{"id":326,"date":"2018-03-06T16:29:16","date_gmt":"2018-03-06T08:29:16","guid":{"rendered":"http:\/\/www.91tfboys.com\/?p=326"},"modified":"2018-03-06T16:29:16","modified_gmt":"2018-03-06T08:29:16","slug":"%e6%95%b0%e5%ad%a6%e9%97%ae%e9%a2%98%e5%9c%a8%e7%8e%b0%e4%bb%a3%e5%af%86%e7%a0%81%e5%ad%a6%e5%ad%a6%e4%b9%a0%e4%b8%ad%e7%9a%84%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"https:\/\/www.91tfboys.com\/?p=326","title":{"rendered":"\u6570\u5b66\u95ee\u9898\u5728\u73b0\u4ee3\u5bc6\u7801\u5b66\u5b66\u4e60\u4e2d\u7684\u5e94\u7528"},"content":{"rendered":"<p>\u6570\u5b66\u4f5c\u4e3a\u4e00\u95e8\u81ea\u7136\u79d1\u5b66\uff0c\u5728\u4eba\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u548c\u5b66\u4e60\u4e2d\u6709\u7740\u8bb8\u591a\u4e0d\u53ef\u6216\u7f3a\u7684\u5e94\u7528\uff0c\u5728\u4eba\u4eec\u751f\u6d3b\u7684\u5404\u4e2a\u65b9\u9762\u5747\u80fd\u770b\u89c1\u6570\u5b66\u7684\u5e94\u7528\u3002\u4f5c\u4e3a\u4fe1\u606f\u5b89\u5168\u4e13\u4e1a\u7684\u5b66\u751f\uff0c\u8fd9\u91cc\uff0c\u6211\u4eec\u4e3b\u8981\u63a2\u8ba8\u6570\u5b66\u5728\u73b0\u4ee3\u5bc6\u7801\u5b66\u4e2d\u7684\u5e94\u7528\u4e0e\u4f5c\u7528\u3002<!--more--><\/p>\n<p>\u4e00\u822c\u8ba4\u4e3a\uff0c1949\u5e74\u9999\u519c\u53d1\u8868\u7684\u300a\u4fdd\u5bc6\u7cfb\u7edf\u7684\u901a\u4fe1\u7406\u8bba\u300b\uff08Communication Theory of Secrecy System\uff09\u4e00\u6587\u5f00\u542f\u4e86\u73b0\u4ee3\u5bc6\u7801\u5b66\u7684\u5148\u6cb3\u3002\u6700\u521d\uff0c\u5bc6\u7801\u6280\u672f\u88ab\u5176\u7231\u597d\u8005\u8fdb\u884c\u4e86\u6df1\u5165\u5e7f\u6cdb\u7684\u7814\u7a76\uff0c\u6b64\u65f6\u7684\u5bc6\u7801\u5b66\u4e3b\u8981\u5e94\u7528\u4e8e\u5916\u4ea4\u3001\u519b\u4e8b\u548c\u653f\u5e9c\u7b49\u9886\u57df\u3002\u5bc6\u7801\u5b66\u7684\u5b66\u672f\u7814\u7a76\u59cb\u4e8e20\u4e16\u7eaa70\u5e74\u4ee3\u4e2d\u671f\uff0c1976\u5e74\u4ee5\u524d\u7684\u6240\u6709\u5bc6\u7801\u7cfb\u7edf\u5747\u5c5e\u4e8e\u5bf9\u79f0\u5bc6\u7801\u5b66\u8303\u7574\u30021976\u5e74\uff0cDiffie\u548cHellman\u300a\u5bc6\u7801\u5b66\u7684\u65b0\u65b9\u5411\u300b\u4e00\u6587\u7684\u53d1\u8868\uff0c\u4f7f\u5bc6\u7801\u5b66\u7814\u7a76\u6b65\u5165\u4e00\u4e2a\u65b0\u7684\u65f6\u4ee3\u3002\u968f\u540e\uff0c\u968f\u7740\u5bc6\u7801\u7b97\u6cd5\u4e0e\u6280\u672f\u7684\u8fdb\u6b65\u4e0e\u6539\u8fdb\uff0c\u5bc6\u7801\u5b66\u5f00\u59cb\u8d70\u8fdb\u4eba\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u4e2d\u3002\u73b0\u5728\uff0c\u51e0\u4e4e\u6bcf\u4e2a\u4eba\u6bcf\u5929\u90fd\u5728\u4f7f\u7528\u4e0e\u5bc6\u7801\u6709\u5173\u7684\u5404\u79cd\u4ea7\u54c1