{"id":40,"date":"2021-12-12T02:34:30","date_gmt":"2021-12-12T02:34:30","guid":{"rendered":"http:\/\/www.luluck.com\/?p=40"},"modified":"2021-12-14T11:58:38","modified_gmt":"2021-12-14T11:58:38","slug":"%e9%80%9a%e4%bf%97%e6%98%93%e6%87%82rsa%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"http:\/\/www.luluck.com\/index.php\/2021\/12\/12\/%e9%80%9a%e4%bf%97%e6%98%93%e6%87%82rsa%e7%ae%97%e6%b3%95\/","title":{"rendered":"\u901a\u4fd7\u6613\u61c2RSA\u7b97\u6cd5"},"content":{"rendered":"\n<h2 id=\"autoid-0-0-0\"><strong>RSA\u7b97\u6cd5\u662f\u4ec0\u4e48<\/strong><\/h2>\n\n\n\n<p>\u3000\u30001977\u5e74\uff0c\u4e09\u4f4d\u6570\u5b66\u5bb6 Rivest\u3001Shamir \u548c Adleman \u8bbe\u8ba1\u4e86\u4e00\u79cd\u7b97\u6cd5\uff0c\u53ef\u4ee5\u5b9e\u73b0\u975e\u5bf9\u79f0\u52a0\u5bc6\u3002\u7b97\u6cd5\u7528\u4ed6\u4eec\u4e09\u4e2a\u4eba\u7684\u540d\u5b57\u547d\u540d\uff0c\u53eb\u505a <a href=\"https:\/\/links.jianshu.com\/go?to=http%3A%2F%2Fzh.wikipedia.org%2Fzh-cn%2FRSA%25E5%258A%25A0%25E5%25AF%2586%25E7%25AE%2597%25E6%25B3%2595\" target=\"_blank\" rel=\"noreferrer noopener\">RSA \u7b97\u6cd5<\/a>\u3002<\/p>\n\n\n\n<p>\u3000\u3000RSA\u662f\u7b2c\u4e00\u4e2a\u975e\u5bf9\u79f0\u5bc6\u7801\u7b97\u6cd5\uff0c\u5bc6\u94a5\u6210\u5bf9\u5b58\u5728\uff08\u516c\u94a5\u548c\u79c1\u94a5\uff09\uff0c\u5bc6\u94a5\u5bb9\u6613\u7ba1\u7406\uff0c\u5bb9\u6613\u5206\u53d1\uff0c\u79c1\u94a5\u53ef\u7528\u4e8e\u89e3\u5bc6\u548c\u7b7e\u540d\uff0c\u516c\u94a5\u53ef\u7528\u4e8e\u52a0\u5bc6\u548c\u9a8c\u7b7e\u3002\u4f46\u662f\u7b97\u6cd5\u590d\u6742\uff0c\u7528\u4e8e\u52a0\u5bc6\u5927\u91cf\u6570\u636e\u65f6\u6548\u7387\u4f4e\u4e0b\u4e14\u968f\u7740\u4fdd\u5bc6\u7b49\u7ea7\u7684\u63d0\u9ad8\uff0c\u5176\u5bc6\u94a5\u957f\u5ea6\u6210\u6307\u6570\u589e\u52a0\u3002<\/p>\n\n\n\n<p>\u3000\u3000\u76f4\u5230\u73b0\u5728\uff0cRSA \u7b97\u6cd5\u4ecd\u662f\u6700\u5e7f\u6cdb\u4f7f\u7528\u7684&#8221;\u975e\u5bf9\u79f0\u52a0\u5bc6\u7b97\u6cd5&#8221;\u3002\u6beb\u4e0d\u5938\u5f20\u5730\u8bf4\uff0c\u53ea\u8981\u6709\u8ba1\u7b97\u673a\u7f51\u7edc\u7684\u5730\u65b9\uff0c\u5c31\u6709 RSA \u7b97\u6cd5\u3002<\/p>\n\n\n\n<h2 id=\"autoid-1-0-0\"><strong>\u5b89\u5168\u6027\u7531\u4ec0\u4e48\u51b3\u5b9a<\/strong><\/h2>\n\n\n\n<p><strong>\u3000\u3000\u5927\u8d28\u6570\u505a\u56e0\u6570\u5206\u89e3\u56f0\u96be<\/strong><\/p>\n\n\n\n<h2 