{"id":29107,"date":"2017-08-15T00:11:04","date_gmt":"2017-08-14T16:11:04","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=29107"},"modified":"2018-07-29T11:16:44","modified_gmt":"2018-07-29T03:16:44","slug":"rsa%e5%8a%a0%e5%af%86%e6%b3%95%e9%81%87%e4%b8%8a%e9%87%8f%e5%ad%90%e9%9b%bb%e8%85%a6","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=29107","title":{"rendered":"RSA\u52a0\u5bc6\u6cd5\u9047\u4e0a\u91cf\u5b50\u96fb\u8166"},"content":{"rendered":"<figure id=\"attachment_29108\" aria-describedby=\"caption-attachment-29108\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-29108\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/front.png\" alt=\"\" width=\"650\" height=\"451\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/front.png 980w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/front-600x416.png 600w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/front-800x555.png 800w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-29108\" class=\"wp-caption-text\">\u91cf\u5b50\u96fb\u8166\u662f\u57fa\u65bc\u91cf\u5b50\u529b\u5b78\u7684\u8a08\u7b97\u5de5\u5177\uff0c\u5716\u4e2d\u70ba\u91cf\u5b50\u529b\u5b78\u4e2d\u6ce2\u51fd\u6578\u5e38\u7528\u7684\u7b26\u865f\u3002<\/figcaption><\/figure>\n<p><span style=\"color: #333399;\"><strong>\u25a0\u901a\u8a0a\u548c\u60c5\u5831\u4e00\u76f4\u662f\u5546\u696d\u548c\u570b\u9632\u6700\u91cd\u8981\u7684\u4e00\u74b0\uff0c\u800c\u52a0\u5bc6\u662f\u5176\u4e2d\u7684\u6838\u5fc3\u3002\u4e8c\u5341\u4e16\u7d00\u672b\u4ee5\u4f86\uff0c RSA\u52a0\u5bc6\u6cd5\u6191\u85c9\u8457\u53e4\u5178\u96fb\u8166\u96e3\u4ee5\u4f01\u53ca\u7684\u8907\u96dc\u5ea6\u8b8a\u5f97\u65e5\u8da8\u6d41\u884c\uff0c\u5b89\u5168\u6027\u9ad8\u3002\u4f46\u5c0d\u65bc\u7279\u5b9a\u7684\u8a08\u7b97\u5de5\u4f5c\uff0c\u91cf\u5b50\u96fb\u8166\u7684\u8a08\u7b97\u529b\u9060\u9060\u8d85\u8d8a\u53e4\u5178\u96fb\u8166\uff0c\u9019\u662f\u5426\u6703\u5c0d\u4f60\u6211\u65e5\u5e38\u90fd\u5728\u4f7f\u7528\u7684RSA\u52a0\u5bc6\u9020\u6210\u5a01\u8105\u5462\uff1f\u56de\u7b54\u554f\u984c\u524d\uff0c\u5148\u8b93\u6211\u5011\u770b\u770bRSA\u548c\u91cf\u5b50\u96fb\u8166\u80cc\u5f8c\u5206\u5225\u6709\u4e9b\u4ec0\u9ebc\u3002<\/strong><\/span><\/p>\n<p><strong>\u64b0\u6587\uff5c<\/strong>\u9673\u5955\u5ef7<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