\uff0c\u5982\u8fde\u63a5\u5230\u65e0\u7ebf\u7f51\u7edc\u3001\u7528\u94f6\u884c\u5361\u5728\u5b9e\u4f53\u5e97\u6216\u7f51\u4e0a\u8d2d\u7269\u3001\u6536\u53d1\u7535\u5b50\u90ae\u4ef6\u3001\u62e8\u6253\u8bed\u97f3\u7535\u8bdd\u7b49\u3002\u6bcb\u5eb8\u7f6e\u7591\uff0c\u5bc6\u7801\u4ea7\u54c1\u5728\u4fdd\u969c\u4fe1\u606f\u5b89\u5168\u9886\u57df\u8d77\u7740\u4e0d\u53ef\u66ff\u4ee3\u7684\u4f5c\u7528\uff0c\u56e0\u6b64\u5bc6\u7801\u4ea7\u54c1\u7684\u5b89\u5168\u6027\u66f4\u4e3a\u91cd\u8981\u3002\u51b3\u5b9a\u4e00\u4e2a\u5bc6\u7801\u4ea7\u54c1\u5b89\u5168\u4e0e\u5426\u7684\u6761\u4ef6\u662f\u5176\u4f7f\u7528\u7684\u5bc6\u7801\u7b97\u6cd5\u4e0e\u5bc6\u94a5\u662f\u5426\u8db3\u591f\u5b89\u5168\uff0c\u800c\u51b3\u5b9a\u5bc6\u7801\u7b97\u6cd5\u4e0e\u5bc6\u94a5\u662f\u5426\u5b89\u5168\u7684\u56e0\u7d20\u662f\u5176\u57fa\u4e8e\u7684\u6570\u5b66\u539f\u7406\u662f\u5426\u5b89\u5168\u3002\u5f53\u4e00\u4e2a\u5bc6\u7801\u7b97\u6cd5\u662f\u5efa\u7acb\u5728\u67d0\u4e00\u4e2a\u6570\u5b66\u95ee\u9898\u7684\u96be\u89e3\u6027\u4e4b\u4e0a\uff0c\u4f7f\u7528\u5df2\u77e5\u7684\u7b97\u6cd5\u4e0e\u73b0\u6709\u7684\u8ba1\u7b97\u5de5\u5177\u4e0d\u53ef\u80fd\u5b8c\u6210\u653b\u51fb\u6240\u8981\u6c42\u7684\u8ba1\u7b97\u91cf\u65f6\uff0c\u6211\u4eec\u8ba4\u4e3a\u6b64\u7b97\u6cd5\u662f\u8ba1\u7b97\u4e0a\u5b89\u5168\u7684\u3002\u5728\u5b9e\u9645\u8fd0\u7528\u4e2d\uff0c\u4e00\u822c\u8981\u6c42\u7834\u89e3\u5bc6\u7801\u7cfb\u7edf\u7684\u6210\u672c\u4e0d\u80fd\u8d85\u8fc7\u88ab\u52a0\u5bc6\u4fe1\u606f\u672c\u8eab\u7684\u4ef7\u503c\uff0c\u4e14\u7834\u8bd1\u5bc6\u7801\u7cfb\u7edf\u7684\u65f6\u95f4\u4e0d\u80fd\u8d85\u8fc7\u88ab\u52a0\u5bc6\u4fe1\u606f\u7684\u6709\u6548\u751f\u547d\u5468\u671f\uff0c\u6211\u4eec\u79f0\u5728\u6b64\u7ea6\u675f\u6761\u4ef6\u4e0b\u65e0\u6cd5\u7834\u8bd1\u7684\u5bc6\u7801\u4f53\u5236\u6ee1\u8db3\u5b9e\u9645\u5b89\u5168\u6027\u3002\u5bc6\u7801\u5b66\u7684\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u5373\u4e3a\u4ee5DES\u3001AES\u7b49\u4e3a\u4ee3\u8868\u7684\u5bf9\u79f0\u5bc6\u7801\u7b97\u6cd5\u3002<\/p>\n<p>\u5bf9\u79f0\u5bc6\u7801\u7b97\u6cd5\u662f\u52a0\u5bc6\u4e0e\u89e3\u5bc6\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u76f8\u540c\u5bc6\u94a5\u7684\u5bc6\u7801\u7b97\u6cd5\uff0c\u89e3\u5bc6\u7b97\u6cd5\u4e00\u822c\u662f\u52a0\u5bc6\u7b97\u6cd5\u7684\u9006\u8fd0\u7b97\u3002\u4ee5\u6570\u636e\u52a0\u5bc6\u6807\u51c6\uff08Data Encryption