id=\"autoid-2-0-0\"><strong>\u516c\u79c1\u94a5\u751f\u6210\u6d41\u7a0b<\/strong><\/h2>\n\n\n\n<p>\u3000\u3000\u7b2c\u4e00\u6b65\uff1a\u968f\u673a\u627e\u4e24\u4e2a\u8d28\u6570 P \u548c Q ,P \u4e0e Q \u8d8a\u5927\uff0c\u8d8a\u5b89\u5168\u3002\uff08\u4f8b\u5982\uff1a61\u548c53\uff09<\/p>\n\n\n\n<p>\u3000\u3000\u7b2c\u4e8c\u6b65\uff1a\u8ba1\u7b97p\u548cq\u7684\u4e58\u79efn\u3002\uff08n = 61\u00d753 = 3233\uff0cn\u7684\u957f\u5ea6\u5c31\u662f\u5bc6\u94a5\u957f\u5ea6\u30023233\u5199\u6210\u4e8c\u8fdb\u5236\u662f110010100001\uff0c\u4e00\u5171\u670912\u4f4d\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5bc6\u94a5\u5c31\u662f12\u4f4d\u3002\uff09<\/p>\n\n\n\n<p>\u3000\u3000\u7b2c\u4e09\u6b65\uff1a\u8ba1\u7b97 n \u7684\u6b27\u62c9\u51fd\u6570 \u03c6(n)\u3002\uff08\u6839\u636e\u516c\u5f0f\u03c6(n) = (p-1)(q-1)\u7b97\u51fa\u03c6(3233)\u7b49\u4e8e60\u00d752\uff0c\u53733120\uff09<\/p>\n\n\n\n<p>\u3000\u3000\u7b2c\u56db\u6b65\uff1a\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u6574\u6570 e\uff0c\u6761\u4ef6\u662f1&lt; e &lt; \u03c6(n)\uff0c\u4e14 e \u4e0e \u03c6(n) \u4e92\u8d28\u3002\uff08\u6761\u4ef6\u662f1&lt; e &lt; \u03c6(n)\uff0c\u4e14e\u4e0e\u03c6(n) \u4e92\u8d28\u30021\u52303120\u4e4b\u95f4\uff0c\u968f\u673a\u9009\u62e9\u4e8617\u3002\uff09<\/p>\n\n\n\n<p>\u3000\u3000\u7b2c\u4e94\u6b65\uff1a\u6709\u4e00\u4e2a\u6574\u6570 d\uff0c\u53ef\u4ee5\u4f7f\u5f97 e*d \u9664\u4ee5 \u03c6(n) \u7684\u4f59\u6570\u4e3a 1\u3002\uff08e*d \u2261 1 (mod \u03c6(n))\uff0c\u537317*2753 mode 3120 = 1\uff09<\/p>\n\n\n\n<p>\u3000\u3000\u7b2c\u516d\u6b65\uff1a\u5c06n\u548ce\u5c01\u88c5\u6210\u516c\u94a5\uff0cn\u548cd\u5c01\u88c5\u6210\u79c1\u94a5\u3002\uff08n=3233\uff0ce=17\uff0cd=2753\uff0c\u6240\u4ee5\u516c\u94a5\u5c31\u662f (3233,17)\uff0c\u79c1\u94a5\u5c31\u662f\uff083233, 2753\uff09\u3002\uff09<\/p>\n\n\n\n<h2 