{"id":901,"date":"2026-02-07T09:15:37","date_gmt":"2026-02-07T09:15:37","guid":{"rendered":"http:\/\/www.selinuxplus.com\/?p=901"},"modified":"2026-02-07T09:15:37","modified_gmt":"2026-02-07T09:15:37","slug":"fhe-%e5%85%a8%e5%90%8c%e6%80%81%e5%8a%a0%e5%af%86%ef%bc%88fully-homomorphic-encryption%ef%bc%89","status":"publish","type":"post","link":"http:\/\/www.selinuxplus.com\/?p=901","title":{"rendered":"FHE \/ \u5168\u540c\u6001\u52a0\u5bc6\uff08Fully Homomorphic Encryption\uff09"},"content":{"rendered":"\n<p> <a href=\"https:\/\/x.com\/0xTodd\/status\/1810989860620226900\/photo\/1\"><\/a> \u90a3\u4e48 FHE \u5230\u5e95\u662f\u4e00\u95e8\u4ec0\u4e48\u6280\u672f\uff1f <\/p>\n\n\n\n<p><strong>1. \u4ec0\u4e48\u662f\u52a0\u5bc6\uff1f<\/strong> <\/p>\n\n\n\n<p>\u666e\u901a\u7684\u52a0\u5bc6\u5927\u5bb6\u6700\u719f\u6089\u3002<\/p>\n\n\n\n<p>\u4e3e\u4e2a\u4f8b\u5b50\uff0cAlice \u8981\u53d1\u4e2a\u53e3\u4fe1\u7ed9 Bob\uff0c\u6bd4\u5982\u8981\u53d1\u4e2a \u201c1314 520\u201d\u3002 \u5982\u679c\u73b0\u5728\uff0c\u65e2\u8981\u7b2c\u4e09\u65b9 C \u6765\u9001\u4fe1\uff0c\u53c8\u8981\u505a\u5230\u4fe1\u606f\u4fdd\u5bc6\uff0c\u90a3\u4e48\u5f88\u7b80\u5355\u2014\u2014\u53ea\u9700\u8981\u5c06\u6bcf\u4e2a\u6570\u5b57 x2 \u6765\u52a0\u5bc6\uff0c\u6bd4\u5982\u53d8\u6210 \u201c2628 1040\u201d\u5373\u53ef\u3002 <\/p>\n\n\n\n<p>\u5f53 Bob \u6536\u5230\u540e\uff0c\u5c06\u6bcf\u4e2a\u6570\u5b57\u4f9d\u6b21\u9664 2\uff0c\u5c31\u89e3\u5bc6\u51fa\u4e86\u539f\u6765 Alice \u5728\u8bf4 \u201c1314 520\u201d\u3002<\/p>\n\n\n\n<p> \u770b\u5230\u4e86\u4e48\uff0c\u4e24\u4eba\u901a\u8fc7\u5bf9\u79f0\u52a0\u5bc6\uff0c\u5728\u65e2\u8981\u96c7 C \u51fa\u529b\u5374\u53c8\u8981 C \u4e0d\u77e5\u9053\u4fe1\u606f\u7684\u60c5\u51b5\u4e0b\uff0c\u5b8c\u6210\u4e86\u4fe1\u606f\u4f20\u9012\u3002<\/p>\n\n\n\n<p>\u4e00\u822c\uff0c\u8c0d\u6218\u7247\u91cc\uff0c\u4e24\u4e2a\u8054\u7edc\u5458\u76f8\u4e92\u901a\u4fe1\u5927\u62b5\u4e0d\u4f1a\u8d85\u8fc7\u8fd9\u4e2a\u8303\u7574\u3002 <\/p>\n\n\n\n<p><a href=\"https:\/\/x.com\/0xTodd\/status\/1810989860620226900\/photo\/2\"><\/a><strong>2. \u90a3\u4ec0\u4e48\u662f\u540c\u6001\u52a0\u5bc6\u5462\uff1f<\/strong> <\/p>\n\n\n\n<p>\u73b0\u5728 