{"id":840,"date":"2022-02-10T07:50:27","date_gmt":"2022-02-10T07:50:27","guid":{"rendered":"http:\/\/www.selinuxplus.com\/?p=840"},"modified":"2022-02-10T08:09:12","modified_gmt":"2022-02-10T08:09:12","slug":"%e4%bb%8e%e6%a4%ad%e5%9c%86%e6%9b%b2%e7%ba%bf%e5%88%b0anyswap%e7%9a%84mpc%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"http:\/\/www.selinuxplus.com\/?p=840","title":{"rendered":"\u4ece\u692d\u5706\u66f2\u7ebf\u5230Anyswap\u7684MPC\u5b66\u4e60"},"content":{"rendered":"\n<h3>0x01 \u9677\u95e8\u51fd\u6570<\/h3>\n\n\n\n<p><strong>trapdoor function<\/strong>\u662f\u4e00\u79cd\u91cd\u8981\u7684\u51fd\u6570\u3002\u4e5f\u662f\u73b0\u4ee3\u5bc6\u7801\u5b66\u4f9d\u8d56\u7684\u51e0\u79cd\u7279\u6b8a\u51fd\u6570\u4e4b\u4e00\u3002trapdoor function\u4e0e\u54c8\u5e0c\u51fd\u6570\u6709\u4e9b\u7c7b\u4f3c\uff0c\u5373\u6b63\u5411\u5bb9\u6613\u6c42\u89e3\uff0c\u53cd\u5411\u5f88\u96be\u6216\u8005\u4e0d\u53ef\u80fd\u6c42\u89e3\uff08\u9664\u975e\u77e5\u9053\u539f\u59cb\u4fe1\u606f\uff09\u3002\u5373\uff0c\u5982\u679c\u6ca1\u6709\u4eba\u6709\u5bc6\u94a5\u6216\u94a5\u5319\uff0c\u4ed6\u4eec\u4e0d\u80fd\u53cd\u8f6c\u529f\u80fd\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"1024\" height=\"724\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/1-1-1024x724.png\" alt=\"\" class=\"wp-image-842\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/1-1-1024x724.png 1024w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/1-1-300x212.png 300w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/1-1-768x543.png 768w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/1-1.png 1280w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>trapdoor function\uff1a\u9677\u95e8\u51fd\u6570\u3002\u6570\u5b66\u672f\u8bed\u6765\u8bf4\uff0c\u5982\u679cf\u662f\u6d3b\u677f\u95e8\u51fd\u6570\uff0c\u5219\u5b58\u5728\u4e00\u4e9b\u79d8\u5bc6\u4fe1\u606ft\uff0c\u4f7f\u5f97\u7ed9\u5b9af\uff08x\uff09\u548ct\uff0c\u5c31\u5f88\u5bb9\u6613\u8ba1\u7b97x\u3002\u8003\u8651\u4e00\u4e2a\u6302\u9501\u53ca\u5176\u94a5\u5319\u3002\u901a\u8fc7\u5c06\u94a9\u73af\u63a8\u5165\u9501\u5b9a\u673a\u6784\uff0c\u65e0\u9700\u4f7f\u7528\u94a5\u5319\u5373\u53ef\u5c06\u6302\u9501\u4ece\u6253\u5f00\u72b6\u6001\u66f4\u6539\u4e3a\u5173\u95ed\u72b6\u6001\uff0c\u8fd9\u5f88\u7b80\u5355\u3002\u4f46\u662f\uff0c\u8f7b\u677e\u6253\u5f00\u6302\u9501\u9700\u8981\u4f7f\u7528\u94a5\u5319\u3002\u8fd9\u91cc\u7684\u94a5\u5319\u662f\u6d3b\u677f\u95e8\uff0c\u6302\u9501\u662f\u6d3b\u677f\u95e8\u529f\u80fd\u3002\ntrapdoor function\u6784\u6210\u4e86\u73b0\u4ee3\u5bc6\u7801\u6280\u672f\u7684\u57fa\u7840\uff0c\u8fd9\u4e9b\u6280\u672f\u5728\u7f51\u4e0a\u88ab\u5e7f\u6cdb\u4f7f\u7528\u3002\n<\/p>\n\n\n\n<h3>0x02 \u516c\u94a5\u5bc6\u7801\u5b66<\/h3>\n\n\n\n<p>\u5bc6\u7801\u5b66\u7684\u5386\u53f2\u53ef\u4ee5\u5206\u4e3a\u4e24\u4e2a\u65f6\u4ee3\uff1a\u53e4\u5178\u65f6\u4ee3\u548c\u73b0\u4ee3\u65f6\u4ee3\u3002\u4e24\u8005\u7684\u8f6c\u6298\u70b9\u53d1\u751f\u5728 1977 \u5e74\uff0c\u5f53\u65f6\u540c\u65f6\u5f15\u5165\u4e86<a href=\"https:\/\/en.wikipedia.org\/wiki\/RSA_(algorithm)\">RSA \u7b97\u6cd5<\/a>\u548c<a href=\"https:\/\/en.wikipedia.org\/wiki\/Diffie%E2%80%93Hellman_key_exchange\">Diffie-Hellman<\/a>\u5bc6\u94a5\u4ea4\u6362\u7b97\u6cd5\u3002\u8fd9\u4e9b\u65b0\u7b97\u6cd5\u662f\u9769\u547d\u6027\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u4ee3\u8868\u4e86\u7b2c\u4e00\u4e2a\u53ef\u884c\u7684\u5bc6\u7801\u65b9\u6848\uff0c\u5176\u4e2d\u5b89\u5168\u6027\u57fa\u4e8e\u6570\u8bba\u3002\u5b83\u662f\u7b2c\u4e00\u4e2a\u5728\u6ca1\u6709\u5171\u4eab\u79d8\u5bc6\u7684\u60c5\u51b5\u4e0b\u5b9e\u73b0\u4e24\u65b9\u4e4b\u95f4\u5b89\u5168\u901a\u4fe1\u7684\u6280\u672f\u3002\u5bc6\u7801\u5b66\u4ece\u5173\u4e8e\u5728\u4e16\u754c\u5404\u5730\u5b89\u5168\u5730\u4f20\u8f93\u79d8\u5bc6\u5bc6\u7801\u672c\u53d1\u5c55\u5230\u80fd\u591f\u5728\u4efb\u4f55\u4e24\u65b9\u4e4b\u95f4\u8fdb\u884c\u53ef\u8bc1\u660e\u7684\u5b89\u5168\u901a\u4fe1\uff0c\u800c\u65e0\u9700\u62c5\u5fc3\u6709\u4eba\u5728\u7a83\u542c\u5bc6\u94a5\u4ea4\u6362\u3002<\/p>\n\n\n\n<p>\u73b0\u4ee3\u5bc6\u7801\u5b66\u662f\u5efa\u7acb\u5728\u8fd9\u6837\u4e00\u79cd\u601d\u60f3\u4e4b\u4e0a\u7684\uff0c\u5373\u60a8\u7528\u4e8e\u52a0\u5bc6\u6570\u636e\u7684\u5bc6\u94a5\u53ef\u4ee5\u516c\u5f00\uff0c\u800c\u7528\u4e8e\u89e3\u5bc6\u6570\u636e\u7684\u5bc6\u94a5\u53ef\u4ee5\u4fdd\u5bc6\u3002\u56e0\u6b64\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u88ab\u79f0\u4e3a\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u3002\u7b2c\u4e00\u4e2a\uff0c\u4e5f\u662f\u6700\u5e7f\u6cdb\u4f7f\u7528\u7684\u7cfb\u7edf\uff0c\u88ab\u79f0\u4e3a RSA\u2014\u2014\u4ee5\u9996\u6b21\u516c\u5f00\u63cf\u8ff0\u8be5\u7b97\u6cd5\u7684\u4e09\u4e2a\u4eba\u7684\u9996\u5b57\u6bcd\u547d\u540d\uff1aRon Rivest\u3001Adi Shamir \u548c Leonard