue\">\u516c\u958b\u9375\u6697\u53f7\u65b9\u5f0f\u3068\u306f\u3001\u6697\u53f7\u9375\u3068\u5fa9\u53f7\u9375\u304c\u5225\u3005\u306e\u6697\u53f7\u65b9\u5f0f\u3067\u3059<\/span>\u3002\u30c7\u30fc\u30bf\u3092\u89e3\u8aad\u3059\u308b\u305f\u3081\u306b\u4f7f\u3046\u306e\u306f\u5fa9\u53f7\u9375\u3067\u3042\u3063\u3066\u3001\u6697\u53f7\u9375\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u6697\u53f7\u9375\u306f\u7b2c\u4e09\u8005\u306b\u898b\u3089\u308c\u3066\u3082\u554f\u984c\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u6697\u53f7\u9375\u306f\u7b2c\u4e09\u8005\u3092\u542b\u3081\u8ab0\u306b\u3067\u3082\u516c\u958b\u3055\u308c\u3066\u4f7f\u308f\u308c\u308b\u3053\u3068\u304b\u3089\u3001\u516c\u958b\u9375\u6697\u53f7\u65b9\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<p><span class=\"marker_blue\">\u3000RSA\u6697\u53f7\u3082\u516c\u958b\u9375\u6697\u53f7\u65b9\u5f0f\u3067\u4f7f\u308f\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u7a2e\u3067\u3059\u304c\u3001\u9375\u306e\u4ea4\u63db\u3060\u3051\u3067\u306a\u304f\u6697\u53f7\u5316\u3068\u30c7\u30b8\u30bf\u30eb\u7f72\u540d\u3092\u5b9f\u73fe\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/span>\u3067\u3059\u3002\u6697\u53f7\u3068\u30c7\u30b8\u30bf\u30eb\u7f72\u540d\u3092\u4e21\u65b9\u3068\u3082\u9054\u6210\u3067\u304d\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u3001\u4e16\u754c\u3067\u521d\u3081\u3066\u767b\u5834\u3057\u307e\u3057\u305f\u3002<\/p>\n<h2 id=\"chapter-2\">RSA\u6697\u53f7\u3092\u4f7f\u3063\u305f\u3084\u308a\u53d6\u308a\u306e\u4ed5\u7d44\u307f<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/static.it-trend.jp\/article\/img\/64-0056_1_2_1.png\" alt=\"RSA\u6697\u53f7\u3092\u4f7f\u3063\u305f\u3084\u308a\u53d6\u308a\u306e\u4ed5\u7d44\u307f\" width=\"730px\" height=\"400px\" \/>\u3000<\/p>\n<p>&nbsp;<\/p>\n<p>RSA\u6697\u53f7\u306b\u304a\u3051\u308b\u3001\u9375\u3092\u4ea4\u63db\u3059\u308b\u4ed5\u7d44\u307f\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\uff11\uff0e\u53d7\u4fe1\u8005\u304c\u516c\u958b\u9375\u3068\u79d8\u5bc6\u9375\u3092\u751f\u6210\u3059\u308b<\/h3>\n<p>\u3000<span style=\"color: #ff0000;\"><strong>\u59cb\u3081\u306b\u3001\u30c7\u30fc\u30bf\u3092\u53d7\u4fe1\u3059\u308b\u5074\u304c\u516c\u958b\u9375\u3068\u79d8\u5bc6\u9375\u3092\u6e96\u5099<\/strong><\/span>\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u4ee5\u4e0b\u306e\u624b\u9806\u3067\u9375\u3092\u751f\u6210\u3057\u307e\u3059\u3002<\/p>\n<ol