Alice \u7684\u9700\u6c42\u96be\u5ea6\u5347\u7ea7\u4e86\uff1a <\/p>\n\n\n\n<ul><li>\u6bd4\u5982 Alice \u53ea\u6709 7 \u5c81\uff1b <\/li><li>Alice \u53ea\u4f1a\u7b97 x2 \u548c \u00f72 \u8fd9\u6837\u6700\u7b80\u5355\u7684\u7b97\u672f\uff0c\u5176\u4ed6\u8fd0\u7b97\u5219\u4e00\u6982\u4e0d\u61c2\u3002<\/li><\/ul>\n\n\n\n<p>\u597d\uff0c\u90a3\u73b0\u5728\u5047\u8bbe Alice \u8981\u4ea4\u7535\u8d39\u4e86\uff0cAlice \u5bb6\u6bcf\u6708\u7535\u8d39\u662f 400 \u5143\uff0c\u4e00\u5171\u62d6\u6b20\u4e86 12 \u4e2a\u6708\u3002 \u7136\u800c\uff0c400*12= \u51e0\uff0c\u8fd9\u9053\u9898\u76ee\u8d85\u8fc7\u4e86\u5e74\u4ec5 7 \u5c81\u7684 Alice \u7684\u8ba1\u7b97\u8303\u56f4\uff0c\u5979\u4e0d\u4f1a\u8fd9\u4e48\u590d\u6742\u7684\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p> \u4f46\u662f\uff0c\u5979\u4e0d\u60f3\u8ba9\u522b\u4eba\u77e5\u9053\u5979\u5bb6\u7535\u8d39\u591a\u5c11\u94b1 \/ \u51e0\u4e2a\u6708\uff0c\u56e0\u4e3a\u8fd9\u662f\u654f\u611f\u4fe1\u606f\u3002 \u56e0\u6b64\uff0cAlice \u5728\u4e0d\u4fe1\u4efb C \u7684\u60c5\u51b5\u4e0b\uff0c\u62dc\u6258 C \u6765\u5e2e\u5fd9\u8ba1\u7b97\u3002 \u56e0\u4e3a\u5979\u53ea\u4f1a x2 \u00f72\uff0c\u56e0\u6b64\u5979\u4f7f\u7528 x2 \u4e58\u6cd5\u7ed9\u5979\u7684\u6570\u5b57\u505a\u4e86\u7b80\u5355\u7684\u52a0\u5bc6\uff0c\u4e8e\u662f\uff0c\u5979\u544a\u8bc9 C\uff0c\u8ba9 C \u8ba1\u7b97 800&#215;24= \u591a\u5c11\uff0c\u5373\uff1a\uff08400&#215;2\uff09\u4e58\uff0812&#215;2\uff09\u3002 <\/p>\n\n\n\n<p>C \u662f\u6210\u5e74\u4eba\uff0c<strong>\u62e5\u6709\u5f3a\u5927\u7684\u8ba1\u7b97\u8111\u529b<\/strong>\uff0c\u5f88\u5feb\u5c31\u53e3\u7b97\u51fa\u4e86 800*24=19200\uff0c\u5e76\u4e14\u628a\u6570\u5b57\u544a\u8bc9\u4e86 Alice\u3002\u7136\u540e\uff0cAlice \u5c06\u7ed3\u679c\uff0c\u4e5f\u5c31\u662f 19200\u00f72\u00f72\uff0c\u5f88\u5feb\u5c31\u77e5\u9053\u539f\u6765\u81ea\u5df1\u8981\u7f34\u7eb3 4800 \u5143\u6c34\u8d39\u3002 <\/p>\n\n\n\n<p>\u770b\u5230\u4e86\u4e48\uff1f\u8fd9\u5c31\u662f\u6700\u7b80\u5355\u7684\u4e00\u4e2a\u4e58\u6cd5\u540c\u6001\u52a0\u5bc6\uff0c800*24 \u53ea\u662f 