Standard, DES\uff09\u4e3a\u4f8b\uff0c\u5176\u52a0\u5bc6\u65f6\u670916\u8f6e\u7b97\u672f\u903b\u8f91\u548c\u975e\u7ebf\u6027\u8fd0\u7b97\uff0c\u89e3\u5bc6\u65f6\u4e5f\u670916\u8f6e\u4e0e\u4e4b\u5bf9\u5e94\u7684\u9006\u8fd0\u7b97\u3002\u5728\u52a0\u5bc6\u9636\u6bb5\uff0c\u4e3a\u5b9e\u73b0\u6df7\u6dc6\uff0c\u4f7f\u7528\u4e86\u521d\u59cb\u7f6e\u6362IP\u4ee3\u6362\uff0c\u5219\u89e3\u5bc6\u9636\u6bb5\u4f7f\u7528\u5176\u9006\u8fd0\u7b97IP<sup>-1<\/sup>\u8fdb\u884c\u4ee3\u6362\u3002IP\u5e8f\u5217\u4e0eIP<sup>-1<\/sup>\u5982\u56fe1\u6240\u793a\uff0c\u4ece\u56fe\u4e2d\u53ef\u4ee5\u770b\u51faIP\u8868\u4e0eIP<sup>-1<\/sup>\u8868\u662f\u6709\u5173\u8054\u7684\u3002\u4e3a\u4e86\u4fdd\u8bc1\u5b89\u5168\uff0c\u9664\u4e86\u4e00\u822c\u7684\u7ebf\u6027\u8fd0\u7b97\u4e0e\u786e\u5b9a\u7684\u66ff\u6362\u5916\uff0cDES\u7b97\u6cd5\u8fd8\u5f15\u5165\u4e86\u975e\u7ebf\u6027\u7684S\u76d2\u3002DES\u5305\u542b8\u4e2aS\u76d2\uff0c\u5206\u522b\u5bf9\u5e94\u77408\u4e2a\u975e\u7ebf\u6027\u7684\u4ee3\u6362\u8868\uff0c\u5176\u529f\u80fd\u5c31\u662f\u8fdb\u884c\u975e\u7ebf\u6027\u4ee3\u6362\uff0c\u4f7f\u5f97<em>S<\/em>(<em>a<\/em>)\u2a01<em>S<\/em>(<em>b<\/em>) \u2260\u00a0<em>S<\/em>(<em>a<\/em>\u2a01<em>b<\/em>)\u3002\u5176\u4e2d\u7b2c\u4e00\u4e2aS\u76d2\u5982\u56fe2\u6240\u793a\u3002\u4f46\u7531\u4e8eDES\u7684\u5bc6\u94a5\u957f\u5ea6\u8fc7\u77ed\uff0856\u6bd4\u7279\uff09\uff0c\u968f\u7740\u6280\u672f\u6c34\u5e73\u7684\u63d0\u5347\uff0c\u7834\u89e3DES\u53d8\u5f97\u8d8a\u6765\u8d8a\u5bb9\u6613\u3002\u523090\u5e74\u4ee3\u540e\u671f\uff0c\u77ed\u77ed\u51e0\u4e2a\u5c0f\u65f6\u5185\u5c31\u53ef\u4ee5\u5b8c\u6210DES\u7684\u7834\u8bd1\uff0c\u5355\u91cdDES\u5df2\u7ecf\u4e0d\u80fd\u6ee1\u8db3\u5b9e\u9645\u7684\u9700\u8981\u4e86\u3002\u6b64\u65f6\uff0c\u66f4\u5b89\u5168\u7684\u9ad8\u7ea7\u52a0\u5bc6\u7b97\u6cd5\uff08Advanced Encryption Standard, AES\uff09\u5df2\u88ab\u9009\u51fa\uff0c\u5e76\u4f5c\u4e3a\u65b0\u7684\u5546\u7528\u6570\u636e\u4fdd\u5bc6\u7684\u79d8\u5bc6\u7b97\u6cd5\uff0c\u4e8e2002\u5e74\u6b63\u5f0f\u751f\u6548\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-327 aligncenter\" src=\"http:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_IP.png\" alt=\"\" width=\"493\" height=\"184\" srcset=\"https:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_IP.png 493w, https:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_IP-300x112.png 300w\" sizes=\"auto, (max-width: 493px) 100vw, 493px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe1\u00a0 \u521d\u59cb\u53d8\u6362IP\u548c\u9006\u521d\u59cb\u53d8\u6362IP<sup>-1<\/sup><\/p>\n<p style=\"text-align: center;\">\uff08IP\u8868\u4e2d\u7684\u7b2c1\u4f4d\u662f58\uff0cIP<sup>-1<\/sup>\u8868\u4e2d\u7684\u7b2c58\u4f4d\u662f1\uff09<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-328\" src=\"http:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_S1.png\" alt=\"\" width=\"361\" height=\"107\" srcset=\"https:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_S1.png 361w, https:\/\/www.91tfboys.com\/wp-content\/uploads\/2018\/03\/DES_S1-300x89.png 300w\" sizes=\"auto, (max-width: 361px) 100vw, 361px\" \/><\/p>\n<p style=\"text-align: center;\">\u56fe2\u00a0 S\u76d2S<sub>1<\/sub><\/p>\n<p>\u7531\u4e8e\u5bf9\u79f0\u5bc6\u7801\u4f53\u5236\u4e2d\u52a0\u89e3\u5bc6\u9700\u8981\u7684\u5bc6\u94a5\u662f\u76f8\u540c\u7684\uff0c\u6240\u4ee5\u5bc6\u94a5\u7684\u4f20\u8f93\u9700\u8981\u4e25\u683c\u7684\u4fdd\u5bc6\uff0c\u8981\u5728\u5b89\u5168\u7684\u4fe1\u9053\u4e2d\u8fdb\u884c\u901a\u4fe1\uff0c\u800c\u5b89\u5168\u4fe1\u9053\u662f\u4e0d\u6613\u5b9e\u73b0\u7684\u3002\u540c\u65f6\uff0c\u5bf9\u79f0\u5bc6\u7801\u4f53\u5236\u8fd8\u5b58\u5728\u5bc6\u94a5\u7ba1\u7406\u95ee\u9898\u4e0e\u6570\u5b57\u7b7e\u540d\u95ee\u9898\u7b49\uff0c\u968f\u7740\u8ba1\u7b97\u673a\u548c\u7f51\u7edc\u7684\u98de\u901f\u53d1\u5c55\uff0c\u5176\u5c40\u9650\u6027\u9010\u6e10\u663e\u73b0\u51fa\u6765\u30021976\u5e74\uff0cDiffie\u548cHellman\u5728\u8bba\u6587\u300a\u5bc6\u7801\u5b66\u7684\u65b0\u65b9\u5411\u300b\uff08New Direction in Cryptography\uff09\u4e2d\u9996\u6b21\u63d0\u51fa\u4e86\u516c\u94a5\u5bc6\u7801\u601d\u60f3\uff1a\u7528\u6237A\u6709\u4e00\u5bf9\u5bc6\u94a5\uff1a\u52a0\u5bc6\u5bc6\u94a5<em>P<sub>k<\/sub><\/em>\u548c\u89e3\u5bc6\u5bc6\u94a5<em>S<sub>k<\/sub><\/em>\uff0c\u516c\u5f00<em>P<sub>k<\/sub><\/em>\uff0c\u4fdd\u5bc6<em>S<sub>k<\/sub><\/em>\uff0c\u82e5B\u8981\u7ed9A\u53d1\u9001\u52a0\u5bc6\u4fe1\u606f\uff0c\u4ed6\u9700\u8981\u5728\u516c\u5f00\u7684\u76ee\u5f55\u4e2d\u67e5\u51faA\u7684\u516c\u94a5<em>P<sub>k<\/sub><\/em>\uff0c\u7528\u5b83\u52a0\u5bc6\u4fe1\u606f\uff1bA\u6536\u5230\u5bc6\u6587\u540e\uff0c\u7528\u81ea\u5df1\u7684\u79c1\u94a5<em>S<sub>k<\/sub><\/em>\u89e3\u5bc6\u5bc6\u6587\uff0c\u7531\u4e8e\u522b\u4eba\u4e0d\u77e5\u9053<em>S<sub>k<\/sub><\/em>\uff0c\u5373\u4f7f\u622a\u83b7\u4e86\u5bc6\u6587\uff0c\u4e5f\u65e0\u6cd5\u6062\u590d\u660e\u6587\u30021978\u5e74\uff0cRSA\u7b97\u6cd5\u63d0\u51fa\uff0c\u5e76\u5f97\u4ee5\u5e7f\u6cdb\u7684\u5e94\u7528\u3002RSA\u7684\u57fa\u7840\u662f\u6570\u8bba\u7684\u6b27\u62c9\u5b9a\u7406\uff0c\u5b83\u7684\u5b89\u5168\u6027\u4f9d\u8d56\u4e8e\u5927\u6574\u6570\u56e0\u5b50\u5206\u89e3\u7684\u56f0\u96be\u6027\u3002<\/p>\n<p>RSA\u5bc6\u94a5\u751f\u6210\u7b97\u6cd5\u5206\u4e3