class=\"aroundline_red\">\n<li>\uff11\uff0e\u7570\u306a\u308b\uff12\u3064\u306e\u5927\u304d\u306a\u7d20\u6570\u300cp\u300d\u300cq\u300d\u3092\u4efb\u610f\u306b\u3068\u308b<\/li>\n<li>\uff12\uff0en\uff1dpq\u3068\u3059\u308b<\/li>\n<li>\uff13\uff0e(p-1)(q-1)\u3068\u4e92\u3044\u306b\u7d20\u306a\u81ea\u7136\u6570e\u3092\u4efb\u610f\u306b\u3068\u308b<\/li>\n<li>\uff14\uff0eed\u3092(p-1)(q-1)\u3067\u5272\u3063\u305f\u4f59\u308a\u304c\uff11\u3068\u306a\u308b\u81ea\u7136\u6570d\u3092\u4efb\u610f\u306b\u3068\u308b<\/li>\n<\/ol>\n<p>\u3000\u300c\u4e92\u3044\u306b\u7d20\u300d\u3068\u306f\u3001\u6700\u5927\u516c\u7d04\u6570\u304c\uff11\u3068\u3044\u3046\u610f\u5473\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u7528\u610f\u3057\u305fn\u3068e\u3092\u516c\u958b\u9375\u3068\u3057\u3066\u30e1\u30c3\u30bb\u30fc\u30b8\u9001\u4fe1\u5074\u306b\u6e21\u3057\u307e\u3059\u3002p\u30fbq\u30fbd\u306f\u79d8\u5bc6\u9375\u3067\u3042\u308b\u305f\u3081\u516c\u958b\u3057\u307e\u305b\u3093\u3002\u3067\u306f\u3001\u4e0a\u306e\u624b\u9806\u306e\u5177\u4f53\u4f8b\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ol class=\"aroundline_gray\">\n<li>\uff11\uff0ep\uff1d\uff17\u3001q\uff1d\uff15\u3068\u3059\u308b<\/li>\n<li>\uff12\uff0en\uff1d\uff17\u00d7\uff15\uff1d35<\/li>\n<li>\uff13\uff0e(p-1)(q-1)\uff1d\uff16\u00d7\uff14\uff1d24\u306a\u305f\u3081\u3001e\uff1d\uff15\u3068\u3059\u308b<\/li>\n<li>\uff14\uff0ed\uff1d\uff15\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001<br \/>\n\u3000\u3000ed\u00f7((p-1)(q-1))\uff1d26\u00f725\uff1d\uff11\u4f59\u308a\uff11<br \/>\n\u3000\u3000\u3068\u306a\u308b<\/li>\n<\/ol>\n<h3>\uff12\uff0e\u9001\u4fe1\u8005\u304c\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u6697\u53f7\u5316\u3059\u308b<\/h3>\n<p>\u3000\u6b21\u306f\u30e1\u30c3\u30bb\u30fc\u30b8\u306e<span style=\"color: #ff0000;\"><strong>\u9001\u4fe1\u5074\u304c\u4f5c\u696d\u3057\u307e\u3059\u3002\u53d7\u4fe1\u5074\u304b\u3089\u53d7\u3051\u53d6\u3063\u305f\u516c\u958b\u9375\u3067\u3042\u308bn\u3068e\u3092\u4f7f\u3044\u3001\u4ee5\u4e0b\u306e\u624b\u9806\u3067\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u6697\u53f7\u5316<\/strong><\/span>\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ol class=\"aroundline_red\">\n<li>\uff11\uff0e\u9001\u308a\u305f\u3044\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u81ea\u7136\u6570x\u3068\u3059\u308b\u3002\u305f\u3060\u3057x\uff1cn\u3068\u3059\u308b<\/li>\n<li>\uff12\uff0ex\u3092e\u4e57\u3057\u3001\u3053\u308c\u3092n\u3067\u5272\u3063\u305f\u4f59\u308a\u3092y\u3068\u3059\u308b<\/li>\n<\/ol>\n<p>\u3000\u3053\u3046\u3057\u3066\u7b97\u51fa\u3055\u308c\u305fy\u304c\u6697\u53f7\u6587\u3067\u3059\u3002\u3053\u308c\u3092\u53d7\u4fe1\u5074\u306b\u9001\u4fe1\u3057\u307e\u3059\u3002\u3067\u306f\u3001\u4e0a\u306e\u624b\u9806\u306e\u5177\u4f53\u4f8b\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ol class=\"aroundline_gray\">\n<li>\uff11\uff0ex\uff1d12\u3068\u3059\u308b\u3002\u3053\u308c\u306fx\uff1cn\u3092\u6e80\u305f\u3059\uff08n\uff1d35\uff09<\/li>\n<li>\uff12\uff0e12\u3092\uff15\u4e57\u3057\uff08\uff1d248832\uff09\u3053\u308c\u309235\u3067\u5272\u308b\u3068\u4f59\u308ay\uff1d17\u3068\u306a\u308b<\/li>\n<\/ol>\n<h3>\uff13\uff0e\u53d7\u4fe1\u8005\u304c\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u5fa9\u53f7\u3059\u308b<\/h3>\n<p>\u3000\u6700\u5f8c\u306b\u3001<span