5728RSA\u4e4b\u524d\uff1a\u5c0d\u7a31\u6027\u52a0\u5bc6<\/strong><\/span><\/p>\n<p>\u95dc\u65bc\u5c0d\u7a31\u6027\u52a0\u5bc6\uff0c\u6700\u5ee3\u70ba\u4eba\u77e5\u7684\u662f\u4e8c\u6b21\u5927\u6230\u4e2d\u5fb7\u8ecd\u7684\u5bc6\u78bc\u7cfb\u7d71\u300cEnigma\u300d\u3002\u6bcf\u4f4d\u8ecd\u58eb\u5b98\u64c1\u6709\u4e00\u4efd\u5bc6\u78bc\u8868(\u91d1\u9470)\uff0c\u7576\u6536\u5230\u52a0\u5bc6\u8a0a\u606f\u6642(\u5716\u4e00)\uff0c\u5fc5\u9808\u7528\u76f8\u540c\u7684\u5bc6\u78bc\u8868\u624d\u80fd\u7ffb\u8b6f\u5bc6\u6587\u3002\u6575\u8ecd\u7aca\u807d\u8005\u7f3a\u5c11\u4e86\u5bc6\u78bc\u8868\uff0c\u5c31\u7b97\u6514\u622a\u5230\u8a0a\u865f\u4e5f\u7121\u6cd5\u89e3\u958b\u5bc6\u6587\u3002\u9019\u7a2e\u5bc6\u78bc\u7cfb\u7d71\u975e\u5e38\u6210\u529f\uff0c\u7576\u6642\u5fb7\u8ecd\u9760\u8457\u5b83\uff0c\u900f\u904e\u9583\u96fb\u6230\u9806\u5229\u64ca\u6557\u5468\u570d\u570b\u5bb6\u3002<\/p>\n<figure id=\"attachment_29109\" aria-describedby=\"caption-attachment-29109\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-29109\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/fig1.png\" alt=\"\" width=\"650\" height=\"392\" \/><figcaption id=\"caption-attachment-29109\" class=\"wp-caption-text\">\u5716\u4e00\u3001\u5c0d\u7a31\u6027\u52a0\u5bc6\u793a\u610f\u5716\u3002\u5c0d\u7a31\u6027\u52a0\u5bc6\u4e2d\u7684\u300c\u5c0d\u7a31\u300d\u6307\u7684\u662f\u52a0\u5bc6\u548c\u89e3\u5bc6\u4f7f\u7528\u76f8\u540c\u7684\u91d1\u9470(\u5bc6\u78bc\u8868)\u3002\u4ed6\u7684\u512a\u9ede\u662f\u52a0\u5bc6\u904e\u7a0b\u7c21\u55ae\u660e\u77ad\uff0c\u4e14\u5728\u91d1\u9470\u4e0d\u5916\u6d41\u7684\u60c5\u6cc1\u4e0b\u5b89\u5168\u6027\u5f88\u9ad8\u3002\u4f46\u7f3a\u9ede\u662f\u4e00\u65e6\u91d1\u9470\u5916\u6d41\uff0c\u6574\u500b\u5bc6\u78bc\u7cfb\u7d71\u5c31\u74e6\u89e3\u4e86\u3002\u7121\u8ad6\u662f\u904e\u53bb\u6230\u722d\u6216\u662f\u73fe\u4ee3\u751f\u6d3b\uff0c\u4fdd\u8b49\u91d1\u9470\u7d55\u4e0d\u5916\u6d41\u662f\u4e00\u4ef6\u4e0d\u5207\u5be6\u969b\u7684\u4e8b\uff0c\u56e0\u6b64\u5c0d\u7a31\u6027\u52a0\u5bc6\u7684\u5b89\u5168\u6027\u4e26\u4e0d\u662f\u771f\u7684\u5f88\u53ef\u9760\u3002<\/figcaption><\/figure>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u975e\u5c0d\u7a31\u6027\u52a0\u5bc6<\/strong><\/span><\/p>\n<p>\u5fb7\u8ecd\u5c07\u5bc6\u78bc\u8868\u5370\u5728\u6c34\u6eb6\u6027\u6750\u6599\u4e0a\uff0c\u6bcf\u500b\u6708\u66f4\u65b0\u4e00\u6b21\u3002\u82e5\u906d\u5230\u4fd8\u865c\uff0c\u5bc6\u78bc\u8868\u53ef\u4ee5\u7acb\u5373\u88ab\u92b7\u6bc0\u3002\u5373\u4f7f\u5bc6\u78bc\u8868\u771f\u7684\u88ab\u62ff\u8d70\uff0c\u4e5f\u53ea\u80fd\u7528\u4e00\u500b\u6708\u800c\u5df2\u3002\u4f46\u9019\u4ecd\u975e\u5b8c\u7f8e\uff0c\u5982\u679c\u5718\u9ad4\u4e2d\u6709\u9593\u8adc\u5b9a\u671f\u5916\u6d41\u5bc6\u78bc\u8868\uff0c\u5bc6\u78bc\u7cfb\u7d71\u5c31\u74e6\u89e3\u4e86\u3002\u53ef\u80fd\u7684\u5c0d\u7b56\u662f\u6bcf\u5169\u500b\u4eba\u4e4b\u9593\u90fd\u6709\u4e00\u4efd\u7368\u7279\u7684\u5bc6\u78bc\u8868\uff0c\u82e5\u5718\u9ad4\u4e2d\u6709n\u500b\u4eba\uff0c\u4e00\u500b\u9593\u8adc\u5916\u6d41\u7684\u5bc6\u78bc\u8868\u4e0d\u6703\u5f71\u97ff\u5230\u5176\u4ed6(n-1)\u4eba\u3002\u4f46\u5982\u6b64\u4e00\u4f86\uff0c\u5718\u9ad4\u7e3d\u5171\u9700\u8981\u7d04n\u5e73\u65b9\u7d44\u5bc6\u78bc\u8868[\u8a3b1]\uff0c\u975e\u5e38\u4e0d\u65b9\u4fbf\u3002\u518d\u8005\uff0c\u8981\u548c\u4e00\u4f4d\u65b0\u6210\u54e1\u79d8\u5bc6\u901a\u8a0a\uff0c\u5982\u4f55\u5b89\u5168\u50b3\u905e\u5bc6\u78bc\u8868\u4e5f\u662f\u4e00\u500b\u5927\u554f\u984c\u3002\u91dd\u5c0d\u9019\u4e9b\u96e3\u984c\uff0c\u975e\u5c0d\u7a31\u6027\u52a0\u5bc6\u56e0\u61c9\u800c\u751f\u3002<\/p>\n<p>\u975e\u5c0d\u7a31\u6027\u52a0\u5bc6\u7684\u7cbe\u96a8\u5728\u65bc\u52a0\u5bc6\u548c\u89e3\u5bc6\u9700\u8981\u4e0d\u540c\u7684\u9470\u5319\uff0c\u5206\u5225\u70ba\u516c\u958b\u91d1\u9470\u548c\u79c1\u6709\u91d1\u9470\u3002\u4efb\u4f55\u64c1\u6709\u516c\u958b\u91d1\u9470\u7684\u4eba\u90fd\u53ef\u4ee5\u52a0\u5bc6\u4efb\u4f55\u8a0a\u606f\uff0c\u4f46\u552f\u6709\u79c1\u6709\u91d1\u9470\u624d\u80fd\u89e3\u958b\u5bc6\u6587\u3002\u5716\u4e8c\u4e2d\uff0c\u7537\u5b69\u70ba\u4e86\u5b89\u5168\u5730\u5411\u5973\u5b69\u767c\u9001\u8a0a\u606f\uff0c\u4e8b\u5148\u5411\u5973\u5b69\u7d22\u53d6\u4e00\u4efd\u7528\u4f86\u52a0\u5bc6\u7684\u516c\u958b\u91d1\u9470\u3002\u5973\u5b69\u6536\u5230\u52a0\u5bc6\u8a0a\u606f\u5f8c\u7528\u79c1\u6709\u91d1\u9470\u89e3\u5bc6\u3002\u82e5\u6709\u7aca\u807d\u8005\u6514\u622a\u8a0a\u865f\uff0c\u4ed6\u4e5f\u53ea\u80fd\u5f97\u5230\u5df2\u52a0\u5bc6\u7684\u8a0a\u606f\u548c\u52a0\u5bc6\u7528\u7684\u516c\u958b\u91d1\u9470\uff0c\u7121\u6cd5\u89e3\u5bc6\u3002\u503c\u5f97\u4e00\u63d0\u5730\uff