a\u4ee5\u4e0b\u51e0\u4e2a\u6b65\u9aa4\uff1a<\/p>\n<ul>\n<li>\u9009\u53d6\u4e24\u4e2a\u5b89\u5168\u5927\u7d20\u6570<em>p<\/em>\u548c<em>q<\/em>\uff08\u201c\u5927\u201d\u6307\u5176\u957f\u5ea6\u8981\u8db3\u591f\u957f\uff0c\u76ee\u524d\u63a8\u8350\u957f\u5ea6\u4e3a\u81f3\u5c111024\u6bd4\u7279\uff09\uff1b<\/li>\n<li>\u8ba1\u7b97\u4e58\u79ef<em>n<\/em>=<em>p<\/em>\u00d7<em>q<\/em>, <em>\u03c6<\/em>(<em>n<\/em>)=(<em>p<\/em>-1)(<em>q<\/em>-1)\uff0c\u5176\u4e2d<em>\u03c6<\/em>(<em>n<\/em>)\u4e3a<em>n<\/em>\u7684\u6b27\u62c9\u51fd\u6570\uff1b<\/li>\n<li>\u968f\u673a\u9009\u53d6\u6574\u6570<em>e<\/em> (1&lt;<em>e<\/em>&lt;<em>\u03c6<\/em>(<em>n<\/em>))\u4f5c\u4e3a\u516c\u94a5\uff0c\u8981\u6c42\u6ee1\u8db3gcd(<em>e<\/em>,\u00a0<em>\u03c6<\/em>(<em>n<\/em>))=1\uff0c\u5373<em>e<\/em>\u4e0e<em>\u03c6<\/em>(<em>n<\/em>)\u4e92\u7d20\uff1b<\/li>\n<li>\u7528\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\u8ba1\u7b97\u79c1\u94a5<em>d<\/em>\uff0c\u4ee5\u6ee1\u8db3<em>d<\/em>\u00d7<em>e<\/em>\u22611 mod <em>\u03c6<\/em>(<em>n<\/em>)\uff0c\u5373<em>e<\/em>\u548c<em>n<\/em>\u662f\u516c\u94a5\uff0c<em>d<\/em>\u662f\u79c1\u94a5\u3002<\/li>\n<\/ul>\n<p>\u7b97\u6cd5\u4e2d<em>p<\/em>\u548c<em>q<\/em>\u4e0d\u80fd\u6cc4\u9732\u3002\u8bbe\u660e\u6587\u4e3a<em>m<\/em>\uff0c\u5219\u52a0\u5bc6\u65f6\uff0c\u5bc6\u6587<em>c\u00a0<\/em>\u2261 <em>m<sup>e<\/sup><\/em> mod <em>n<\/em>\uff0c\u89e3\u5bc6\u5f97\u5230\u660e\u6587<em>m\u00a0<\/em>\u2261 <em>c<sup>d<\/sup><\/em> mod <em>n<\/em>\u3002<\/p>\n<p>\u53ef\u4ee5\u770b\u51fa\uff0c\u6570\u5b66\u77e5\u8bc6\u5728\u73b0\u4ee3\u5bc6\u7801\u5b66\u4e2d\u7684\u5e94\u7528\u975e\u5e38\u5e7f\u6cdb\u3002\u5728\u5bf9\u79f0\u5bc6\u94a5\u4f53\u5236\u4e2d\uff0c\u4f1a\u7528\u5230\u7ebf\u6027\u4ee3\u6570\u7684\u77e5\u8bc6\u8fdb\u884c\u6c42\u89e3\uff0c\u5728\u975e\u5bf9\u79f0\uff08\u516c\u94a5\uff09\u5bc6\u7801\u4f53\u5236\u4e2d\uff0c\u6570\u8bba\u7b49\u77e5\u8bc6\u968f\u5904\u53ef\u89c1\u3002\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\uff08Euclidean Algorithm, EA\uff09\u4f7f\u5f97\u6c42\u4e24\u4e2a\u6570\uff08<em>p<\/em>\u548c<em>q<\/em>\uff09\u7684\u6700\u5927\u516c\u7ea6\u6570gcd(<em>p<\/em>, <em>q<\/em>)\u53d8\u5f97\u7b80\u4fbf\uff0c\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\uff08Extended Euclidean