Adleman\u3002<\/p>\n\n\n\n<p>\u8981\u4f7f\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u6b63\u5e38\u5de5\u4f5c\uff0c\u60a8\u9700\u8981\u4e00\u7ec4\u7b97\u6cd5\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u6613\u4e8e\u5355\u5411\u5904\u7406\uff0c\u4f46\u96be\u4ee5\u64a4\u6d88\u3002\u5728 RSA \u7684\u60c5\u51b5\u4e0b\uff0c\u7b80\u5355\u7b97\u6cd5\u5c06\u4e24\u4e2a\u7d20\u6570\u76f8\u4e58\u3002\u5982\u679c\u4e58\u6cd5\u662f\u7b80\u5355\u7684\u7b97\u6cd5\uff0c\u90a3\u4e48\u5b83\u7684\u56f0\u96be\u914d\u5bf9\u7b97\u6cd5\u662f\u5c06\u4e58\u6cd5\u7684\u4e58\u79ef\u5206\u89e3\u4e3a\u5176\u4e24\u4e2a\u5206\u91cf\u7d20\u6570\u3002\u5177\u6709\u8fd9\u4e00\u7279\u5f81\u7684\u7b97\u6cd5\u2014\u2014\u4e00\u4e2a\u65b9\u5411\u5bb9\u6613\uff0c\u53e6\u4e00\u4e2a\u65b9\u5411\u96be\u2014\u2014\u88ab\u79f0\u4e3a<a href=\"https:\/\/en.wikipedia.org\/wiki\/Trapdoor_function\">\u9677\u9631\u95e8\u51fd\u6570<\/a>\u3002\u627e\u5230\u4e00\u4e2a\u597d\u7684\u9677\u95e8\u51fd\u6570\u5bf9\u4e8e\u5236\u4f5c\u5b89\u5168\u7684\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u81f3\u5173\u91cd\u8981\u3002\u7b80\u5355\u5730\u8bf4\uff1a\u5728\u9677\u95e8\u51fd\u6570\u4e2d\u5411\u4e00\u4e2a\u65b9\u5411\u524d\u8fdb\u7684\u96be\u5ea6\u4e0e\u5411\u53e6\u4e00\u4e2a\u65b9\u5411\u524d\u8fdb\u7684\u96be\u5ea6\u4e4b\u95f4\u7684\u5dee\u8ddd\u8d8a\u5927\uff0c\u57fa\u4e8e\u5b83\u7684\u5bc6\u7801\u7cfb\u7edf\u5c31\u8d8a\u5b89\u5168\u3002<\/p>\n\n\n\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u516c\u94a5\u52a0\u5bc6\u7cfb\u7edf\u6709\u4e24\u4e2a\u7ec4\u6210\u90e8\u5206\uff0c\u4e00\u4e2a\u516c\u94a5\u548c\u4e00\u4e2a\u79c1\u94a5\u3002\u52a0\u5bc6\u7684\u5de5\u4f5c\u539f\u7406\u662f\u83b7\u53d6\u4e00\u6761\u6d88\u606f\u5e76\u5bf9\u5b83\u5e94\u7528\u6570\u5b66\u8fd0\u7b97\u4ee5\u83b7\u5f97\u4e00\u4e2a\u770b\u8d77\u6765\u968f\u673a\u7684\u6570\u5b57\u3002\u89e3\u5bc6\u91c7\u7528\u968f\u673a\u6570\u5b57\u5e76\u5e94\u7528\u4e0d\u540c\u7684\u64cd\u4f5c\u6765\u6062\u590d\u539f\u59cb\u6570\u5b57\u3002\u4f7f\u7528\u516c\u94a5\u52a0\u5bc6\u53ea\u80fd\u901a\u8fc7\u4f7f\u7528\u79c1\u94a5\u89e3\u5bc6\u6765\u64a4\u9500\u3002<\/p>\n\n\n\n<p>\u8ba1\u7b97\u673a\u4e0d\u80fd\u5f88\u597d\u5730\u5904\u7406\u4efb\u610f\u5927\u7684\u6570\u5b57\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9009\u62e9\u6700\u5927\u6570\u5b57\u5e76\u4ec5\u5904\u7406\u5c0f\u4e8e\u6700\u5927\u503c\u7684\u6570\u5b57\u6765\u786e\u4fdd\u6211\u4eec\u6b63\u5728\u5904\u7406\u7684\u6570\u5b57\u4e0d\u4f1a\u53d8\u5f97\u592a\u5927\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u5b57\u89c6\u4e3a\u6a21\u62df\u65f6\u949f\u4e0a\u7684\u6570\u5b57\u3002\u4efb\u4f55\u5bfc\u81f4\u6570\u5b57\u5927\u4e8e\u6700\u5927\u503c\u7684\u8ba1\u7b97\u90fd\u4f1a\u88ab\u73af\u7ed5\u5230\u6709\u6548\u8303\u56f4\u5185\u7684\u6570\u5b57\u3002<\/p>\n\n\n\n<h3>0x03 RSA \u7b97\u6cd5<\/h3>\n\n\n\n<p>RSA \u7b97\u6cd5\u662f\u6700\u6d41\u884c\u548c\u6700\u5bb9\u6613\u7406\u89e3\u7684\u516c\u94a5\u5bc6\u7801\u7cfb\u7edf\u3002<\/p>\n\n\n\n<p>\u5728 RSA \u4e2d\uff0c\u8fd9\u4e2a\u6700\u5927\u503c\uff08\u79f0\u4e3a<em>max<\/em>\uff09\u662f\u901a\u8fc7\u5c06\u4e24\u4e2a\u968f\u673a\u7d20\u6570\u76f8\u4e58\u83b7\u5f97\u7684\u3002\u516c\u94a5\u548c\u79c1\u94a5\u662f\u4e24\u4e2a\u7279\u522b\u9009\u62e9\u7684\u5927\u4e8e\u96f6\u4e14\u5c0f\u4e8e\u6700\u5927\u503c\u7684\u6570\u5b57\uff0c\u79f0\u4e3a<em>pub<\/em>\u548c<em>priv<\/em>\u3002\u8981\u52a0\u5bc6\u4e00\u4e2a\u6570\u5b57\uff0c\u8bf7\u5c06\u5176\u4e58\u4ee5\u5b83\u672c\u8eab\u7684<em>\u53d1\u5e03<\/em>\u65f6\u95f4\uff0c\u786e\u4fdd\u5728\u8fbe\u5230\u6700\u5927\u503c\u65f6\u56de\u7ed5\u3002\u8981\u89e3\u5bc6\u6d88\u606f\uff0c\u60a8\u5c06\u5176\u4e58\u4ee5<em>priv<\/em>\u65f6\u95f4\uff0c\u7136\u540e\u8fd4\u56de\u539f\u59cb\u6570\u5b57\u3002\u8fd9\u542c\u8d77\u6765\u4ee4\u4eba\u60ca\u8bb6\uff0c\u4f46\u5b83\u786e\u5b9e\u6709\u6548\u3002\u8fd9\u4e00\u7279\u6027\u5728\u88ab\u53d1\u73b0\u65f6\u662f\u4e00\u4e2a\u91cd\u5927\u7a81\u7834\u3002<\/p>\n\n\n\n<p>\u8981\u521b\u5efa RSA \u5bc6\u94a5\u5bf9\uff0c\u9996\u5148\u968f\u673a\u9009\u62e9\u4e24\u4e2a\u7d20\u6570\u4ee5\u83b7\u5f97\u6700\u5927\u503c<em>(max)<\/em>\u3002\u7136\u540e\u9009\u62e9\u4e00\u4e2a\u6570\u5b57\u4f5c\u4e3a\u516c\u94a5<em>pub<\/em>\u3002\u53ea\u8981\u77e5\u9053\u8fd9\u4e24\u4e2a\u7d20\u6570\uff0c\u5c31\u53ef\u4ee5\u6839\u636e\u8fd9\u4e2a\u516c\u94a5\u8ba1\u7b97\u51fa\u5bf9\u5e94\u7684\u79c1\u94a5<em>priv<\/em>\u3002\u8fd9\u5c31\u662f\u5206\u89e3\u4e0e\u7834\u574f RSA \u7684\u5173\u7cfb\u2014\u2014\u5c06\u6700\u5927\u6570\u91cf\u5206\u89e3\u4e3a\u5176\u7ec4\u6210\u7d20\u6570\u5141\u8bb8\u60a8\u4ece\u516c\u94a5\u8ba1\u7b97\u67d0\u4eba\u7684\u79c1\u94a5\u5e76\u89e3\u5bc6\u4ed6\u4eec\u7684\u79c1\u4eba\u6d88\u606f\u3002<\/p>\n\n\n\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u66f4\u5177\u4f53\u5730\u8bf4\u660e\u8fd9\u4e00\u70b9\u3002\u4ee5\u8d28\u6570 13 \u548c 7 \u4e3a\u4f8b\uff0c\u5b83\u4eec\u7684\u4e58\u79ef\u7ed9\u51fa\u4e86\u6211\u4eec\u7684\u6700\u5927\u503c 91\u3002\u8ba9\u6211\u4eec\u628a\u6211\u4eec\u7684\u516c\u5171\u52a0\u5bc6\u5bc6\u94a5\u4f5c\u4e3a\u6570\u5b57 