400*12 \u7684\u6620\u5c04\uff0c\u53d8\u5e7b\u524d\u540e\u5b9e\u9645\u4e0a\u5f62\u6001\u662f\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u79f0\u4e4b\u4e3a\u201c\u540c\u6001\u201d\u3002<\/p>\n\n\n\n<p> \u8fd9\u6837\u7684\u52a0\u5bc6\u65b9\u5f0f\u5b9e\u73b0\u4e86\uff1a<strong>\u67d0\u4eba\u8981\u59d4\u6258\u4e00\u4e2a\u4e0d\u4fe1\u4efb\u7684\u5b9e\u4f53\u8ba1\u7b97\u7ed3\u679c\uff0c\u5374\u80fd\u4fdd\u8bc1\u81ea\u5df1\u7684\u654f\u611f\u6570\u5b57\u4e0d\u6cc4\u9732\u3002<\/strong><\/p>\n\n\n\n<p><strong>3. \u90a3\u4e3a\u4ec0\u4e48\u201c\u540c\u6001\u52a0\u5bc6\u201d\u8fd8\u8981\u201c\u5168\u201d\u5462\uff1f<\/strong> <\/p>\n\n\n\n<p>\u521a\u521a\u53ea\u662f\u7406\u60f3\u4e16\u754c\u91cc\u7684\u95ee\u9898\uff0c\u73b0\u5b9e\u4e16\u754c\u4e0a\u7684\u95ee\u9898\u5e76\u6ca1\u6709\u8fd9\u4e48\u7b80\u5355\uff0c\u4e0d\u662f\u6240\u6709\u4eba\u90fd\u662f 7 \u5c81\uff0c\u6216\u8005\u90fd\u50cf C \u90a3\u4e48\u8001\u5b9e\u3002 <\/p>\n\n\n\n<p>\u6211\u4eec\u5047\u8bbe\u4e00\u79cd<strong>\u5f88\u574f\u7684\u60c5\u51b5<\/strong>\uff0c\u6bd4\u5982 C \u53ef\u80fd\u4f1a\u5c1d\u8bd5\u53cd\u63a8\uff0cC \u901a\u8fc7\u7a77\u4e3e\u6cd5\u4e5f\u80fd\u7834\u8bd1\u51fa Alice \u8981\u8ba1\u7b97\u7684\u662f 400 \u548c 12\u3002 <\/p>\n\n\n\n<p><strong>\u8fd9\u65f6\u5019\uff0c\u5c31\u9700\u8981\u201c\u5168\u540c\u6001\u52a0\u5bc6\u201d\u6765\u89e3\u51b3\u3002<\/strong><\/p>\n\n\n\n<p> Alice \u7ed9\u6bcf\u4e2a\u6570\u5b57\u90fd\u00d72\uff0c\u8fd9\u4e2a 2 \u53ef\u4ee5\u89c6\u4f5c\u4e00\u4e2a\u566a\u58f0\u3002\u566a\u58f0\u592a\u5c11\uff0c\u5c31\u5bb9\u6613\u88ab C \u7834\u89e3\u3002 \u6240\u4ee5\uff0cAlice \u53ef\u4ee5\u5728\u4e58\u6cd5\u57fa\u7840\u4e0a\uff0c\u518d\u5f15\u5165\u4e00\u9053\u52a0\u6cd5\u3002 \u5f53\u7136\uff0c\u6700\u597d\u8fd9\u4e2a\u566a\u58f0\u72b9\u5982\u65e9\u4e5d\u70b9\u7684\u4e3b\u5e72\u9053\u5341\u5b57\u8def\u53e3\uff0c\u90a3\u4e48 C \u7684\u7834\u89e3\u96be\u5ea6\u5c31\u6bd4\u767b\u5929\u8fd8\u96be\u3002 \u6240\u4ee5\uff0cAlice \u53ef\u4ee5\u518d\u4e58 4 \u6b21\uff0c\u52a0 8 \u6b21\uff0c\u8fd9\u6837 C \u7834\u89e3\u6982\u7387\u5c31\u5927\u5e45\u964d\u4f4e\u4e86\u3002<\/p>\n\n\n\n<p> \u7136\u800c\uff0c\u8fd9\u6837 