{"id":6599,"date":"2022-12-17T15:47:11","date_gmt":"2022-12-17T07:47:11","guid":{"rendered":"https:\/\/www.chenqing.work\/?p=6599"},"modified":"2023-01-01T20:17:20","modified_gmt":"2023-01-01T12:17:20","slug":"%e5%af%86%e7%a0%81%e6%8a%80%e6%9c%af%e6%89%ab%e7%9b%b2%ef%bc%9a%e9%9d%9e%e5%af%b9%e7%a7%b0%e5%8a%a0%e5%af%86","status":"publish","type":"post","link":"https:\/\/www.chenqing.work\/?p=6599","title":{"rendered":"\u5bc6\u7801\u6280\u672f\u626b\u76f2\uff0cPart 2\uff1a\u975e\u5bf9\u79f0\u52a0\u5bc6"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1280\" src=\"https:\/\/www.chenqing.work\/wp-content\/uploads\/2022\/12\/sajjad-ahmadi-edzVv0hEd7E-unsplash.jpg\" alt=\"\" class=\"wp-image-6601\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.chenqing.work\/?p=6176\" data-type=\"URL\" data-id=\"https:\/\/www.chenqing.work\/?p=6176\">\u5bc6\u7801\u6280\u672f\u626b\u76f2\uff0cPart 1\uff1a\u5bf9\u79f0\u52a0\u5bc6<\/a><\/li>\n\n\n\n<li>\ud83c\udfaf <strong>\u5bc6\u7801\u6280\u672f\u626b\u76f2\uff0cPart 2\uff1a\u975e\u5bf9\u79f0\u52a0\u5bc6<\/strong><\/li>\n\n\n\n<li><a href=\"https:\/\/www.chenqing.work\/?p=6669\" data-type=\"URL\" data-id=\"https:\/\/www.chenqing.work\/?p=6669\">\u5bc6\u7801\u6280\u672f\u626b\u76f2\uff0cPart 3\uff1a\u8ba4\u8bc1<\/a><\/li>\n<\/ul>\n\n\n\n<p>\u5728\u4e0a\u4e00\u7bc7<a href=\"https:\/\/www.chenqing.work\/?p=6176\" data-type=\"URL\" data-id=\"https:\/\/www.chenqing.work\/?p=6176\">\u5bf9\u79f0\u52a0\u5bc6\u7684\u4ecb\u7ecd<\/a>\u4e2d\uff0c\u6211\u4eec\u4e86\u89e3\u5230\u5bf9\u660e\u6587\u7684\u52a0\u5bc6\u9700\u8981\u7528\u5230\u5bc6\u94a5\uff0c\u800c\u89e3\u5bc6\u65f6\u4e5f\u5fc5\u987b\u7528\u540c\u4e00\u628a\u5bc6\u94a5\uff0c\u4e5f\u5c31\u662f\u8bf4\u53d1\u9001\u8005\u548c\u63a5\u6536\u8005\u90fd\u6709\u8fd9\u628a\u5bc6\u94a5\uff0c\u53cc\u65b9\u90fd\u53ef\u4ee5\u505a\u52a0\u5bc6\u3001\u89e3\u5bc6\u64cd\u4f5c\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u60f3\u8981\u5b89\u5168\u5730\u4f20\u9012\u4fe1\u606f\uff0c\u6240\u4ee5\u91c7\u7528\u5bc6\u94a5\u5bf9\u4fe1\u606f\u8fdb\u884c\u52a0\u5bc6\u540e\u518d\u4f20\u9001\uff0c\u8fd9\u6837\u5373\u4f7f\u5728\u4f20\u9012\u8fc7\u7a0b\u88ab\u7a83\u542c\uff0c\u4e5f\u4e0d\u4f1a\u6cc4\u9732\u5177\u4f53\u5185\u5bb9\u3002<\/p>\n\n\n\n<p>\u73b0\u5728\u63a5\u6536\u8005\u6536\u5230\u7684\u662f\u5bc6\u6587\uff0c\u9700\u8981