Algorithm, EEA\uff09\u5728\u6c42\u5176\u9006\u5143\u65b9\u9762\u4f5c\u7528\u5f88\u5927\u3002\u6b64\u5916\uff0c\u6b27\u62c9\u5b9a\u7406\u3001\u8d39\u9a6c\u5c0f\u5b9a\u7406\u7b49\u90fd\u5728\u516c\u94a5\u5bc6\u7801\u4f53\u5236\u4e2d\u90fd\u8d77\u5230\u4e86\u91cd\u8981\u4f5c\u7528\u3002<\/p>\n<p>\u9664\u4e86RSA\u7b97\u6cd5\u5916\uff0c\u5728\u73b0\u4ee3\u5bc6\u7801\u5b66\u4e2d\u5e38\u7528\u7684\u7b97\u6cd5\u8fd8\u6709\u57fa\u4e8e\u6709\u9650\u57df\u4e0a\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u7684\u516c\u94a5\u52a0\u5bc6\u4f53\u5236ElGamal\u52a0\u5bc6\u4f53\u5236\u3001\u57fa\u4e8e\u692d\u5706\u66f2\u7ebf\u7684\u79bb\u6563\u5bc6\u7801\u4f53\u5236ECC\u7b49\u3002ElGamal\u52a0\u5bc6\u4f53\u5236\u5982\u88681\u3002<\/p>\n<p style=\"text-align: center;\">\u88681\u00a0 ElGamal\u516c\u94a5\u52a0\u5bc6\u7b97\u6cd5<\/p>\n<table style=\"height: 288px;\" width=\"526\">\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"119\">\u5bc6\u94a5\u751f\u6210\u7b97\u6cd5<\/td>\n<td width=\"89\">\u516c\u94a5<\/td>\n<td width=\"217\"><em>p<\/em>\uff1a\u5927\u7d20\u6570\uff1b<em>g<\/em>\uff1a\u751f\u6210\u5143 <em>g<\/em>\u2208<strong><em>Z<\/em><\/strong><sub>p<\/sub><sup>*<\/sup><\/p>\n<p><em>y<\/em>\uff1a<em>y\u00a0<\/em>\u2261\u00a0<em>g<sup>x<\/sup><\/em> mod p<\/td>\n<\/tr>\n<tr>\n<td width=\"89\">\u79c1\u94a5<\/td>\n<td width=\"217\"><em>x<\/em>\uff1a1&lt;<em>x<\/em>&lt;<em>p<\/em>-1<\/td>\n<\/tr>\n<tr>\n<td width=\"119\">\u52a0\u5bc6\u7b97\u6cd5<\/td>\n<td colspan=\"2\" width=\"307\"><em>r<sub>i<\/sub><\/em>: \u968f\u673a\u9009\u62e9\uff0c1&lt;<em>r<sub>i<\/sub><\/em>&lt;<em>p<\/em>-1<\/p>\n<p>\u5bc6\u6587\uff1a<em>c<\/em><sub>i\u00a0<\/sub>\u2261\u00a0<em>g<\/em>^(<em>r<\/em><sub>i<\/sub> ) mod <em>p<\/em>\uff0c<em>c<\/em><sub>i<\/sub><sup>&#8216;\u00a0<\/sup>\u2261\u00a0<em>m<\/em><sub>i<\/sub> <em>y<\/em>^(<em>r<\/em><sub>i<\/sub> ) mod <em>p<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"119\">\u89e3\u5bc6\u7b97\u6cd5<\/td>\n<td colspan=\"2\" width=\"307\">\u660e\u6587\uff1a<em>m<\/em><sub>i<\/sub> \u2261 (<em>c<\/em><sub>i<\/sub><sup>&#8216;<\/sup>)\/(<em>c<\/em><sub>i<\/sub><em><sup>x<\/sup><\/em> ) mod <em>p<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>ElGamal\u7b97\u6cd5\u7684\u5b89\u5168\u6027\u57fa\u4e8e\u79bb\u6563\u5bf9\u6570\u6c42\u89e3\u7684\u56f0\u96be\u6027\u3002\u76ee\u524d\u5bf9\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u7684\u7814\u7a76\u53d6\u5f97\u4e86\u4e00\u4e9b\u6210\u679c\uff0c\u5df2\u7ecf\u6709\u4e86\u4e00\u4e9b\u653b\u51fb\u7b97\u79bb\u6563\u5bf9\u6570\u7684\u7b97\u6cd5\uff0c\u5982\u5c0f\u6b65\u5927\u6b65\u6cd5\u3001\u6307\u6570\u79ef\u5206\u6cd5\u7b49\u3002\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u7b97\u6cd5\u5982\u88682\u6240\u793a\u3002ECC\u7684\u5b89\u5168\u6027\u57fa\u4e8e\u692d\u5706\u66f2\u7ebf\u4e0a\u7684\u79bb\u6563\u5bf9\u6570\u95ee\u9898\u7684\u96be\u89e3\u6027\uff0c\u5b83\u4f18\u4e8e\u57fa\u4e8e\u6709\u9650\u4e58\u6cd5\u7fa4\u4e0a\u7684\u79bb\u6563\u5bf9\u6570\u5bc6\u7801\u4f53\u5236\u3002<\/p>\n<p