Alice \u4ecd\u7136\u53ea\u662f\u201c\u90e8\u5206\u201d\u540c\u6001\u52a0\u5bc6\uff0c\u5373\uff1a <\/p>\n\n\n\n<p>\uff081\uff09\u5979\u52a0\u5bc6\u5185\u5bb9\u53ea\u80fd\u9488\u5bf9\u7279\u5b9a\u90e8\u5206\u95ee\u9898\uff1b <\/p>\n\n\n\n<p>\uff082\uff09\u5979\u53ea\u80fd\u4f7f\u7528\u7279\u5b9a\u90e8\u5206\u8fd0\u7b97\u6cd5\u5219\uff0c\u56e0\u4e3a\u52a0\u6cd5\u4e58\u6cd5\u6b21\u6570\u4e0d\u53ef\u592a\u591a\uff08\u4e00\u822c\u4e0d\u80fd\u8d85\u8fc7 15 \u6b21\uff09\u3002<\/p>\n\n\n\n<p> \u800c\u201c\u5168\u201d\u7684\u610f\u601d\u662f\u8bf4\uff0c\u8981\u5141\u8bb8 Alice \u9488\u5bf9\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u80fd\u591f\u505a\u52a0\u6cd5\u52a0\u5bc6\u4efb\u610f\u6b21\uff0c\u505a\u4e58\u6cd5\u52a0\u5bc6\u4efb\u610f\u6b21\uff0c\u8fd9\u6837\u59d4\u6258\u7b2c\u4e09\u65b9\u5b8c\u5168\u8ba1\u7b97\uff0c\u89e3\u5bc6\u540e\u8fd8\u80fd\u5f97\u5230\u6b63\u786e\u7ed3\u679c\u3002 \u4e00\u4e2a\u8d85\u7ea7\u957f\u7684\u591a\u9879\u5f0f\uff0c\u51e0\u4e4e\u53ef\u4ee5\u8868\u8fbe\u4e16\u754c\u4e0a\u7edd\u5927\u90e8\u5206\u7684\u6570\u5b66\u95ee\u9898\uff0c\u800c\u4e0d\u4ec5\u4ec5\u8ba1\u7b97\u7535\u8d39\u8fd9\u79cd 7 \u5c81\u5c0f\u670b\u53cb\u7684\u95ee\u9898\u3002 \u518d\u52a0\u5957\u4e0a\u4e86\u4efb\u610f\u6b21\u7684\u52a0\u5bc6\uff0c<\/p>\n\n\n\n<p><strong>\u4ece\u6839\u672c\u4e0a\u5c31\u51e0\u4e4e\u675c\u7edd\u4e86 C \u60f3\u8981\u7aa5\u63a2\u9690\u79c1\u6570\u636e\u7684\u53ef\u80fd\u6027\uff0c\u771f\u6b63\u5b9e\u73b0\u4e86\u201c\u65e2\u8981\u53c8\u8981\u201d\u3002<\/strong><\/p>\n\n\n\n<p> \u56e0\u6b64\uff0c\u201c\u5168\u540c\u6001\u52a0\u5bc6\u201d\u8fd9\u95e8\u6280\u672f\uff0c\u4e00\u76f4\u662f\u52a0\u5bc6\u5b66\u5723\u676f\u4e0a\u7684\u4e00\u9897\u660e\u73e0\u3002 \u4e8b\u5b9e\u4e0a\uff0c\u540c\u6001\u52a0\u5bc6\u8fd9\u95e8\u6280\u672f\u4e00\u76f4\u5230 2009 \u5e74\u4e4b\u524d\uff0c\u90fd\u53ea\u652f\u6301\u201c\u90e8\u5206\u540c\u6001\u52a0\u5bc6\u201d\u3002 \u800c 2009 \u5e74 Gentry \u7b49\u5b66\u8005\u63d0\u51fa\u7684\u65b0\u601d\u8def\uff0c\u624d\u6253\u5f00\u4e86\u5168\u540c\u6001\u52a0\u5bc6\u53ef\u80fd\u6027\u7684\u5927\u95e8\u3002<\/p>\n\n\n\n<p> <a