0c\u82e5\u7537\u5b69\u8aa4\u522a\u81ea\u5df1\u7684\u8a0a\u606f\u539f\u6587\uff0c\u4ed6\u672c\u4eba\u4e5f\u7121\u6cd5\u900f\u904e\u516c\u9470\u9084\u539f\u8a0a\u606f\uff0c\u5730\u4f4d\u8b8a\u5f97\u548c\u7aca\u807d\u8005\u4e00\u6a23\u3002\u9019\u6a23\u7684\u5bc6\u78bc\u67b6\u69cb\u4e0b\uff0c\u96d6\u7136\u9700\u8981\u82b1\u6642\u9593\u4e8b\u5148\u7d22\u53d6\u516c\u9470\uff0c\u4f46\u514d\u53bb\u4e86\u50b3\u9001\u5bc6\u78bc\u8868\u7684\u98a8\u96aa\uff0c\u5b89\u5168\u5ea6\u5927\u5e45\u63d0\u5347\u3002<\/p>\n<figure id=\"attachment_29110\" aria-describedby=\"caption-attachment-29110\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-29110\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/fig2.png\" alt=\"\" width=\"650\" height=\"358\" \/><figcaption id=\"caption-attachment-29110\" class=\"wp-caption-text\">\u5716\u4e8c\u3001\u975e\u5c0d\u7a31\u52a0\u5bc6\u793a\u610f\u5716\u3002\u300c\u975e\u5c0d\u7a31\u300d\u6307\u7684\u662f\u52a0\u5bc6\u548c\u89e3\u5bc6\u4f7f\u7528\u4e0d\u540c\u7684\u91d1\u9470\uff0c\u56e0\u6b64\u6211\u5011\u53ef\u4ee5\u4efb\u610f\u7684\u767c\u9001\u53ea\u80fd\u7528\u4f86\u52a0\u5bc6\u7684\u516c\u958b\u91d1\u9470\u3002\u5716\u4e2d\u7537\u5b69\u50cf\u5973\u5b69\u767c\u9001\u8a0a\u606f\u524d\uff0c\u5fc5\u9808\u5148\u7d22\u53d6\u4e00\u4efd\u516c\u9470\uff0c\u50b3\u9001\u8a0a\u606f\u6b65\u9a5f\u7a0d\u9577\uff0c\u4f46\u5b89\u5168\u6027\u63d0\u9ad8\u5f88\u591a\u3002\u7aca\u807d\u8005\u518d\u600e\u9ebc\u6514\u622a\u8a0a\u865f\uff0c\u90fd\u7121\u6cd5\u5f97\u5230\u89e3\u5bc6\u7528\u7684\u79c1\u9470\uff0c\u56e0\u70ba\u5b83\u5f9e\u4f86\u4e0d\u5b58\u5728\u65bc\u901a\u8a0a\u4e4b\u4e2d\u3002\u552f\u4e00\u80fd\u7aca\u53d6\u79c1\u9470\u7684\u65b9\u6cd5\u5c31\u662f\u4fb5\u5165\u6301\u6709\u8005\u7684\u96fb\u8166\u6216\u5bb6\u4e2d(\u4f46\u5982\u679c\u4ed6\u771f\u7684\u6210\u529f\u5165\u4fb5\uff0c\u4ed6\u76f4\u63a5\u7aca\u53d6\u8a0a\u606f\u5c31\u597d\uff0c\u4e5f\u4e0d\u9700\u8981\u7aca\u53d6\u91d1\u9470\u4e86)\u3002<\/figcaption><\/figure>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5bc6\u78bc\u80cc\u5f8c\u7684\u6578\u5b78\u548c\u5b89\u5168\u6027<\/strong><\/span><\/p>\n<p>\u7576\u4eca\u6700\u5ee3\u70ba\u4f7f\u7528\u7684\u975e\u5c0d\u7a31\u52a0\u5bc6\u6cd5\u662fRSA\u6f14\u7b97\u6cd5\uff0c\u5176\u540d\u7a31\u7531\u767c\u660e\u8005Ron Rivest\u3001 