style=\"text-align: center;\">\u88682\u00a0 ECC\u7b97\u6cd5<\/p>\n<table width=\"0\">\n<tbody>\n<tr>\n<td rowspan=\"2\" width=\"132\">\u5bc6\u94a5\u751f\u6210\u7b97\u6cd5<\/td>\n<td width=\"104\">\u516c\u94a5<\/td>\n<td width=\"340\">E\uff1a\u692d\u5706\u66f2\u7ebf<em>y<\/em><sup>2\u00a0<\/sup>=\u00a0<em>x<\/em><sup>3<\/sup>+<em>ax<\/em>+<em>b<\/em> mod <em>p<\/em><\/p>\n<p><em>n<\/em>: \u975e\u5e38\u5927\u7684\u7d20\u6570<\/p>\n<p><em>G<\/em>\uff1a\u692d\u5706\u66f2\u7ebf<em>E<sub>p<\/sub><\/em>(<em>a<\/em>, <em>b<\/em>)\u7684\u751f\u6210\u5143\uff0c<em>nG<\/em>=<em>O<\/em><\/p>\n<p><em>P<sub>B<\/sub><\/em>\uff1a<em>P<sub>B<\/sub><\/em>=<em>n<sub>B<\/sub>G<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"104\">\u79c1\u94a5<\/td>\n<td width=\"340\"><em>n<sub>B<\/sub><\/em>\uff1a<em>P<sub>B<\/sub><\/em>=<em>n<sub>B<\/sub>G<\/em><\/td>\n<\/tr>\n<tr>\n<td width=\"132\">\u52a0\u5bc6\u7b97\u6cd5<\/td>\n<td colspan=\"2\" width=\"444\"><em>k<\/em>\u3001<em>P<sub>t<\/sub><\/em>(<em>x<sub>t<\/sub><\/em>, <em>y<sub>t<\/sub><\/em>)\uff1a\u968f\u673a\u9009\u62e9<\/p>\n<p><em>m<\/em>\uff1a\u660e\u6587\u4fe1\u606f<\/p>\n<p><em>P<\/em><sub>1<\/sub>=(<em>x<\/em><sub>1<\/sub>, <em>y<\/em><sub>1<\/sub>)=<em>kG<\/em>, <em>P<\/em><sub>2<\/sub>=(<em>x<\/em><sub>2<\/sub>, <em>y<\/em><sub>2<\/sub>)=<em>kP<sub>B<\/sub><\/em><\/p>\n<p><em>C<\/em>=<em>mx<sub>t<\/sub><\/em>+<em>y<sub>t<\/sub><\/em><\/p>\n<p>\u52a0\u5bc6\u6570\u636e\uff1a<em>C<sub>m<\/sub><\/em>=(<em>kG<\/em>, <em>P<sub>t<\/sub><\/em>+<em>kP<sub>B<\/sub><\/em> ,<em>C<\/em> )<\/td>\n<\/tr>\n<tr>\n<td width=\"132\">\u89e3\u5bc6\u7b97\u6cd5<\/td>\n<td colspan=\"2\" width=\"444\"><em>P<sub>t<\/sub><\/em>+<em>kP<sub>B<\/sub><\/em>&#8211;<em>n<sub>B<\/sub><\/em> (<em>kG<\/em>) = <em>P<\/em><sub>t<\/sub> + <em>k<\/em>(<em>n<sub>B<\/sub>G<\/em>) &#8211;<em> n<sub>B<\/sub><\/em> (<em>kG<\/em>)=<em>P<sub>t<\/sub><\/em> = (<em>x<sub>t<\/sub><\/em>, <em>y<sub>t<\/sub><\/em>)<\/p>\n<p>\u660e\u6587\uff1a<em>m<\/em>=(<em>C<\/em>&#8211;<em>y<sub>t<\/sub><\/em>)\/<em>x<sub>t<\/sub><\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u603b\u4f53\u6765\u8bf4\uff0c\u5927\u5b66\u6570\u5b66\u5728\u73b0\u4ee3\u5bc6\u7801\u5b66\u7684\u5b66\u4e60\u4e2d\u8d77\u5230\u4e86\u5f88\u91cd\u8981\u7684\u4f5c\u7528\u3002\u7ebf\u6027\u4ee3\u6570\u77e5\u8bc6\u5728\u7ebf\u6027\u79fb\u4f4d\u53cd\u9988\u5bc4\u5b58\u5668\uff08Linear