href=\"https:\/\/x.com\/0xTodd\/status\/1810989860620226900\/photo\/4\"><\/a><strong>\u5f88\u591a\u670b\u53cb\u5bf9\u8fd9\u95e8\u6280\u672f\u7684\u5e94\u7528\u573a\u666f\uff0c\u4ecd\u7136\u62b1\u6709\u7591\u60d1\uff0c\u4ec0\u4e48\u573a\u666f\u4f1a\u9700\u8981\u4f7f\u7528\u5168\u540c\u6001\u52a0\u5bc6 (FHE) \u6280\u672f\u5462\uff1f<\/strong> <\/p>\n\n\n\n<p>\u6bd4\u5982\u8bf4\u2014\u2014AI\u3002 \u5927\u5bb6\u90fd\u77e5\u9053\uff0c\u4e00\u4e2a\u5f3a\u608d\u7684 AI \u9700\u8981\u8db3\u591f\u591a\u7684\u6570\u636e\u5582\u517b\uff0c\u4f46\u504f\u504f\u5f88\u591a\u6570\u636e\u7684\u9690\u79c1\u4ef7\u503c\u53c8\u592a\u9ad8\u3002\u90a3\u4e48\u80fd\u4e0d\u80fd\u901a\u8fc7 FHE \u5b9e\u73b0\u8fd9\u4e2a\u95ee\u9898\u7684\u201c\u65e2\u8981\u53c8\u8981\u201d\u5462\uff1f <\/p>\n\n\n\n<p><strong>\u7b54\u6848\u662f\u53ef\u4ee5\u7684\u3002<\/strong><\/p>\n\n\n\n<p> \u4f60\u53ef\u4ee5\uff1a <\/p>\n\n\n\n<p>\uff081\uff09\u628a\u4f60\u7684\u654f\u611f\u6570\u636e\u6309\u7167 FHE 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\uff084\uff09\u4f60\u5927\u53ef\u4ee5\u65ad\u5f00\u7f51\u7edc\uff0c\u5728\u672c\u5730\u4ece\u5bb9\u89e3\u5bc6\u8fd9\u4e9b\u4e71\u7801\uff0c\u5c31\u50cf Alice \u4e00\u6837\uff1b <\/p>\n\n\n\n<p>\uff085\uff09\u8fdb\u800c\uff0c\u4f60\u5b9e\u73b0\u4e86\uff1a<strong>\u8ba9 AI \u5bf9\u4f60\u7684\u654f\u611f\u6570\u636e\u5b8c\u5168\u4e0d\u7ecf\u624b\u7684\u6761\u4ef6\u4e0b\uff0c\u8fd0\u7528\u5e9e\u5927\u7b97\u529b\u5e2e\u4f60\u5b8c\u6210\u4e86\u8ba1\u7b97\u3002<\/strong> \u800c\u73b0\u5728\u7684 AI \u5219\u505a\u4e0d\u5230\u8fd9\u70b9\uff0c\u5fc5\u987b\u653e\u5f03\u9690\u79c1\u624d\u884c\uff0c\u60f3\u60f3\u4f60\u660e\u6587\u8f93\u5165\u7ed9 GPT \u7684\u4e00\u5207\u5427\uff01\u8981\u5b9e\u73b0\u8fd9\u4e2a\uff0c\u975e FHE \u4e0d\u53ef\u3002<\/p>\n\n\n\n<p> \u8fd9\u5c31\u662f AI \u548c FHE \u5929\u751f\u5951\u5408\u7684\u6839\u6e90\uff0c\u5343\u8a00\u4e07\u8bed\u5316\u6210\u4e00\u4e2a\u8bcd\uff1a\u65e2\u8981\u53c8\u8981\u3002 \u7531\u4e8e FHE \u548c AI 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