Adi Shamir \u548c Leonard Adleman\u7684\u59d3\u6c0f\u7d44\u6210\u3002\u6982\u5ff5\u5982\u5716\u4e09\uff0cRSA\u7b97\u6cd5\u57fa\u65bc\u5169\u500b\u8cea\u6578p\u548cq\uff0c\u5b83\u5011\u88fd\u9020\u7b26\u5408\u689d\u4ef6\u7684\u516c\u958b\u91d1\u9470(n,e)\u548c\u79c1\u6709\u91d1\u9470(n,d)\u3002 \u52a0\u5bc6\u548c\u89e3\u5bc6\u662f\u5c0d\u8a0a\u606f\u53d6\u6b21\u65b9\u4e26\u53d6\u9918\u6578(mod) [\u8a3b2]\uff0c\u4f8b\u5982\u8981\u4f7f\u7528\u516c\u9470(n=143,e=7)\u52a0\u5bc6\u9ad4\u91cd\u300c72\u300d\u516c\u65a4\uff0c\u8b80\u8005\u52d5\u7b46 (\u6216\u8a08\u7b97\u6a5f) \u7b97\u7b97\u6703\u5f97\u5230\u5bc6\u6587 \u3002\u89e3\u5bc6\u6642\uff0c\u7528\u79c1\u9470\u5c0d\u5bc6\u6587\u505a\u985e\u4f3c\u7684\u904b\u7b97\u53ef\u4ee5\u5f97\u5230 \u3002<\/p>\n<p>\u5c0d\u65bc\u6c92\u6709\u79c1\u9470\u537b\u60f3\u8981\u7834\u89e3\u8a0a\u606f\u7684\u7aca\u807d\u8005\uff0c\u4ed6\u552f\u4e00\u7684\u8cc7\u8a0a\u53ea\u6709\u516c\u9470(n,e)\u3002\u5176\u4e2d\u4e00\u7a2e\u7834\u89e3\u65b9\u5f0f\u662f\u5c0dn\u505a\u8cea\u56e0\u6578\u5206\u89e3\u627e\u51fap\u548cq\uff0c\u5f9e\u800c\u63a8\u5c0e\u51fa\u79c1\u9470d\u3002\u4f46\u662f\u5c0d\u65bc\u6a19\u6e96\u76842048\u4f4d\u5143RSA\u52a0\u5bc6\uff0c\u5c31\u7b97\u7528\u76ee\u524d\u4e16\u754c\u4e0a\u6700\u5f37\u7684\u8d85\u7d1a\u96fb\u8166(\u592a\u6e56\u4e4b\u5149\uff0c\u4e2d\u570b\u88fd)\uff0c\u82b1\u8cbb\u5730\u7403\u5e74\u9f61\u7684\u6642\u9593(46\u5104\u5e74)\u90fd\u7121\u6cd5\u7834\u89e3\u3002RSA\u6f14\u7b97\u6cd5\u5b89\u5168\u6027\u9ad8\uff0c\u53c8\u53ea\u9700\u5206\u4eab\u516c\u958b\u91d1\u9470\uff0c\u56e0\u6b64\u5f9e\u793e\u4ea4\u8edf\u9ad4\u5230\u8ecd\u4e8b\u901a\u8a0a\u90fd\u6709\u4ed6\u7684\u8e64\u5f71\uff0c\u6211\u5011\u7684\u751f\u6d3b\u53ef\u8aaa\u662f\u4e00\u8209\u4e00\u52d5\u96e2\u4e0d\u958bRSA\u3002<\/p>\n<figure id=\"attachment_29111\" aria-describedby=\"caption-attachment-29111\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-29111\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/fig3.png\" alt=\"\" width=\"650\" height=\"270\" \/><figcaption id=\"caption-attachment-29111\" class=\"wp-caption-text\">\u5716\u4e09\u3001\u5728RSA\u7b97\u6cd5\u80cc\u5f8c\uff0c\u516c\u9470\u548c\u79c1\u9470\u5176\u5be6\u662f\u5169\u7d44\u6578\u5b57\uff0c\u5b83\u5011\u7b26\u5408\u5716\u4e2d\u7684\u6578\u5b78\u689d\u4ef6\u3002\u60f3\u8981\u52a0\u5bc6\u4e00\u500b\u8a0a\u606f(Message) m\uff0c\u53ea\u8981\u5c0dm\u505a\u6b21\u65b9\u548c\u9918\u6578\u7684\u904b\u7b97\u5c31\u597d\uff0c\u800c\u89e3\u5bc6\u4e00\u5247\u5bc6\u6587 (Ciphertext) c\u4e5f\u53ea\u9700\u8981\u505a\u985e\u4f3c\u7684\u904b\u7b97\uff0c\u975e\u5e38\u65b9\u4fbf\u3002\u5b89\u5168\u6027\u65b9\u9762\uff0c\u5176\u5be6\u5728\u516c\u958b\u91d1\u9470\u4e2d\u5df2\u7d93\u542b\u6709\u8db3\u4ee5\u7834\u89e3\u5bc6\u6587\u7684\u8cc7\u8a0a\uff0c\u4f46\u662f\u8981\u627e\u5230\u9019\u4e9b\u6b63\u78ba\u7684\u8cc7\u8a0a\u9700\u8981\u8a08\u7b97\u975e\u5e38\u4e45\u7684\u6642\u9593\uff0c\u4e00\u822c\u7684\u53e4\u5178\u96fb\u8166\u6839\u672c\u7121\u6cd5\u6709\u6548\u505a\u5230\u3002\u5c0d\u65bc\u6df1\u5165\u6578\u5b78\u6709\u8208\u8da3\u7684\u8b80\u8005\uff0c\u53ef\u4ee5\u53c3\u8003\u7dad\u57fa\u767e\u79d1\u4e2dRSA\u52a0\u5bc6\u6f14\u7b97\u6cd5\u689d\u76ee\u3002<\/figcaption><\/figure>\n<p><strong><span style=\"color: #008080;\">\u25cf\u91cf\u5b50\u96fb\u8166\u548c\u9031\u671f\u6027<\/span><\/strong><\/p>\n<p>\u91cf\u5b50\u96fb\u8166\u91dd\u5c0d\u7279\u5b9a\u7684\u554f\u984c\uff0c\u8a08\u7b97\u80fd\u529b\u9060\u5927\u65bc\u53e4\u5178\u96fb\u8166\u3002\u7531\u65bc\u91cf\u5b50\u529b\u5b78\u7528\u300c\u6ce2\u52d5\u6027\u300d\u7684\u6982\u5ff5\u4f86\u63cf\u8ff0\u7269\u8cea\uff0c\u6ce2\u52d5\u7684\u300c\u9031\u671f\u300d\u662f\u91cf\u5b50\u529b\u5b78\u4e2d\u6839\u672c\u7684\u6027\u8cea\u4e4b\u4e00\u3002\u5404\u7a2e\u7269\u7406\u91cf\u4e4b\u9593\u5b58\u5728\u5171\u8edb\u6027\uff0c\u800c\u9019\u4e9b\u5171\u8edb\u7684\u7269\u7406\u91cf\u6709\u50cf\u662f\u6ce2\u52d5\u548c\u9031\u671f\u7684\u76f8\u4e92\u95dc\u4fc2\u3002\u4f8b\u5982\uff1a\u52d5\u91cf\u53ef\u4ee5\u60f3\u6210\u662f\u7a7a\u9593\u4e0a\u7684\u5468\u671f\u3001\u80fd\u91cf\u50cf\u662f\u6642\u9593\u4e0a\u7684\u5468\u671f\uff0c\u6216\u66f4\u62bd\u8c61\u5730\uff0c\u7c92\u5b50\u6578\u50cf\u662f\u76f8\u4f4d\u4e2d\u7684\u5468\u671f\u3002\u56e0\u70ba\u9019\u4e9b\u7279\u6027\uff0c\u91cf\u5b50\u96fb\u8166\u7279\u5225\u64c5\u9577\u5c0b\u627e\u9031\u671f\u3002<\/p>\n<p>\u5728\u4e0a\u8ff0RSA\u7b97\u6cd5\u4e2d\uff0c\u4e00\u500b\u6838\u5fc3\u7684\u5143\u7d20\u662f\u300c\u53d6\u9918\u6578(mod)\u300d\u3002\u9019\u500b\u51fd\u6578\u5177\u6709\u9031\u671f\u6027\uff0c\u662f\u4ed6\u7684\u512a\u9ede\u4e5f\u662