5\u3002\u7136\u540e\u5229\u7528\u6211\u4eec\u77e5\u9053 7 \u548c 13 \u662f 91 \u7684\u56e0\u6570\u8fd9\u4e00\u4e8b\u5b9e\uff0c\u5e76\u5e94\u7528\u4e00\u79cd\u79f0\u4e3a<a href=\"https:\/\/en.wikipedia.org\/wiki\/Extended_Euclidean_algorithm\">\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5<\/a>\uff0c\u6211\u4eec\u5f97\u5230\u79c1\u94a5\u662f\u6570\u5b57 29\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e9b\u53c2\u6570\uff08<em>\u6700\u5927\u503c<\/em>\uff1a91\uff0c<em>pub<\/em>\uff1a5\uff1b<em>priv<\/em>\uff1a29\uff09\u5b9a\u4e49\u4e86\u4e00\u4e2a\u529f\u80fd\u9f50\u5168\u7684 RSA \u7cfb\u7edf\u3002\u60a8\u53ef\u4ee5\u53d6\u4e00\u4e2a\u6570\u5b57\u5e76\u5c06\u5176\u81ea\u8eab\u76f8\u4e58 5 \u6b21\u4ee5\u5bf9\u5176\u8fdb\u884c\u52a0\u5bc6\uff0c\u7136\u540e\u53d6\u8be5\u6570\u5b57\u5e76\u5c06\u5176\u81ea\u8eab\u76f8\u4e58 29 \u6b21\uff0c\u5373\u53ef\u5f97\u5230\u539f\u59cb\u6570\u5b57\u3002<\/p>\n\n\n\n<p>\u8ba9\u6211\u4eec\u4f7f\u7528\u8fd9\u4e9b\u503c\u6765\u52a0\u5bc6\u6d88\u606f\u201cCLOUD\u201d\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u5728\u6570\u5b66\u4e0a\u8868\u793a\u6d88\u606f\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u5b57\u6bcd\u8f6c\u6362\u4e3a\u6570\u5b57\u3002\u62c9\u4e01\u5b57\u6bcd\u7684\u5e38\u89c1\u8868\u793a\u662f UTF-8\u3002\u6bcf\u4e2a\u5b57\u7b26\u5bf9\u5e94\u4e00\u4e2a\u6570\u5b57\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"504\" height=\"143\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image02.png\" alt=\"\" class=\"wp-image-843\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image02.png 504w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image02-300x85.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/figure>\n\n\n\n<p>\u5728\u8fd9\u79cd\u7f16\u7801\u4e0b\uff0cCLOUD \u662f 67\u300176\u300179\u300185\u300168\u3002\u8fd9\u4e9b\u6570\u5b57\u4e2d\u7684\u6bcf\u4e00\u4e2a\u90fd\u5c0f\u4e8e\u6211\u4eec\u6700\u5927\u7684 91\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5355\u72ec\u52a0\u5bc6\u5b83\u4eec\u3002\u8ba9\u6211\u4eec\u4ece\u7b2c\u4e00\u4e2a\u5b57\u6bcd\u5f00\u59cb\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u5fc5\u987b\u5c06\u5b83\u81ea\u5df1\u4e58\u4ee5 5 \u6b21\u624d\u80fd\u5f97\u5230\u52a0\u5bc6\u503c\u3002<\/p>\n\n\n\n<p>67\u00d767 = 4489 = 30 *<\/p>\n\n\n\n<p><em>*\u7531\u4e8e 4489 \u5927\u4e8e\u6700\u5927\u503c\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u5176\u73af\u7ed5\u3002\u6211\u4eec\u901a\u8fc7\u9664\u4ee5 91 \u5e76\u53d6\u4f59\u6570\u6765\u505a\u5230\u8fd9\u4e00\u70b9\u3002<\/em><\/p>\n\n\n\n<p>4489 = 91\u00d741 + 30<\/p>\n\n\n\n<p>30\u00d767 = 2010 = 8<\/p>\n\n\n\n<p>8\u00d767 = 536 = 81<\/p>\n\n\n\n<p>81\u00d767 = 5427 = 58<\/p>\n\n\n\n<p>\u8fd9\u610f\u5473\u7740 67 \u7684\u52a0\u5bc6\u7248\u672c\u662f 58\u3002<\/p>\n\n\n\n<p>\u5bf9\u6211\u4eec\u5f97\u5230\u7684\u6bcf\u4e2a\u5b57\u6bcd\u91cd\u590d\u8be5\u8fc7\u7a0b\uff0c\u52a0\u5bc6\u6d88\u606f CLOUD \u53d8\u4e3a\uff1a<\/p>\n\n\n\n<p>58\u300120\u300153\u300150\u300187<\/p>\n\n\n\n<p>\u4e3a\u4e86\u89e3\u5bc6\u8fd9\u4e2a\u52a0\u6270\u7684\u6d88\u606f\uff0c\u6211\u4eec\u5c06\u6bcf\u4e2a\u6570\u5b57\u4e58\u4ee5\u81ea\u8eab 29 \u6b21\uff1a<\/p>\n\n\n\n<p>58\u00d758 = 3364 = 88 \uff08\u8bb0\u4f4f\uff0c\u5f53\u6570\u5b57\u5927\u4e8e<em>max<\/em>\u65f6\u6211\u4eec\u56de\u7ed5\uff09&gt;<\/p>\n\n\n\n<p>88\u00d758 = 5104 = 8<\/p>\n\n\n\n<p>\u2026<\/p>\n\n\n\n<p>9\u00d758 = 522 = 67<\/p>\n\n\n\n<p>\u77a7\uff0c\u6211\u4eec\u56de\u5230\u4e86 67\u3002\u8fd9\u9002\u7528\u4e8e\u5176\u4f59\u6570\u5b57\uff0c\u4ece\u800c\u4ea7\u751f\u539f\u59cb\u6d88\u606f\u3002<\/p>\n\n\n\n<p>\u8981\u70b9\u662f\uff0c\u60a8\u53ef\u4ee5\u53d6\u4e00\u4e2a\u6570\u5b57\uff0c\u5c06\u5176\u4e0e\u81ea\u8eab\u76f8\u4e58\u591a\u6b21\u4ee5\u83b7\u5f97\u770b\u8d77\u6765\u968f\u673a\u7684\u6570\u5b57\uff0c\u7136\u540e\u5c06\u8be5\u6570\u5b57\u4e0e\u81ea\u8eab\u76f8\u4e58\u4e00\u4e2a\u79d8\u5bc6\u6b21\u6570\u4ee5\u8fd4\u56de\u539f\u59cb\u6570\u5b57\u3002<\/p>\n\n\n\n<h3>0x04 \u4e0d\u662f\u5b8c\u7f8e\u7684\u9677\u95e8<\/h3>\n\n\n\n<p>RSA \u548c Diffie-Hellman \u4e4b\u6240\u4ee5\u5982\u6b64\u5f3a\u5927\uff0c\u662f\u56e0\u4e3a\u5b83\u4eec\u5e26\u6709\u4e25\u683c\u7684\u5b89\u5168\u8bc1\u660e\u3002\u4f5c\u8005\u8bc1\u660e\uff0c\u6253\u7834\u7cfb\u7edf\u7b49\u540c\u4e8e\u89e3\u51b3\u4e00\u4e2a\u88ab\u8ba4\u4e3a\u96be\u4ee5\u89e3\u51b3\u7684\u6570\u5b66\u95ee\u9898\u3002\u56e0\u5f0f\u5206\u89e3\u662f\u4e00\u4e2a\u4f17\u6240\u5468\u77e5\u7684\u95ee\u9898\uff0c\u81ea\u53e4\u4ee5\u6765\u5c31\u4e00\u76f4\u5728\u7814\u7a76\uff08\u53c2\u89c1<a href=\"https:\/\/en.wikipedia.org\/wiki\/Sieve_of_Eratosthenes\">\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5<\/a>\uff09\u3002<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u4fdd\u7406\u5e76\u4e0d\u662f\u6700\u96be\u7684\u95ee\u9898\u3002<a