\u7ecf\u8fc7\u89e3\u5bc6\u624d\u80fd\u5f97\u5230\u5177\u4f53\u5185\u5bb9\uff0c\u89e3\u5bc6\u9700\u8981\u5bc6\u94a5\uff0c\u95ee\u9898\u6765\u4e86\uff0c\u63a5\u6536\u8005\u600e\u4e48\u77e5\u9053\u8fd9\u4e2a\u5bc6\u94a5\uff1f\u6216\u8005\u8bf4\uff0c<strong>\u53cc\u65b9\u5982\u4f55\u77e5\u9053\u540c\u4e00\u4e2a\u5bc6\u94a5\uff1f<\/strong>\u5bc6\u94a5\u5728\u53d1\u9001\u8005\u6216\u63a5\u6536\u8005\u624b\u4e0a\uff0c\u90a3\u4e48\u5fc5\u7136\u6709\u4e00\u4e2a\u5c06\u5bc6\u94a5\u4ece\u4e00\u65b9\u8f6c\u79fb\u5230\u53e6\u4e00\u65b9\u7684\u8fc7\u7a0b\u3002\u5230\u8fd9\u91cc\uff0c\u95ee\u9898\u5c31\u8f6c\u5316\u4e3a\u5982\u4f55\u5b89\u5168\u5730\u914d\u9001\u5bc6\u94a5 \u2014\u2014 \u79f0\u4e3a<strong>\u5bc6\u94a5\u914d\u9001\u95ee\u9898<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"661\" height=\"798\" src=\"https:\/\/www.chenqing.work\/wp-content\/uploads\/2022\/12\/image-7.png\" alt=\"\" class=\"wp-image-6623\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u8fd9\u91cc\uff0c\u4e24\u4e2a\u95ee\u9898\u662f\u540c\u8d28\u7684\uff0c\u53ea\u662f\u9700\u8981\u5e94\u5bf9\u7684\u95ee\u9898\u89c4\u6a21\u4e0d\u4e00\u6837\uff0c\u95ee\u9898\u89c4\u6a21\u7684\u7f29\u5c0f\u5e26\u6765\u4e86\u53ef\u64cd\u4f5c\u7a7a\u95f4\u3002\u89e3\u51b3\u5bc6\u94a5\u914d\u9001\u95ee\u9898\u4e00\u822c\u6709 4 \u79cd\u65b9\u6848\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e8b\u5148\u5171\u4eab\uff1b<\/li>\n\n\n\n<li>\u901a\u8fc7\u5bc6\u94a5\u914d\u9001\u4e2d\u5fc3\u4ea4\u6362\uff1b<\/li>\n\n\n\n<li>\u901a\u8fc7 Diffie-Hellman \u7b97\u6cd5\u4ea4\u6362\uff1b<\/li>\n\n\n\n<li>\u901a\u8fc7\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u4ea4\u6362\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u975e\u5bf9\u79f0\u52a0\u5bc6\u7684\u89e3\u51b3\u65b9\u5f0f\u975e\u5e38\u5de7\u5999\u2014\u2014\u4e5f\u662f\u5176\u540d\u79f0\u7684\u7531\u6765\uff0c<strong>\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u6709\u4e24\u4e2a\u552f\u4e00\u6210\u5bf9\u7684\u5bc6\u94a5<\/strong>\uff0c\u4e00\u4e2a\u662f\u516c\u94a5\uff0c\u5bf9\u5916\u516c\u5f00\u7684\uff0c\u4e00\u4e2a\u662f\u79c1\u94a5\uff0c\u5bf9\u5916\u4fdd\u5bc6\u7684\uff0c\u5728\u975e\u5bf9\u79f0\u52a0\u5bc6\u4e2d\u7528\u4e00\u4e2a\u5bc6\u94a5\u52a0\u5bc6\u7684\u4fe1\u606f\u53ea\u6709\u5bf9\u5e94\u7684\u53e6\u4e00\u4e2a\u5bc6\u94a5\u624d\u80fd\u89e3\u5bc6\