f\u4ed6\u7684\u5f31\u9ede\u3002\u56e0\u70ba\u6709\u9031\u671f\u6027\uff0c\u4ed6\u53ef\u4ee5\u6709\u6548\u7387\u5730\u88ab\u7528\u65bc\u52a0\u5bc6\u548c\u89e3\u5bc6\u3002\u4f46\u662f\u82e5\u6709\u4e00\u53f0\u6a5f\u5668\u80fd\u5920\u5feb\u901f\u627e\u51fa\u51fd\u6578\u7684\u5468\u671f\u6027\uff0cRSA\u7b97\u6cd5\u5247\u80fd\u8f15\u9b06\u5730\u88ab\u7834\u89e3[\u8a3b3]\u3002\u91cf\u5b50\u96fb\u8166\u6070\u597d\u5c31\u662f\u9019\u6a23\u7684\u6a5f\u5668\uff0c\u7834\u89e3RSA\u7b97\u6cd5\u662f\u91cf\u5b50\u96fb\u8166\u767c\u5c55\u7684\u76ee\u6a19\u4e4b\u4e00\uff0c\u4e5f\u662f\u5b78\u754c\u3001\u696d\u754c\u548c\u653f\u5e9c\u6295\u5165\u5927\u91cf\u8cc7\u91d1\u9032\u884c\u7814\u767c\u7684\u91cd\u8981\u539f\u56e0\u4e4b\u4e00\u3002<\/p>\n<p>\u82e5\u8981\u7834\u89e3\u4e00\u7d442048\u4f4d\u5143\u7684RSA\u52a0\u5bc6\uff0c\u7406\u8ad6\u4e0a\u5927\u7d04\u9700\u89814000\u500b\u91cf\u5b50\u4f4d\u5143(qubit)\u3002\u76ee\u524dGoogle\u548cIBM\u7684\u91cf\u5b50\u96fb\u8166\u7d04\u670920\u500b\u91cf\u5b50\u4f4d\u5143\u3002\u5118\u7ba1\u6578\u91cf\u4ecd\u9060\u9060\u4e0d\u8db3\uff0c\u4f46\u662f\u76f8\u8f03\u65bc2016\u5e74\u76849\u4f4d\u5143\u548c5\u4f4d\u5143\uff0c\u5169\u5bb6\u516c\u53f8\u90fd\u5c07\u6578\u76ee\u63d0\u5347\u5169\u500d\u4e86\u3002\u672a\u4f86\u80fd\u5426\u7528\u91cf\u5b50\u96fb\u8166\u5c0d\u73fe\u6709\u5bc6\u78bc\u7cfb\u7d71\u9769\u547d\uff0c\u8b93\u6211\u5011\u7e7c\u7e8c\u770b\u4e0b\u53bb\u5427\u3002<\/p>\n<p><strong>\u8a3b\u91cb\uff1a<\/strong><\/p>\n<p>[\u8a3b1] \u5718\u9ad4\u4e2d\u6709n\u4eba\uff0c\u4efb\u5169\u500b\u4eba\u914d\u4e00\u500b\u7368\u7279\u7684\u5bc6\u78bc\u8868\uff0c\u7e3d\u5171\u9700\u8981n(n-1)\/2\u500b\uff0c\u8907\u96dc\u5ea6\u70ban\u5e73\u65b9\u3002<br \/>\n[\u8a3b2] mod\u662f\u53d6\u9918\u6578\u7684\u610f\u601d\uff0c\u4ed6\u7684\u683c\u5f0f\u70ba\u300c\u88ab\u9664\u6578 = \u9918\u6578 mod \u9664\u6578\u300d\u3002\u4f8b\u598217\u9664\u4ee55\u7b49\u65bc3\u99182\uff0c\u53ef\u4ee5\u5beb\u4f5c\u300c17=2 mod 5\u300d\u3002<br \/>\n[\u8a3b3] \u6700\u5ee3\u70ba\u4eba\u77e5\u7684\u7834\u89e3RSA\u7684\u6f14\u7b97\u6cd5\u662f\u300c\u79c0\u723e\u6f14\u7b97\u6cd5(Shor\u2019s Algorithm)\u300d\uff0c\u5c0d\u7d30\u7bc0\u6709\u8208\u8da3\u7684\u8b80\u8005\u53ef\u4ee5\u53c3\u898b\u5176\u7dad\u57fa\u767e\u79d1\u689d\u76ee\u3002<\/p>\n<p><strong>\u53c3\u8003\u8cc7\u6599\uff1a<\/strong>Eleni