href=\"http:\/\/mathworld.wolfram.com\/QuadraticSieve.html\">\u4e8c\u6b21\u7b5b<\/a>\u548c<a href=\"https:\/\/en.wikipedia.org\/wiki\/General_number_field_sieve\">\u901a\u7528\u6570\u57df\u7b5b<\/a>\u7b49\u4e13\u95e8\u7b97\u6cd5\u662f\u4e3a\u4e86\u89e3\u51b3\u7d20\u6570\u5206\u89e3\u95ee\u9898\u800c\u521b\u5efa\u7684\uff0c\u5e76\u4e14\u53d6\u5f97\u4e86\u4e00\u5b9a\u7684\u6210\u529f\u3002\u4e0e\u4ec5\u731c\u6d4b\u5df2\u77e5\u7d20\u6570\u5bf9\u7684\u5929\u771f\u65b9\u6cd5\u76f8\u6bd4\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u66f4\u5feb\u4e14\u8ba1\u7b97\u91cf\u66f4\u5c11\u3002<\/p>\n\n\n\n<p>\u968f\u7740\u88ab\u5206\u89e3\u7684\u6570\u5b57\u7684\u5927\u5c0f\u53d8\u5f97\u8d8a\u6765\u8d8a\u5927\uff0c\u8fd9\u4e9b\u5206\u89e3\u7b97\u6cd5\u53d8\u5f97\u66f4\u52a0\u6709\u6548\u3002\u968f\u7740\u6570\u5b57\uff08\u5373\u5bc6\u94a5\u7684\u4f4d\u957f\u5ea6\uff09\u53d8\u5927\uff0c\u5206\u89e3\u5927\u6570\u548c\u4e58\u4ee5\u5927\u6570\u7684\u96be\u5ea6\u4e4b\u95f4\u7684\u5dee\u8ddd\u6b63\u5728\u7f29\u5c0f\u3002\u968f\u7740\u53ef\u7528\u4e8e\u89e3\u5bc6\u6570\u5b57\u7684\u8d44\u6e90\u7684\u589e\u52a0\uff0c\u5bc6\u94a5\u7684\u5927\u5c0f\u9700\u8981\u589e\u957f\u5f97\u66f4\u5feb\u3002\u5bf9\u4e8e\u8ba1\u7b97\u80fd\u529b\u6709\u9650\u7684\u79fb\u52a8\u548c\u4f4e\u529f\u7387\u8bbe\u5907\u6765\u8bf4\uff0c\u8fd9\u4e0d\u662f\u4e00\u4e2a\u53ef\u6301\u7eed\u7684\u60c5\u51b5\u3002\u4ece\u957f\u8fdc\u6765\u770b\uff0c\u56e0\u5f0f\u5206\u89e3\u548c\u4e58\u6cd5\u4e4b\u95f4\u7684\u5dee\u8ddd\u662f\u4e0d\u53ef\u6301\u7eed\u7684\u3002<\/p>\n\n\n\n<p>\u6240\u6709\u8fd9\u4e00\u5207\u90fd\u610f\u5473\u7740 RSA \u4e0d\u662f\u5bc6\u7801\u5b66\u672a\u6765\u7684\u7406\u60f3\u7cfb\u7edf\u3002\u5728\u7406\u60f3\u7684\u9677\u95e8\u51fd\u6570\u4e2d\uff0c\u76f8\u5bf9\u4e8e\u6240\u8ba8\u8bba\u6570\u5b57\u7684\u5927\u5c0f\uff0c\u7b80\u5355\u65b9\u6cd5\u548c\u56f0\u96be\u65b9\u6cd5\u4ee5\u76f8\u540c\u7684\u901f\u5ea6\u53d8\u5f97\u66f4\u96be\u3002\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u57fa\u4e8e\u66f4\u597d\u9677\u95e8\u7684\u516c\u94a5\u7cfb\u7edf\u3002<\/p>\n\n\n\n<h3>0x05 \u692d\u5706\u66f2\u7ebf<\/h3>\n\n\n\n<p>\u692d\u5706\u66f2\u7ebf\u662f\u6ee1\u8db3\u7279\u5b9a\u6570\u5b66\u65b9\u7a0b\u7684\u4e00\u7ec4\u70b9\u3002\u692d\u5706\u66f2\u7ebf\u7684\u65b9\u7a0b\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n<p>y^2 = x^3 + ax + b<\/p>\n\n\n\n<p>\u8be5\u56fe\u5f62\u770b\u8d77\u6765\u6709\u70b9\u50cf\u4fa7\u9762\u503e\u659c\u7684 Lululemon \u5fbd\u6807\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"409\" height=\"410\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image00.png\" alt=\"\" class=\"wp-image-844\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image00.png 409w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image00-150x150.png 150w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image00-300x300.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/figure>\n\n\n\n<p>\u692d\u5706\u66f2\u7ebf\u8fd8\u6709\u5176\u4ed6\u8868\u793a\uff0c\u4f46\u4ece\u6280\u672f\u4e0a\u8bb2\uff0c\u692d\u5706\u66f2\u7ebf\u662f\u5728\u4e24\u4e2a\u53d8\u91cf\u4e2d\u6ee1\u8db3\u65b9\u7a0b\u7684\u8bbe\u5b9a\u70b9\uff0c\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u7684\u5ea6\u6570\u4e3a 2\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u5ea6\u6570\u4e3a 3\u3002\u692d\u5706\u66f2\u7ebf\u4e0d\u4ec5\u4ec5\u662f\u4e00\u5f20\u6f02\u4eae\u7684\u56fe\u7247\uff0c\u5b83\u8fd8\u5177\u6709\u4e00\u4e9b\u7279\u6027\uff0c\u4f7f\u5176\u6210\u4e3a\u5bc6\u7801\u5b66\u7684\u826f\u597d\u8bbe\u7f6e\u3002<\/p>\n\n\n\n<p>\u4eba\u4eec\u559c\u6b22\u5439\u5618\u52a0\u5bc6\u8d27\u5e01\u201c\u53d7\u6570\u5b66\u4fdd\u62a4\u201d\uff0c\u4f46\u901a\u5e38\u5f88\u5c11\u8c08\u8bba\u6240\u6d89\u53ca\u7684\u5b9e\u9645\u6570\u5b66\u3002\u692d\u5706\u66f2\u7ebf\u770b\u8d77\u6765\u50cf\u4e0a\u9762\u65f6\u9ae6\u7684\u9a6c\u8e44\u5f62\uff0c\u5f88\u5bb9\u6613\u8ba1\u7b97\u4e3a\u6ee1\u8db3\u4e00\u4e2a\u7b80\u5355\u65b9\u7a0b\u7684\u70b9\u96c6\uff1a<\/p>\n\n\n\n<p>y^2 = x^3 + ax + b<a href=\"https:\/\/cdn.substack.com\/image\/fetch\/f_auto,q_auto:good,fl_progressive:steep\/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F1996720d-5422-4feb-991f-3e9b2859867d_17x3.svg\"><\/a><a href=\"https:\/\/cdn.substack.com\/image\/fetch\/f_auto,q_auto:good,fl_progressive:steep\/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F353cbfb8-2d2b-4e36-82f2-ce951121148e_542x149.png\"><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"542\" height=\"149\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image04.png\" alt=\"\" class=\"wp-image-845\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image04.png 542w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image04-300x82.