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f7f\u7528\u516c\u94a5\u52a0\u5bc6\u7684\u4fe1\u606f\u53ea\u6709\u62e5\u6709\u79c1\u94a5\u7684\u4e00\u65b9\u53ef\u4ee5\u89e3\u5bc6\u3002\u4efb\u4f55\u4eba\u62ff\u5230\u516c\u94a5\uff0c\u4e5f\u65e0\u6cd5\u89e3\u5bc6\u88ab\u516c\u94a5\u52a0\u5bc6\u7684\u4fe1\u606f\uff0c\u5982\u6b64\u5c31\u4e0d\u7528\u4fdd\u969c\u516c\u94a5\u914d\u9001\u7684\u5b89\u5168\u6027\u4e86\u3002\u552f\u4e00\u7684\u95ee\u9898\u662f\uff0c\u5982\u4f55\u786e\u8ba4\u516c\u94a5\u7684\u5408\u6cd5\u6027\uff0c\u786e\u4fdd\u4e0d\u88ab\u4e2d\u95f4\u4eba\u653b\u51fb\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"642\" height=\"770\" src=\"https:\/\/www.chenqing.work\/wp-content\/uploads\/2022\/12\/image-8.png\" alt=\"\" class=\"wp-image-6625\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u7684\u4ee3\u8868\u662f RSA\uff0c\u76ee\u524d\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5404\u79cd\u573a\u666f\uff0c\u968f\u7740\u8fd1\u5e74\u5bf9\u4e2a\u4eba\u9690\u79c1\u7684\u5173\u6ce8\u5ea6\u63d0\u9ad8\uff0c\u804a\u5929\u5de5\u5177\u4e2d\u53c8\u5174\u8d77\u91c7\u7528\u975e\u5bf9\u79f0\u52a0\u5bc6\u4fdd\u969c\u7528\u6237\u804a\u5929\u5185\u5bb9\u673a\u5bc6\u6027\u7684\u5e94\u7528\u573a\u666f\uff0c\u79f0\u4e3a\u7aef\u5230\u7aef\u52a0\u5bc6\uff08E2EE\uff0cEnd-to-End Encryption\uff09\u3002<\/p>\n\n\n\n<p>\u548c\u5bf9\u79f0\u52a0\u5bc6\u4f9d\u8d56\u4e8e\u5f02\u6216\u8fd0\u7b97\u4e0d\u540c\uff0cRSA \u7684\u52a0\u89e3\u5bc6\u673a\u5236\u4e3b\u8981\u4f9d\u8d56\u4e8e<strong>\u53d6\u6a21\u8fd0\u7b97<\/strong>\uff08mod\uff09\u2014\u2014 \u9664\u6cd5\u4e4b\u540e\u6c42\u4f59\u6570\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>RSA \u52a0\u5bc6\uff1a<strong>\u5bc6\u6587 = \u660e\u6587<sup>E<\/sup> mod N<\/strong><\/li>\n\n\n\n<li>RSA \u89e3\u5bc6\uff1a<strong>\u660e\u6587 = \u5bc6\u6587<sup>D<\/sup> mod N<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u4ee5\u4e0a\u4e24\u4e2a\u5c31\u662f RSA \u7b97\u6cd5\u52a0\u89e3\u5bc6\u7684\u516c\u5f0f\uff0c\u5176\u4e2d\u660e\u6587\u3001\u5bc6\u6587\u90fd\u662f\u6570\u5b57\uff0c\u660e\u6587\u5fc5\u987b\u5c0f\u4e8e N\uff0c\u516c\u94a5\u5c31\u662f\uff08E\uff0cN\uff09\u7ec4\u5408\uff0c\u79c1\u94a5\u5c31\u662f\uff08D\uff0cN\uff09\u7ec4\u5408\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"647\" height=\"298\" src=\"https:\/\/www.chenqing.work\/wp-content\/uploads\/2022\/12\/image-9.png\" alt=\"\" class=\"wp-image-6638\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u4e0b\u9762\u770b\u770b