id=\"autoid-3-0-0\"><strong>RSA\u52a0\u5bc6<\/strong><\/h2>\n\n\n\n<p>\u3000\u3000\u9996\u5148\u5bf9\u660e\u6587\u8fdb\u884c\u6bd4\u7279\u4e32\u5206\u7ec4\uff0c\u4f7f\u5f97\u6bcf\u4e2a\u5206\u7ec4\u5bf9\u5e94\u7684\u5341\u8fdb\u5236\u6570\u5c0f\u4e8en\uff08\u5bc6\u94a5\u957f\u5ea6\uff09\uff0c\u7136\u540e\u4f9d\u6b21\u5bf9\u6bcf\u4e2a\u5206\u7ec4m\u505a\u4e00\u6b21\u52a0\u5bc6\uff0c\u6240\u6709\u5206\u7ec4\u7684\u5bc6\u6587\u6784\u6210\u7684\u5e8f\u5217\u5c31\u662f\u539f\u59cb\u6d88\u606f\u7684\u52a0\u5bc6\u7ed3\u679c\uff0c\u5373m\u6ee1\u8db30\u2264m&lt;n\u3002<\/p>\n\n\n\n<p>\u3000\u3000\u52a0\u5bc6\u7b97\u6cd5\u4e3a\uff1a c\u2261 m<sup>e<\/sup> mod n; c\u4e3a\u5bc6\u6587\uff0c\u4e140\u2264c&lt;n\u3002<\/p>\n\n\n\n<h2 id=\"autoid-4-0-0\"><strong>RSA\u89e3\u5bc6<\/strong><\/h2>\n\n\n\n<p>\u3000\u3000\u5bf9\u4e8e\u5bc6\u65870\u2264c&lt;n\uff0c\u89e3\u5bc6\u7b97\u6cd5\u4e3a\uff1a m\u2261 c<sup>d<\/sup> mod n\u3002<\/p>\n\n\n\n<h2 id=\"autoid-5-0-0\"><strong>RSA\u7b7e\u540d\u9a8c\u8bc1<\/strong><\/h2>\n\n\n\n<p>\u3000\u3000RSA\u5bc6\u7801\u4f53\u5236\u65e2\u53ef\u4ee5\u7528\u4e8e\u52a0\u5bc6\u53c8\u53ef\u4ee5\u7528\u4e8e\u6570\u5b57\u7b7e\u540d\u3002<\/p>\n\n\n\n<p>\u3000\u3000\u5df2\u77e5\u516c\u94a5\uff08e\uff0cn\uff09\uff0c\u79c1\u94a5d\u3002<\/p>\n\n\n\n<p>\u3000\u3000\u3000\u30001.\u5bf9\u4e8e\u6d88\u606fm\u7b7e\u540d\u4e3a\uff1asign \u2261 m<sup>d<\/sup> mod n<\/p>\n\n\n\n<p>\u3000\u3000\u3000\u30002.\u9a8c\u8bc1\uff1a\u5bf9\u4e8e\u6d88\u606f\u7b7e\u540d\u5bf9\uff08m\uff0csign\uff09\uff0c\u5982\u679cm \u2261 sign<sup>e<\/sup> mod n\uff0c\u5219sign\u662fm\u7684\u6709\u6548\u7b7e\u540d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>RSA\u7b97\u6cd5\u662f\u4ec0\u4e48 \u3000\u30001977\u5e74\uff0c\u4e09\u4f4d\u6570\u5b66\u5bb6 Rivest\u3001Shamir \u548c Adleman \u8bbe\u8ba1\u4e86&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[],"_links":{"self":[{"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/posts\/40"}],"collection":[{"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":1,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/posts\/40\/revisions"}],"predecessor-version":[{"id":41,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/posts\/40\/revisions\/41"}],"wp:attachment":[{"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/media?parent=40"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/categories?post=40"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.luluck.com\/index.php\/wp-json\/wp\/v2\/tags?post=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}