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u4e9b\u66f2\u7ebf\u5177\u6709\u5f88\u597d\u7684\u7279\u6027\uff0c\u5373\u5728\u66f2\u7ebf\u4e0a\u4e24\u70b9\u4e4b\u95f4\u7ed8\u5236\u7684\u4efb\u4f55\u975e\u5782\u76f4\u7ebf\u6700\u591a\u4e0e\u53e6\u4e00\u70b9\u76f8\u4ea4\u3002\u8fd9\u4f7f\u5f97\u5b83\u4eec\u53ef\u7528\u4e8e\u751f\u6210\u975e\u5bf9\u79f0\u5bc6\u94a5\u5bf9\u3002<\/p>\n\n\n\n<h3>0x06 \u5947\u602a\u7684\u5bf9\u79f0<\/h3>\n\n\n\n<p>\u4ed4\u7ec6\u770b\u770b\u4e0a\u9762\u7ed8\u5236\u7684\u692d\u5706\u66f2\u7ebf\u3002\u5b83\u6709\u51e0\u4e2a\u6709\u8da3\u7684\u7279\u6027\u3002<\/p>\n\n\n\n<p>\u5176\u4e2d\u4e4b\u4e00\u662f\u6c34\u5e73\u5bf9\u79f0\u3002\u66f2\u7ebf\u4e0a\u7684\u4efb\u4f55\u70b9\u90fd\u53ef\u4ee5\u53cd\u6620\u5728 x \u8f74\u4e0a\u5e76\u4fdd\u6301\u76f8\u540c\u7684\u66f2\u7ebf\u3002\u4e00\u4e2a\u66f4\u6709\u8da3\u7684\u7279\u6027\u662f\u4efb\u4f55\u975e\u5782\u76f4\u7ebf\u5c06\u4e0e\u66f2\u7ebf\u76f8\u4ea4\u6700\u591a\u4e09\u4e2a\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u8ba9\u6211\u4eec\u628a\u8fd9\u6761\u66f2\u7ebf\u60f3\u8c61\u6210\u4e00\u573a\u5947\u5f02\u7684\u53f0\u7403\u6bd4\u8d5b\u3002\u53d6\u66f2\u7ebf\u4e0a\u7684\u4efb\u610f\u4e24\u70b9\u5e76\u5728\u5b83\u4eec\u4e4b\u95f4\u753b\u4e00\u6761\u7ebf\uff0c\u5b83\u5c06\u4e0e\u66f2\u7ebf\u76f8\u4ea4\u7684\u5730\u65b9\u6070\u597d\u662f\u53e6\u4e00\u5904\u3002\u5728\u8fd9\u4e2a\u53f0\u7403\u6e38\u620f\u4e2d\uff0c\u4f60\u5728 A \u70b9\u62ff\u4e00\u4e2a\u7403\uff0c\u5c06\u5b83\u5c04\u5411 B \u70b9\u3002\u5f53\u5b83\u51fb\u4e2d\u66f2\u7ebf\u65f6\uff0c\u7403\u4f1a\u76f4\u63a5\u5411\u4e0a\u5f39\u8df3\uff08\u5982\u679c\u5b83\u4f4e\u4e8e x \u8f74\uff09\u6216\u76f4\u63a5\u5411\u4e0b\u5f39\u8df3\uff08\u5982\u679c\u5b83\u9ad8\u4e8e x -axis) \u5230\u66f2\u7ebf\u7684\u53e6\u4e00\u4fa7\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"410\" height=\"410\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image05.gif\" alt=\"\" class=\"wp-image-846\"\/><\/figure>\n\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u79cd\u53f0\u7403\u79fb\u52a8\u79f0\u4e3a\u4e24\u70b9\u201cdot\u201d\u3002\u66f2\u7ebf\u4e0a\u7684\u4efb\u610f\u4e24\u70b9\u90fd\u53ef\u4ee5\u70b9\u5728\u4e00\u8d77\u5f97\u5230\u4e00\u4e2a\u65b0\u70b9\u3002<\/p>\n\n\n\n<p>A dot B = C<\/p>\n\n\n\n<p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u52a8\u4f5c\u4e32\u5728\u4e00\u8d77\uff0c\u4e00\u904d\u53c8\u4e00\u904d\u5730\u7528\u5b83\u81ea\u5df1\u201cdot\u201d\u4e00\u4e2a\u70b9\u3002<\/p>\n\n\n\n<p>A dot A = B<\/p>\n\n\n\n<p>A dot B = C<\/p>\n\n\n\n<p>A dot C = D<\/p>\n\n\n\n<p>&#8230;<\/p>\n\n\n\n<p>\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5982\u679c\u4f60\u6709\u4e24\u4e2a\u70b9\uff0c\u4e00\u4e2a\u521d\u59cb\u70b9\u7528\u5b83\u81ea\u5df1\u201c\u70b9\u201dn\u6b21\u5230\u8fbe\u4e00\u4e2a\u7ec8\u70b9\uff0c\u5f53\u4f60\u53ea\u77e5\u9053\u7ec8\u70b9\u800c\u7b2c\u4e00\u4e2a\u70b9\u5f88\u96be\u65f6\u627e\u51fan\u3002\u7ee7\u7eed\u6211\u4eec\u7684bizzaro\u53f0\u7403\u6bd4\u55bb\uff0c\u60f3\u8c61\u4e00\u4e2a\u4eba\u5728\u4e00\u4e2a\u623f\u95f4\u91cc\u72ec\u81ea\u73a9\u6211\u4eec\u7684\u6e38\u620f\u4e00\u6bb5\u65f6\u95f4\u3002\u6309\u7167\u4e0a\u8ff0\u89c4\u5219\uff0c\u4ed6\u5f88\u5bb9\u6613\u4e00\u904d\u53c8\u4e00\u904d\u5730\u51fb\u7403\u3002\u5982\u679c\u6709\u4eba\u7a0d\u540e\u8d70\u8fdb\u623f\u95f4\u5e76\u770b\u5230\u7403\u5728\u54ea\u91cc\u7ed3\u675f\uff0c\u5373\u4f7f\u4ed6\u4eec\u77e5\u9053\u6240\u6709\u6e38\u620f\u89c4\u5219\u4ee5\u53ca\u7403\u4ece\u54ea\u91cc\u5f00\u59cb\uff0c\u4ed6\u4eec\u4e5f\u65e0\u6cd5\u786e\u5b9a\u5728\u6ca1\u6709\u7a7f\u8fc7\u7403\u7684\u60c5\u51b5\u4e0b\u5c06\u7403\u51fb\u5230\u90a3\u91cc\u7684\u6b21\u6570\u518d\u6b21\u6574\u573a\u6bd4\u8d5b\uff0c\u76f4\u5230\u7403\u5230\u8fbe\u540c\u4e00\u70b9\u3002\u6613\u505a\u96be\u64a4\u9500\uff1a\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u9677\u95e8\u529f\u80fd\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p>\u975e\u5bf9\u79f0\u5bc6\u94a5\u5bf9\u5fc5\u987b\u6613\u4e8e\u751f\u6210\u4f46\u96be\u4ee5\u9a8c\u8bc1\u3002\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u8fc7\u7a0b\u662f\u4f7f\u7528\u4e24\u4e2a\u70b9\u6765\u627e\u5230\u4ece\u8fd9\u5bf9\u4ea7\u751f\u7684\u552f\u4e00\u7684\u7b2c\u4e09\u4e2a\u70b9\u3002\u4f7f\u7528\u7ed3\u679c\u4ee5\u786e\u5b9a\u7684\u65b9\u5f0f\u63a8\u5bfc\u51fa\u4e00\u4e9b\u76f8\u5173\u70b9\u3002\u8be5\u8fc7\u7a0b\u8fed\u4ee3\u4e86 n \u6b21\u4ee5\u5230\u8fbe\u6700\u7ec8\u70b9\u3002\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5982\u679c\u7ed9\u4f60\u7b2c\u4e00\u4e2a\u70b9\u548c\u6700\u540e\u4e00\u4e2a\u70b9\uff0c\u5728\u6570\u5b66\u4e0a\u8ba1\u7b97 n \u662f\u5f88\u56f0\u96be\u7684\uff0cn \u662f\u4f60\u5728\u5b83\u4eec\u4e4b\u95f4\u5fc5\u987b\u91c7\u53d6\u7684\u65c5\u884c\u6b21\u6570\u3002\u7136\u800c\uff0c\u5b83\u5f88\u5bb9\u6613\u9a8c\u8bc1\u2014\u2014\u6b63\u662f\u6211\u4eec\u9700\u8981\u7684\u975e\u5bf9\u79f0\u5bc6\u94a5\u5bf9\u3002<\/p>\n\n\n\n<h3>0x07 \u8ba9\u6211\u4eec\u75af\u72c2\u5427<\/h3>\n\n\n\n<p>\u4e0a\u9762\u8fd9\u6761\u7b80\u5316\u66f2\u7ebf\u975e\u5e38\u9002\u5408\u67e5\u770b\u548c\u89e3\u91ca\u692d\u5706\u66f2\u7ebf\u7684\u4e00\u822c\u6982\u5ff5\uff0c\u4f46\u5b83\u5e76\u4e0d\u4ee3\u8868\u7528\u4e8e\u5bc6\u7801\u5b66\u7684\u66f2\u7ebf\u662f\u4ec0\u4e48\u6837\u5b50\u3002<\/p>\n\n\n\n<p>\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u81ea\u5df1\u9650\u5236\u5728\u56fa\u5b9a\u8303\u56f4\u5185\u7684\u6570\u5b57\u4e0a\uff0c\u5c31\u50cf\u5728 RSA \u4e2d\u4e00\u6837\u3002\u6211\u4eec\u4e0d\u5141\u8bb8\u66f2\u7ebf\u4e0a\u7684\u70b9\u6709\u4efb\u4f55\u503c\uff0c\u800c\u662f\u5c06\u81ea\u5df1\u9650\u5236\u4e3a\u56fa\u5b9a\u8303\u56f4\u5185\u7684\u6574\u6570\u3002\u5728\u8ba1\u7b97\u692d\u5706\u66f2\u7ebf\u7684\u516c\u5f0f\uff08y 2 = x 3 + ax + b\uff09\u65f6\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u540c\u7684\u6280\u5de7\uff0c\u5728\u8fbe\u5230\u6700\u5927\u503c\u65f6\u7ffb\u8f6c\u6570\u5b57\u3002\u5982\u679c\u6211\u4eec\u9009\u62e9\u6700\u5927\u503c\u4f5c\u4e3a\u7d20\u6570\uff0c\u5219\u692d\u5706\u66f2\u7ebf\u79f0\u4e3a\u7d20\u6570\u66f2\u7ebf\uff0c\u5177\u6709\u51fa\u8272\u7684\u5bc6\u7801\u5b66\u7279\u6027\u3002<\/p>\n\n\n\n<p>\u8fd9\u662f\u4e3a\u6240\u6709\u6570\u5b57\u7ed8\u5236\u7684\u66f2\u7ebf (y 2 = x 3 &#8211; x + 1) \u793a\u4f8b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"784\" height=\"584\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image06.png\" alt=\"\" class=\"wp-image-847\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image06.png 784w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image06-300x223.png 300w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image06-768x572.png 768w\" sizes=\"(max-width: 784px) 100vw, 784px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u662f\u540c\u4e00\u6761\u66f2\u7ebf\u7684\u56fe\uff0c\u4ec5\u7528\u6700\u5927 97 \u8868\u793a\u6574\u6570\u70b9\uff1a<\/p>\n\n\n\n<p>\u8fd9\u770b\u8d77\u6765\u4e0d\u50cf\u4f20\u7edf\u610f\u4e49\u4e0a\u7684\u66f2\u7ebf\uff0c\u4f46\u786e\u5b9e\u5982\u6b64\u3002\u5c31\u50cf\u539f\u59cb\u66f2\u7ebf\u5728\u8fb9\u7f18\u88ab\u7f20\u7ed5\uff0c\u53ea\u6709\u66f2\u7ebf\u4e2d\u5230\u8fbe\u6574\u6570\u5750\u6807\u7684\u90e8\u5206\u88ab\u7740\u8272\u3002\u4f60\u751a\u81f3\u53ef\u4ee5\u770b\u5230\u6c34\u5e73\u5bf9\u79f0\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"954\" height=\"680\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image07.png\" alt=\"\" class=\"wp-image-848\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image07.png 954w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image07-300x214.png 300w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image07-768x547.png 768w\" sizes=\"(max-width: 954px) 100vw, 954px\" \/><\/figure>\n\n\n\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u4f60\u4ecd\u7136\u53ef\u4ee5\u5728\u8fd9\u6761\u66f2\u7ebf\u548c\u5706\u70b9\u4e0a\u4e00\u8d77\u73a9\u53f0\u7403\u6e38\u620f\u3002\u66f2\u7ebf\u4e0a\u7684\u76f4\u7ebf\u65b9\u7a0b\u4ecd\u7136\u5177\u6709\u76f8\u540c\u7684\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u8ba1\u7b97\u70b9\u8fd0\u7b97\u3002\u60a8\u53ef\u4ee5\u5c06\u4e24\u70b9\u4e4b\u95f4\u7684\u7ebf\u53ef\u89c6\u5316\u4e3a\u4e00\u6761\u5728\u8fb9\u754c\u5904\u73af\u7ed5\u76f4\u5230\u5230\u8fbe\u4e00\u4e2a\u70b9\u7684\u7ebf\u3002\u5c31\u597d\u50cf\u5728\u6211\u4eec\u5947\u602a\u7684\u53f0\u7403\u6e38\u620f\u4e2d\uff0c\u5f53\u4e00\u4e2a\u7403\u78b0\u5230\u677f\u7684\u8fb9\u7f18\uff08\u6700\u5927\u503c\uff09\u7136\u540e\u5b83\u88ab\u795e\u5947\u5730\u4f20\u9001\u5230\u684c\u5b50\u7684\u53e6\u4e00\u8fb9\u5e76\u7ee7\u7eed\u524d\u8fdb\u76f4\u5230\u5230\u8fbe\u4e00\u4e2a\u70b9\uff0c\u6709\u70b9\u50cf\u6e38\u620f<a href=\"https:\/\/en.wikipedia.org\/wiki\/Asteroids_(video_game)\">\u5c0f\u884c\u661f<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"954\" height=\"680\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image08.gif\" alt=\"\" class=\"wp-image-849\"\/><\/figure>\n\n\n\n<p>\u4f7f\u7528\u8fd9\u79cd\u65b0\u7684\u66f2\u7ebf\u8868\u793a\uff0c\u60a8\u53ef\u4ee5\u83b7\u53d6\u6d88\u606f\u5e76\u5c06\u5b83\u4eec\u8868\u793a\u4e3a\u66f2\u7ebf\u4e0a\u7684\u70b9\u3002\u60a8\u53ef\u4ee5\u60f3\u8c61\u63a5\u6536\u4e00\u6761\u6d88\u606f\u5e76\u5c06\u5176\u8bbe\u7f6e\u4e3a x \u5750\u6807\uff0c\u7136\u540e\u6c42\u89e3 y \u4ee5\u83b7\u5f97\u66f2\u7ebf\u4e0a\u7684\u4e00\u4e2a\u70b9\u3002\u5728\u5b9e\u8df5\u4e2d\u5b83\u6bd4\u8fd9\u7a0d\u5fae\u590d\u6742\u4e00\u4e9b\uff0c\u4f46\u8fd9\u662f\u4e00\u822c\u7684\u60f3\u6cd5\u3002<\/p>\n\n\n\n<p>\u4f60\u5f97\u5230\u79ef\u5206<\/p>\n\n\n\n<p>(70,6), (76,48), -, (82,6), (69,22)<\/p>\n\n\n\n<p>*x \u503c\u6ca1\u6709 65 \u7684\u5750\u6807\uff0c\u8fd9\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u662f\u53ef\u4ee5\u907f\u514d\u7684<\/p>\n\n\n\n<p>\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u7cfb\u7edf\u53ef\u4ee5\u901a\u8fc7\u9009\u62e9\u4e00\u4e2a\u7d20\u6570\u4f5c\u4e3a\u6700\u5927\u503c\u3001\u4e00\u4e2a\u66f2\u7ebf\u65b9\u7a0b\u548c\u66f2\u7ebf\u4e0a\u7684\u4e00\u4e2a\u516c\u5171\u70b9\u6765\u5b9a\u4e49\u3002\u79c1\u94a5\u662f\u4e00\u4e2a\u6570\u5b57<em>priv<\/em>\uff0c\u800c\u516c\u94a5\u662f\u70b9\u7f00\u7740\u81ea\u8eab<em>priv<\/em>\u65f6\u95f4\u7684\u516c\u5171\u70b9\u3002\u5728\u8fd9\u79cd\u5bc6\u7801\u7cfb\u7edf\u4e2d\u4ece\u516c\u94a5\u8ba1\u7b97\u51fa\u79c1\u94a5\u79f0\u4e3a\u692d\u5706\u66f2\u7ebf\u79bb\u6563\u5bf9\u6570\u51fd\u6570\u3002\u8fd9\u5c31\u662f\u6211\u4eec\u6b63\u5728\u5bfb\u627e\u7684\u9677\u95e8\u51fd\u6570\u3002<\/p>\n\n\n\n<p>\u692d\u5706\u66f2\u7ebf\u79bb\u6563\u5bf9\u6570\u662f\u652f\u6491\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u5b66\u7684\u96be\u9898\u3002\u5c3d\u7ba1\u8fdb\u884c\u4e86\u8fd1\u4e09\u5e74\u7684\u7814\u7a76\uff0c\u6570\u5b66\u5bb6\u4ecd\u7136\u6ca1\u6709\u627e\u5230\u4e00\u79cd\u7b97\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6539\u8fdb\u4e86\u5e7c\u7a1a\u7684\u65b9\u6cd5\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e0e\u56e0\u5f0f\u5206\u89e3\u4e0d\u540c\uff0c\u6839\u636e\u76ee\u524d\u7406\u89e3\u7684\u6570\u5b66\uff0c\u4f3c\u4e4e\u6ca1\u6709\u6377\u5f84\u53ef\u4ee5\u7f29\u5c0f\u57fa\u4e8e\u6b64\u95ee\u9898\u7684\u9677\u95e8\u51fd\u6570\u7684\u5dee\u8ddd\u3002\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u76f8\u540c\u5927\u5c0f\u7684\u6570\u5b57\uff0c\u6c42\u89e3\u692d\u5706\u66f2\u7ebf\u79bb\u6563\u5bf9\u6570\u6bd4\u5206\u89e3\u8981\u56f0\u96be\u5f97\u591a\u3002\u7531\u4e8e\u8ba1\u7b97\u91cf\u66f4\u5927\u7684\u96be\u9898\u610f\u5473\u7740\u66f4\u5f3a\u5927\u7684\u5bc6\u7801\u7cfb\u7edf\uff0c\u56e0\u6b64\u692d\u5706\u66f2\u7ebf\u5bc6\u7801\u7cfb\u7edf\u6bd4 RSA \u548c Diffie-Hellman \u66f4\u96be\u7834\u89e3\u3002<\/p>\n\n\n\n<p>\u8fd9\u662f\u692d\u5706\u66f2\u7ebf\u6570\u5b57\u7b7e\u540d\u7b97\u6cd5 ECDSA \u7684\u6838\u5fc3\u3002<a href=\"https:\/\/en.wikipedia.org\/wiki\/Elliptic_Curve_Digital_Signature_Algorithm\">\u6839\u636e\u7ef4\u57fa\u767e\u79d1<\/a>\uff0c\u5177\u4f53\u6b65\u9aa4\u6982\u8ff0\u5982\u4e0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"907\" height=\"197\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image12-1.png\" alt=\"\" class=\"wp-image-851\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image12-1.png 907w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image12-1-300x65.png 300w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image12-1-768x167.png 768w\" sizes=\"(max-width: 907px) 100vw, 907px\" \/><\/figure>\n\n\n\n<p>\u4e0e RSA \u76f8\u6bd4\uff0cECDSA \u6570\u5b57\u7b7e\u540d\u6709\u4e00\u4e2a\u7f3a\u70b9\uff0c\u5373\u5b83\u9700\u8981\u826f\u597d\u7684\u71b5\u6e90\u3002\u5982\u679c\u6ca1\u6709\u9002\u5f53\u7684\u968f\u673a\u6027\uff0c\u79c1\u94a5\u53ef\u80fd\u4f1a\u88ab\u6cc4\u9732\u3002Wikipedia \u7ee7\u7eed\u6307\u51fa\u201c\u4e0d\u4ec5\u8981\u6c42 k \u662f\u79d8\u5bc6\u7684\uff0c\u800c\u4e14\u4e3a\u4e0d\u540c\u7684\u7b7e\u540d\u9009\u62e9\u4e0d\u540c\u7684 k \u4e5f\u662f\u81f3\u5173\u91cd\u8981\u7684\uff0c\u5426\u5219\u6b65\u9aa4 6 \u4e2d\u7684\u65b9\u7a0b\u53ef\u4ee5\u6c42\u89e3 d_A\uff0c\u5373\u79c1\u94a5\u3002\u8fd9\u79cd\u653b\u51fb\u65b9\u6cd5<a href=\"https:\/\/web.archive.org\/web\/20160308014317\/http:\/\/www.nilsschneider.net\/2013\/01\/28\/recovering-bitcoin-private-keys.html\">\u65e9\u5728 2012 \u5e74\u5c31\u5df2\u88ab\u63cf\u8ff0<\/a>\u3002\u5982\u679c\u4f60\u78b0\u5de7\u91cd\u7528\u4e86k\uff0c\u5c31\u5f88\u5bb9\u6613\u89e3\u51fa\u79c1\u94a5\uff0c\u76f4\u63a5\u638f\u7a7a\u94b1\u5305\u3002<\/p>\n\n\n\n<h3>0x08 \u95e8\u9650\u7b7e\u540d<\/h3>\n\n\n\n<p>\u901a\u8fc7\uff08t, n\uff09\u95e8\u9650\u7b7e\u540d\uff0c\u5373\u53ef\u5c06\u4e00\u4e2a\u79d8\u5bc6\uff08\u79c1\u94a5\uff09\u5206\u6210n\u4efd\uff0c\u4efb\u610f t+1\u4e2a\u6210\u5458\u53ef\u4ee5\u901a\u8fc7\u591a\u8f6e\u4ea4\u4e92\uff0c\u5728\u4e0d\u91cd\u6784\u79c1\u94a5\u7684\u60c5\u51b5\u4e0b\uff0c\u751f\u6210\u4e00\u4e2a\u6709\u6548\u7684\u7b7e\u540d\u3002<\/p>\n\n\n\n<p>\u76ee\u524d\u4e3b\u8981\u91c7\u7528<a href=\"https:\/\/links.jianshu.com\/go?to=https%3A%2F%2Feprint.iacr.org%2F2019%2F114.pdf,\">GG18<\/a>,gg20\u95e8\u9650\u7b7e\u540d\u65b9\u6848\uff0c\u5176\u5bc6\u7801\u751f\u6210\u9636\u6bb5\u9700\u89815\u8f6e\u4ea4\u4e92\uff0c\u7b7e\u540d\u9636\u6bb5\u9700\u898110\u8f6e\u4ea4\u4e92\u3002<\/p>\n\n\n\n<h3>0x09 Nonce\u98ce\u9669<\/h3>\n\n\n\n<p>\u5982\u679c\u8be5\u540c\u4e00\u8d26\u6237\u7b7e\u540d\u7684\u4ea4\u6613\u62e5\u6709\u76f8\u540c\u7684 <a href=\"https:\/\/www.wikibit.us\/tk\/6182709245920.html\">RSV<\/a> \u7b7e\u540d\u7684 r \u503c\uff0c\u7b7e\u540d\u8fc7\u7a0b\u4f7f\u7528\u4e86\u76f8\u540c\u7684\u968f\u673a\u6570 k\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"349\" height=\"82\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image09.jpg\" alt=\"\" class=\"wp-image-852\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image09.jpg 349w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image09-300x70.jpg 