E\u3001D\u3001N \u662f\u5982\u4f55\u8ba1\u7b97\u51fa\u6765\u7684\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2460 <strong>N = p * q<\/strong>\uff0c  p\u3001q \u4e3a\u4e24\u4e2a\u6311\u9009\u51fa\u7684\u8d28\u6570<\/li>\n\n\n\n<li>\u2461 <strong>L = lcm (p-1, q-1)<\/strong>\uff0c  lcm \u8868\u793a\u6c42\u6700\u5c0f\u516c\u500d\u6570\uff0c\u6c42 E\u3001D \u65f6\u9700\u8981<\/li>\n\n\n\n<li>\u2462 <strong>gcd (E, L) = 1, 1 &lt; E &lt; L<\/strong>\uff0c gcd \u8868\u793a\u6c42\u6700\u5927\u516c\u7ea6\u6570<\/li>\n\n\n\n<li>\u2463 (<strong>E * D) mod L = 1, 1 &lt; D &lt; L<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u56e0\u4e3a\u516c\u94a5\u5c31\u662f\uff08E\uff0cN\uff09\uff0c\u662f\u516c\u5f00\u7684\uff0c\u53ea\u8981\u6c42\u51fa D\uff0c\u79c1\u94a5\u5c31\u88ab\u7834\u89e3\u4e86\u3002\u8ba1\u7b97 D \u9700\u8981\u77e5\u9053 L\uff0c\u8ba1\u7b97 L \u9700\u8981\u77e5\u9053 p\u3001q\uff0cN \u662f\u77e5\u9053\u7684\uff0c\u6240\u4ee5\u95ee\u9898\u6838\u5fc3\u5c31\u662f\u5c06 N \u8d28\u56e0\u6570\u5206\u89e3\u5f97\u5230 p\u3001q\u3002<strong>\u76ee\u524d\u6ca1\u6709\u53d1\u73b0\u5bf9\u5927\u6574\u6570\u8fdb\u884c\u8d28\u56e0\u6570\u5206\u89e3\u7684\u9ad8\u6548\u7b97\u6cd5\uff0c\u4e5f\u5c1a\u672a\u8bc1\u660e\u8d28\u56e0\u6570\u5206\u89e3\u662f\u5426\u771f\u662f\u975e\u5e38\u56f0\u96be\u7684\u95ee\u9898\uff0c\u751a\u81f3\u4e0d\u77e5\u9053\u662f\u5426\u5b58\u5728\u4e00\u79cd\u5206\u89e3\u8d28\u56e0\u6570\u7684\u7b80\u5355\u65b9\u6cd5<\/strong>\u3002\u5728\u73b0\u5b9e\u7684\u65f6\u95f4\u91cc\uff0c\u65e0\u6cd5\u6709\u6548\u5730\u5bf9 N \u8fdb\u884c\u8d28\u56e0\u6570\u5206\u89e3\uff0cRSA \u7684\u5b89\u5168\u6027\u5c31\u5728\u8fd9\u91cc\u3002<\/p>\n\n\n\n<p>\u975e\u5bf9\u79f0\u52a0\u5bc6\u867d\u7136\u975e\u5e38\u4f18\u79c0\uff0c\u4f46\u5728\u91c7\u7528\u540c\u7b49\u673a\u5bc6\u6027\u5bc6\u94a5\u6761\u4ef6\u4e0b\uff0c<strong>\u975e\u5bf9\u79f0\u52a0\u5bc6\u6548\u7387\u53ea\u6709\u5bf9\u79f0\u52a0\u5bc6\u7684\u51e0\u767e\u5206\u4e4b\u4e00<\/strong>\uff0c\u6240\u4ee5\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u5e76\u4e0d\u80fd\u53d6\u4ee3\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5\u3002\u5728 TLS \u8fd9\u6837\u7684\u573a\u666f\u4e2d\uff0c\u4f1a\u91c7\u7528\u975e\u5bf9\u79f0\u52a0\u5bc6\u6765\u4f20\u9012\u5bf9\u79f0\u5bc6\u94a5\uff0c\u4f7f\u7528\u5bf9\u79f0\u52a0\u5bc6\u6765\u52a0\u5bc6\u5e94\u7528\u6570\u636e\uff0c\u6df7\u5408\u4f7f\u7528\u975e\u5bf9\u79f0\u52a0\u5bc6\u548c\u5bf9\u79f0\u52a0\u5bc6\uff0c\u540c\u65f6\u517c\u987e\u5b89\u5168\u6027\u548c\u6548\u7387\u3002<\/p>\n\n\n\n<p>\u5728 TLS \u4e2d\uff0c\u4f20\u9012\u5bc6\u94a5\u53ef\u4ee5\u9009\u62e9\u4f7f\u7528 RSA \u8fdb\u884c\u52a0\u5bc6\u4f20\u9012\uff0c\u8fd8\u6709\u4e00\u79cd\u9009\u62e9\u662f Diffie-Hellman \u7b97\u6cd5\uff0cDiffie-Hellman \u4e5f\u5f88\u5de7\u5999\uff0c\u6709\u5fc5\u8981\u5199\u4e00\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2460 <strong>\u9009\u62e9\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u8d28\u6570 P \u53ca\u5176\u751f\u6210\u5143 G\uff08G<sup>1<\/sup> mod P \u5230 G<sup>P-1<\/sup> mod P \u8981\u80fd\u6620\u5c04\u51fa\u6240\u6709 1 \u5230 P-1 \u8fd9 P-1 \u4e2a\u6570\u5b57\uff09\uff0cP\u3001G \u516c\u5f00<\/strong><\/li>\n\n\n\n<li>\u2461 <strong>\u53d1\u9001\u7aef\u751f\u6210\u4e00\u4e2a\u968f\u673a\u6570 A\uff0c\u4e0d\u516c\u5f00\uff0c1 &lt; A &lt; P-2<\/strong><\/li>\n\n\n\n<li>\u2462 <strong>\u63a5\u6536\u7aef\u751f\u6210\u4e00\u4e2a\u968f\u673a\u6570 B\uff0c\u4e0d\u516c\u5f00\uff0c1 &lt; B &lt; P-2<\/strong><\/li>\n\n\n\n<li>\u2463 <strong>\u53d1\u9001\u7aef\u8ba1\u7b97 G<sup>A<\/sup> mod P \u7ed9\u63a5\u6536\u7aef\uff0c\u63a5\u6536\u7aef\u8ba1\u7b97\u5bc6\u94a5 (G<sup>A<\/sup> mod P)<sup>B<\/sup> mod P<\/strong><\/li>\n\n\n\n<li>\u2464 <strong>\u63a5\u6536\u7aef\u8ba1\u7b97 G<sup>B<\/sup> mod P \u7ed9\u53d1\u9001\u7aef\uff0c\u53d1\u9001\u7aef\u8ba1\u7b97\u5bc6\u94a5 (G<sup>B<\/sup> mod P)<sup>A<\/sup> mod P<\/strong><\/li>\n\n\n\n<li>\u2465 <strong>\u6700\u540e\u53d1\u9001\u7aef\u548c\u63a5\u6536\u7aef\u90fd\u5f97\u5230\u5bc6\u94a5 G<sup>A*B<\/sup> mod P<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"643\" height=\"545\" src=\"https:\/\/www.chenqing.work\/wp-content\/uploads\/2022\/12\/image-10.png\" alt=\"\" class=\"wp-image-6663\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>P\u3001G\u3001G<sup>A<\/sup> mod P\u3001G<sup>B<\/sup> mod P \u662f\u516c\u5f00\u7684\uff0c\u53ea\u8981\u80fd\u8ba1\u7b97\u51fa A \u6216\u8005 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