Diamanti et al., Best of both worlds, Nature Physics 13, 3\u20134 (2017)<\/p>\n<p>&nbsp;<\/p>\n<p>--<br \/>\n<span style=\"color: #333399;\"><strong>\u4f5c\u8005\uff1a\u9673\u5955\u5ef7\uff0c\u53f0\u5927\u7269\u7406\u7cfb\u5b78\u58eb\uff0c\u53f2\u4e39\u4f5b\u5927\u5b78\u61c9\u7528\u7269\u7406\u7cfb\u535a\u58eb\u73ed\u5c31\u8b80\u4e2d\u3002<wbr \/>\u5c0d\u5404\u9818\u57df\u7684\u79d1\u5b78\u90fd\u975e\u5e38\u597d\u5947\uff0c\u6b61\u8fce\u4e92\u76f8\u4ea4\u6d41\u3002<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0\u901a\u8a0a\u548c\u60c5\u5831\u4e00\u76f4\u662f\u5546\u696d\u548c\u570b\u9632\u6700\u91cd\u8981\u7684\u4e00\u74b0\uff0c\u800c\u52a0\u5bc6\u662f\u5176\u4e2d\u7684\u6838\u5fc3\u3002\u4e8c\u5341\u4e16\u7d00\u672b\u4ee5\u4f86\uff0c RSA\u52a0\u5bc6\u6cd5\u6191\u85c9\u8457\u53e4\u5178\u96fb\u8166\u96e3\u4ee5\u4f01\u53ca\u7684\u8907\u96dc\u5ea6\u8b8a\u5f97\u65e5\u8da8\u6d41\u884c\uff0c\u5b89\u5168\u6027\u9ad8\u3002\u4f46\u5c0d\u65bc\u7279\u5b9a\u7684\u8a08\u7b97\u5de5\u4f5c\uff0c\u91cf\u5b50\u96fb\u8166\u7684\u8a08\u7b97\u529b\u9060\u9060\u8d85\u8d8a\u53e4\u5178\u96fb\u8166\uff0c\u9019\u662f\u5426\u6703\u5c0d\u4f60\u6211\u65e5\u5e38\u90fd\u5728\u4f7f\u7528\u7684RSA\u52a0\u5bc6\u9020\u6210\u5a01\u8105\u5462\uff1f\u56de\u7b54\u554f\u984c\u524d\uff0c\u5148\u8b93\u6211\u5011\u770b\u770bRSA\u548c\u91cf\u5b50\u96fb\u8166\u80cc\u5f8c\u5206\u5225\u6709\u4e9b\u4ec0\u9ebc\u3002<\/p>\n","protected":false},"author":20,"featured_media":29108,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1023,3293,148,2977],"tags":[3510,3491,134,3511,2972],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/08\/front.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/29107"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=29107"}],"version-history":[{"count":4,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/29107\/revisions"}],"predecessor-version":[{"id":31823,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/29107\/revisions\/31823"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/29108"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=29107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=29107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=29107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}