style=\"color: #ff0000;\"><strong>\u53d7\u4fe1\u5074\u306f\u9001\u3089\u308c\u3066\u304d\u305f\u6697\u53f7\u6587y\u3092\u5fa9\u53f7\u3057\u3001\u5e73\u6587\uff08\u6697\u53f7\u5316\u3055\u308c\u3066\u3044\u306a\u3044\u30c7\u30fc\u30bf\uff09<\/strong><\/span>\u3092\u5f97\u307e\u3059\u3002\u89e3\u304d\u65b9\u306e\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ol class=\"aroundline_red\">\n<li>\uff11\uff0ey\u3092d\u4e57\u3059\u308b<\/li>\n<li>\uff12\uff0e\u3053\u308c\u3092n\u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u5e73\u6587x\u3068\u306a\u308b<\/li>\n<\/ol>\n<p>\u3000\u3067\u306f\u3001\u4e0a\u306e\u624b\u9806\u306e\u5177\u4f53\u4f8b\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<ol class=\"aroundline_gray\">\n<li>\uff11\uff0e17\u3092\uff15\u4e57\u3059\u308b\uff08\uff1d1419857\uff09<\/li>\n<li>\uff12\uff0e\u3053\u308c\u309235\u3067\u5272\u3063\u305f\u4f59\u308a\u304c\u5e73\u658712\u3068\u306a\u308b<\/li>\n<\/ol>\n<p>\u3000\u5fa9\u53f7\u3059\u308b\u306b\u306fd\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u3053\u308c\u306f\u53d7\u4fe1\u8005\u3057\u304b\u6301\u305f\u306a\u3044\u79d8\u5bc6\u9375\u3067\u3042\u308b\u305f\u3081\u3001\u7b2c\u4e09\u8005\u306b\u306f\u5fa9\u53f7\u3055\u308c\u307e\u305b\u3093\u3002<\/p>\n<p>\u3000<span style=\"color: #0000ff;\"><strong>\u7b2c\u4e09\u8005\u304cd\u3092\u5f97\u308b\u306b\u306fp\u3068q\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u3053\u308c\u3089\u3082\u79d8\u5bc6\u9375\u3067\u3059\u3002p\u00d7q\u3067\u7b97\u51fa\u3055\u308c\u308bn\u306f\u516c\u958b\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001n\u304b\u3089p\u3068q\u3092\u9006\u7b97\u3059\u308b\u306b\u306f\u7d20\u56e0\u6570\u5206\u89e3\u3092\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u81a8\u5927\u306a\u624b\u9593\u304c\u304b\u304b\u308b\u305f\u3081\u3001\u73fe\u5b9f\u7684\u306a\u6642\u9593\u3067\u306f\u7b2c\u4e09\u8005\u306b\u89e3\u8aad\u3055\u308c\u308b\u3053\u3068\u304c\u306a\u3044\u3068\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/strong><\/span><\/p>\n<p><span style=\"font-size: 16px;\"><strong>\u4ee5\u4e0b\u7701\u7565<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<h3>\u3053\u306e\u3088\u3046\u306aRSA\u6697\u53f7\u30b7\u30b9\u30c6\u30e0\u3092\u6210\u308a\u7acb\u305f\u305b\u308b\u305f\u3081\u306b\u306f\u4f55\u304c\u5fc5\u8981\u306a\u306e\uff1f<\/h3>\n<p>RSA\u6697\u53f7\u304c\u4f7f\u3048\u308b\u305f\u3081\u306b\u306f\u3001\u6975\u7aef\u306b\u5927\u304d\u306a\u6570\u3068\u306a\u308b\u3079\u304d\u4e57\uff08\u591a\u6570\u56de\u306e\u4e57\u6570\uff09\u8a08\u7b97\u3068\u3001\u5272\u308a\u7b97\u306e\u3042\u307e\u308a\u6f14\u7b97\u304c\u9ad8\u901f\u3067\u884c\u3048\u308b\u3053\u3068\u304c\u5fc5\u8981\u3067\u3059\u3002<br \/>\nGemini\u306b\u8cea\u554f\u3057\u305f\u7d50\u679c\u3092\u4ee5\u4e0b\u3054\u7d39\u4ecb\uff08\u3053\u308c\u304c\u6b63\u3057\u3044\u306e\u304b\u3069\u3046\u304b\u5224\u65ad\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u8abf\u67fb\u306e\u4e00\u52a9\u306b\u306f\u306a\u308a\u305d\u3046\uff09<\/p>\n<div class=\"user-query-container user-query-bubble-container ng-star-inserted\">\n<div id=\"user-query-content-0\" class=\"query-content ng-star-inserted\">\n<div class=\"query-text gds-body-l\" dir=\"ltr\" role=\"heading\" aria-level=\"2\">\n<p class=\"query-text-line ng-star-inserted\">Q:\u3000RSA\u6697\u53f7\u304c\u6210\u7acb\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u4e57\u6570\u8a08\u7b97\u3068\u5272\u308a\u7b97\u306e\u4f59\u308a\u8a08\u7b97\u304c\u9ad8\u901f\u306b\u3067\u304d\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3069\u3093\u306a\u65b9\u6cd5\u304c\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n<\/div>\n<\/div>\n<div class=\"file-preview-container\">Ans\u3000\uff1a\u3000<span style=\"font-size: 14.08px;\">RSA\u6697\u53f7\u306e\u6210\u7acb\u306b\u306f\u3001\u78ba\u304b\u306b\u4e57\u6570\u8a08\u7b97\u3068\u5270\u4f59\u8a08\u7b97\u306e\u9ad8\u901f\u5316\u304c\u4e0d\u53ef\u6b20\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u8a08\u7b97\u3092\u52b9\u7387\u7684\u306b\u884c\u3046\u305f\u3081\u306e\u4e3b\u306a\u65b9\u6cd5\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/span><\/div>\n<\/div>\n<div>\n<div class=\"response-container ng-tns-c3678907294-8 response-optimization response-container-with-gpi is-mobile tts-removed ng-star-inserted response-container-has-multiple-responses\">\n<div class=\"presented-response-container ng-tns-c3678907294-8\">\n<div class=\"response-container-content ng-tns-c3678907294-8\">\n<div class=\"response-content ng-tns-c3678907294-8\">\n<div id=\"model-response-message-contentr_d698b772284574ca\" class=\"markdown markdown-main-panel stronger\" dir=\"ltr\">\n<p data-sourcepos=\"3:1-3:15\"><strong>1. \u4e57\u6570\u8a08\u7b97\u306e\u9ad8\u901f\u5316<\/strong><\/p>\n<ul data-sourcepos=\"5:1-13:0\">\n<li data-sourcepos=\"5:1-9:55\"><strong>\u30d0\u30a4\u30ca\u30ea\u6cd5\uff08\u7e70\u308a\u8fd4\u3057\u4e8c\u4e57\u6cd5\uff09:<\/strong>\n<ul data-sourcepos=\"6:5-9:55\">\n<li data-sourcepos=\"6:5-6:36\">\u3079\u304d\u4e57\u6307\u6570\u30922\u9032\u6570\u3067\u8868\u73fe\u3057\u3001\u6307\u6570\u3092\u5de6\u304b\u3089\u53f3\u306b\u30b9\u30ad\u30e3\u30f3\u3057\u307e\u3059\u3002<\/li>\n<li data-sourcepos=\"7:5-7:48\">\u5404\u30d3\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u3001\u81ea\u4e57\u3068\u4e57\u7b97\u3092\u6761\u4ef6\u306b\u5fdc\u3058\u3066\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3067\u3001\u8a08\u7b97\u91cf\u3092\u5927\u5e45\u306b\u524a\u6e1b\u3057\u307e\u3059\u3002<\/li>\n<li data-sourcepos=\"8:5-8:39\">\u4f8b\u3048\u3070\u3001x^13\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u300113\u30922\u9032\u6570\u3067\u8868\u3059\u30681101\u3067\u3059\u3002<\/li>\n<li