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"510\" height=\"93\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image10.jpg\" alt=\"\" class=\"wp-image-853\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image10.jpg 510w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image10-300x55.jpg 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\">#\u5bf9\u4e8e\u7b7e\u540d: \u9009\u62e9\u968f\u673a\u6570$k$, \u8ba1\u7b97$R = kG, r = R_x, s = k ^ {-1}(z + rd_A)$, \u5bf9\u4e8e\u4e24\u4e2a\u91c7\u7528\u76f8\u540c\u968f\u673a\u6570\u7684\u7b7e\u540d\uff1a$(r, s)$ \u548c $(r, s')$,  \u5bf9\u5e94\u7684\u7b7e\u540d\u6d88\u606f\u5206\u522b\u4e3a\uff1a$z$ \u548c $z'$, &nbsp; \u53ef\u4ee5\u5f97\u5230\uff1a<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"498\" height=\"296\" src=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image11.png\" alt=\"\" class=\"wp-image-854\" srcset=\"http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image11.png 498w, http:\/\/www.selinuxplus.com\/wp-content\/uploads\/2022\/02\/image11-300x178.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/figure>\n\n\n\n<h3>0x10 \u5178\u578b\u7684 MPC <\/h3>\n\n\n\n<p>\u591a\u65b9\u5b89\u5168\u8ba1\u7b97 MPC\uff0cMulti-party Computation<\/p>\n\n\n\n<p>\u5728\u94fe\u6865\u673a\u5236\u4e2d\uff0c\u8de8\u94fe\u8d44\u4ea7\u662f\u6709\u9501\u5b9a\u8d26\u6237\u4fdd\u7ba1\uff0c\u800c\u9501\u5b9a\u8d26\u6237\u5219\u662f\u6709N\u4e2a\u533f\u540d\u8282\u70b9\u7ecf\u8fc7\u591a\u65b9\u8ba1\u7b97\uff08MPC\uff09\u7684\u65b9\u5f0f\u5171\u540c\u7ba1\u7406\u3002\u5728\u9501\u5b9a\u8d26\u6237\u7b7e\u540d\u8fc7\u7a0b\u4e2d\uff0cR\u503c\u662f\u901a\u8fc7N\u4e2aMPCNode\u8282\u70b9\u901a\u8fc7\u53ef\u9a8c\u8bc1\u79d8\u5bc6\u5206\u4eabPVSS\u5171\u540c\u51b3\u5b9a\uff0c\u4fdd\u8bc1\u4e0d\u4f1a\u53d1\u751f\u4e24\u5e01\u4ea4\u6613\u7b7e\u540d\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>1\u3001\u5404Node\u8282\u70b9\u5728\u672c\u5730\u901a\u8fc7\u771f\u968f\u673a\u6570\u53d1\u751f\u5668\u751f\u6210\u4e00\u4e2a\u968f\u673a\u6570<\/p>\n\n\n\n<p>2\u3001\u5404Node\u8282\u70b9\u5c06\u8fdb\u884cShamir\u79d8\u5bc6\u5206\u4eab\uff0c\u5e76\u5c06\u79d8\u5bc6\u788e\u7247\u901a\u8fc7\u5b89\u5168\u4fe1\u9053\u4f20\u8f93\u7ed9\u5176\u4ed6\u8282\u70b9<\/p>\n\n\n\n<p>3\u3001\u6536\u5230\u5176\u4ed6\u8282\u70b9\u4f20\u8f93\u7684\u79d8\u5bc6\u788e\u7247\u540e\uff0c\u5404Node\u8282\u70b9\u5728\u672c\u5730\u8fdb\u884c\u7d2f\u52a0\uff0c\u5f97\u5230\u4e00\u7ec4\u79d8\u5bc6\u788e\u7247\uff0c\u7136\u540e\u5c06\u8be5\u7ec4\u79d8\u5bc6\u788e\u7247\u4e0e\u692d\u5706\u66f2\u7ebf\u57fa\u70b9\u76f8\u4e58\uff0c\u5e76\u5c06\u7ed3\u679c\u5e7f\u64ad\u3002<\/p>\n\n\n\n<p>4\u3001\u5404Node\u8282\u70b9\u5bf9\u5e7f\u64ad\u7684\u6570\u636e\u8fdb\u884c\u62c9\u683c\u6717\u65e5\u63d2\u503c\u8ba1\u7b97\uff0c\u5f97\u5230\u4e00\u4e2a\u692d\u5706\u66f2\u7ebf\u70b9\uff0c\u5176\u6a2a\u5750\u6807\u5373\u4e3aR\u503c\u3002<\/p>\n\n\n\n<p>\u9996\u5148\uff0cR \u503c\u662f\u6709 N\u5404 \u8282\u70b9\u5171\u540c\u786e\u5b9a\u7684\uff0c\u800c\u4e0d\u662f\u7531\u5355\u4e00\u8282\u70b9\u786e\u5b9a\uff0c\u7406\u8bba\u4e0a\u53ea\u8981 N\u4e2a \u8282\u70b9\u4e2d\u5b58\u5728 1 \u4e2a\u8bda\u5b9e\u8282\u70b9\uff0c\u90a3\u4e48 R \u503c\u5c31\u662f\u968f\u673a\u7684\uff1b\u5176\u6b21\uff0c\u5404\u8282\u70b9\u5bf9 R \u503c\u8d21\u732e\u7684\u90e8\u5206\u662f\u901a\u8fc7\u771f\u968f\u673a\u6570\u53d1\u751f\u5668\u4ea7\u751f\u7684\uff0c\u5206\u5e03\u8db3\u591f\u5747\u5300\u3002<\/p>\n\n\n\n<p>k \u662f\u7531 N\u4e2aNode \u8282\u70b9\u5171\u540c\u51b3\u5b9a\uff0c\u4f46\u662f\u7531\u4e8e\u79d8\u5bc6\u788e\u7247\u662f\u901a\u8fc7\u5b89\u5168\u4fe1\u9053\u4f20\u8f93\u7ed9\u5404\u8282\u70b9\uff0c\u56e0\u6b64\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u8282\u70b9\u80fd\u591f\u6062\u590d\u51fa\u5b8c\u6574\u7684 k \u503c\u3002\u4e5f\u5c31\u662f\u8bf4\uff0ck \u503c\u662f\u4ec5\u4ec5\u662f\u4e00\u79cd\u7406\u8bba\u4e2d\u7684\u5b58\u5728\uff0c\u80fd\u591f\u6b63\u5e38\u5b8c\u6210 MPC \u7b7e\u540d\u8fc7\u7a0b\uff0c\u4f46\u662f\u786e\u5b9e\u4efb\u4f55\u4eba\u90fd\u4e0d\u53ef\u89c1\u7684\u3002<\/p>\n\n\n\n<h3>0x11 anyswap\u7684\u89e3\u51b3<\/h3>\n\n\n\n<p>1\u3001\u907f\u514dR\u91cd\u590d [<a href=\"https:\/\/github.com\/anyswap\/Anyswap-MPCNode\/commit\/31f94ff2c8fac19549f6c82b849977730f63bd63\">https:\/\/github.com\/anyswap\/Anyswap-MPCNode\/commit\/31f94ff2c8fac19549f6c82b849977730f63bd63<\/a>]<\/p>\n\n\n\n<p>2\u3001\u5386\u53f2\u7684\u7b7e\u540d\u4f1a\u4fdd\u5b58\u5728\u6570\u636e\u5e93\u4e2d\uff0c\u65b0\u751f\u6210\u7684\u7b7e\u540d\u968f\u673a\u6570\u5224\u65ad\u662f\u5426\u91cd\u590d[<a href=\"https:\/\/github.com\/anyswap\/CrossChain-Router\/commit\/ac88cc6861d98645fcdc19d8b985689dd54f5c22\">https:\/\/github.com\/anyswap\/CrossChain-Router\/commit\/ac88cc6861d98645fcdc19d8b985689dd54f5c22<\/a>]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>0x01 \u9677\u95e8\u51fd\u6570 trapdoor 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