Feedback Shift Registers, LFSR\uff09\u7684\u6c42\u89e3\u3001AES\u7684\u5b57\u8282\u4ee3\u6362\u8fc7\u7a0b\u7b49\u8d77\u7740\u5173\u952e\u4f5c\u7528\uff0c\u79bb\u6563\u6570\u5b66\u3001\u6570\u8bba\u7b49\u77e5\u8bc6\u5728AES\u7b97\u6cd5\u3001\u516c\u94a5\u5bc6\u7801\u7b97\u6cd5\u4e2d\u7684\u5e94\u7528\u589e\u5f3a\u4e86\u5bc6\u7801\u7b97\u6cd5\u7684\u5b89\u5168\u6027\uff0c\u5728\u4fdd\u969c\u4eba\u4eec\u4fe1\u606f\u5b89\u5168\u65b9\u9762\u7684\u4f5c\u7528\u4e0d\u53ef\u66ff\u4ee3\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u53c2\u8003\u6587\u732e\uff1a<\/p>\n<p>[1] Christof Paar, Jan Pelzl. Understanding Cryptography. Springer. 2010<\/p>\n<p>[2] \u8c37\u5229\u6cfd\uff0c\u90d1\u4e16\u6167\uff0c\u6768\u4e49\u5148. \u300a\u73b0\u4ee3\u5bc6\u7801\u5b66\u6559\u7a0b\uff08\u7b2c2\u7248\uff09\u300b. \u5317\u4eac\u90ae\u7535\u5927\u5b66\u51fa\u7248\u793e. 2015\u5e743\u6708<\/p>\n<p>[3] \uff08\u7f8e\uff09Christof Paar, Jan Pelzl\u8457\uff0c\u9a6c\u5c0f\u5a77\u8bd1. \u300a\u6df1\u5165\u6d45\u51fa\u5bc6\u7801\u5b66\u2014\u2014\u5e38\u7528\u52a0\u5bc6\u6280\u672f\u539f\u7406\u4e0e\u5e94\u7528\u300b. \u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e. 2012\u5e749\u6708<\/p>\n<p>\uff08\u672c\u6587\u4e3a\u4e2d\u56fd\u6c11\u822a\u5927\u5b662015-2016\u5b66\u5e74\u7b2c\u4e00\u5b66\u671f\u300a\u6570\u5b66\u5b66\u79d1\u5bfc\u8bba\u300b\u8bfe\u7a0b\u4f5c\u4e1a\uff0c\u5b8c\u6210\u65f6\u95f4\u4e3a2015\u5e7411\u670818\u65e5\u3002\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5b66\u4f5c\u4e3a\u4e00\u95e8\u81ea\u7136\u79d1\u5b66\uff0c\u5728\u4eba\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u548c\u5b66\u4e60\u4e2d\u6709\u7740\u8bb8\u591a\u4e0d\u53ef\u6216\u7f3a\u7684\u5e94\u7528\uff0c\u5728\u4eba\u4eec\u751f\u6d3b\u7684\u5404\u4e2a\u65b9\u9762\u5747\u80fd\u770b\u89c1\u6570\u5b66\u7684\u5e94\u7528\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":329,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-326","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathing"],"_links":{"self":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=326"}],"version-history":[{"count":1,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/326\/revisions"}],"predecessor-version":[{"id":330,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/326\/revisions\/330"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/media\/329"}],"wp:attachment":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}