data-sourcepos=\"9:5-9:55\">\u3053\u306e2\u9032\u6570\u8868\u73fe\u306b\u5f93\u3063\u3066\u3001x^1, x^2, x^4, x^8\u3092\u8a08\u7b97\u3057\u3001\u5fc5\u8981\u306a\u3082\u306e\u3092\u639b\u3051\u5408\u308f\u305b\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li data-sourcepos=\"10:1-13:0\"><strong>\u30e2\u30f3\u30b4\u30e1\u30ea\u4e57\u7b97:<\/strong>\n<ul data-sourcepos=\"11:5-13:0\">\n<li data-sourcepos=\"11:5-11:37\">\u5270\u4f59\u6f14\u7b97\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u3055\u3089\u306b\u9ad8\u901f\u306a\u4e57\u7b97\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002<\/li>\n<li data-sourcepos=\"12:5-13:0\">\u7279\u306b\u3001\u5927\u304d\u306a\u6570\u306e\u4e57\u7b97\u306b\u304a\u3044\u3066\u52b9\u679c\u3092\u767a\u63ee\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p data-sourcepos=\"14:1-14:15\"><strong>2. \u5270\u4f59\u8a08\u7b97\u306e\u9ad8\u901f\u5316<\/strong><\/p>\n<ul data-sourcepos=\"16:1-22:0\">\n<li data-sourcepos=\"16:1-18:33\"><strong>\u30d0\u30ec\u30c3\u30c8\u30ea\u30c0\u30af\u30b7\u30e7\u30f3:<\/strong>\n<ul data-sourcepos=\"17:5-18:33\">\n<li data-sourcepos=\"17:5-17:37\">\u9664\u6570\u306e\u9006\u6570\u3092\u4e8b\u524d\u306b\u8a08\u7b97\u3057\u3066\u304a\u304f\u3053\u3068\u3067\u3001\u5270\u4f59\u8a08\u7b97\u3092\u9ad8\u901f\u5316\u3057\u307e\u3059\u3002<\/li>\n<li data-sourcepos=\"18:5-18:33\">\u7279\u306b\u3001\u540c\u3058\u9664\u6570\u3067\u7e70\u308a\u8fd4\u3057\u5270\u4f59\u8a08\u7b97\u3092\u884c\u3046\u5834\u5408\u306b\u6709\u52b9\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li data-sourcepos=\"19:1-22:0\"><strong>\u30e2\u30f3\u30b4\u30e1\u30ea\u30ea\u30c0\u30af\u30b7\u30e7\u30f3:<\/strong>\n<ul data-sourcepos=\"20:5-22:0\">\n<li data-sourcepos=\"20:5-20:39\">\u30e2\u30f3\u30b4\u30e1\u30ea\u4e57\u7b97\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u52b9\u7387\u7684\u306a\u5270\u4f59\u8a08\u7b97\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002<\/li>\n<li data-sourcepos=\"21:5-22:0\">\u9664\u7b97\u3092\u4f34\u308f\u306a\u3044\u6f14\u7b97\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u9ad8\u901f\u5316\u3092\u56f3\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p data-sourcepos=\"23:1-23:19\"><strong>3. \u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306b\u3088\u308b\u9ad8\u901f\u5316<\/strong><\/p>\n<ul data-sourcepos=\"25:1-29:0\">\n<li data-sourcepos=\"25:1-26:58\"><strong>\u5c02\u7528\u306e\u6697\u53f7\u51e6\u7406\u30d7\u30ed\u30bb\u30c3\u30b5:<\/strong>\n<ul data-sourcepos=\"26:5-26:58\">\n<li data-sourcepos=\"26:5-26:58\">RSA\u6697\u53f7\u306e\u6f14\u7b97\u306b\u7279\u5316\u3057\u305f\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u9ad8\u901f\u306a\u51e6\u7406\u304c\u53ef\u80fd\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li data-sourcepos=\"27:1-29:0\"><strong>GPU\uff08Graphics Processing 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