{"id":38380,"date":"2020-02-13T00:00:23","date_gmt":"2020-02-12T16:00:23","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=38380"},"modified":"2022-01-03T21:33:53","modified_gmt":"2022-01-03T13:33:53","slug":"%e5%af%86%e7%a2%bc%e5%ad%b8%e7%9a%84%e5%8f%8d%e6%93%8a","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=38380","title":{"rendered":"\u5bc6\u78bc\u5b78\u7684\u53cd\u64ca"},"content":{"rendered":"
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\"\u5bc6\u78bc\u5b78\u7684\u53cd\u64ca\"<\/div>\n<\/div>\n
\n
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\u7de8\u8b6f\uff0f\u738b\u660a\u8b19<\/strong><\/p>\n

\u55ae\u5411\u51fd\u6578<\/strong><\/p>\n

RSA\u52a0\u5bc6\u6f14\u7b97\u6cd5<\/a>\uff08Rivest\u2013Shamir\u2013Adleman\uff0c\u4e09\u4f4d\u5275\u59cb\u4eba\u7684\u59d3\u6c0f\uff09\u7684\u539f\u7406\u662f\u6bcf\u500b\u4f7f\u7528\u8005\u7522\u751f\u4e00\u5c0d\u516c\u9470\uff08public key\uff09\u548c\u79c1\u9470\uff08private key\uff09\uff0c\u900f\u904e\u516c\u9470\u52a0\u5bc6\u7684\u8a0a\u606f\u53ef\u4ee5\u4e14\u53ea\u80fd\u900f\u904e\u79c1\u9470\u4f86\u89e3\u5bc6\uff0c\u4f46\u5f88\u96e3\u5f9e\u516c\u9470\u63a8\u5f97\u79c1\u9470\u3002\u56e0\u6b64\uff0c\u82e5Alice\u8981\u5c07\u4e00\u5247\u8a0a\u606f\u50b3\u7d66Bob\uff0c\u5b83\u53ea\u9700\u8981\u5c07\u6b64\u8a0a\u606f\u7528Bob\u7684\u516c\u9470\u52a0\u5bc6\uff0cBob\u5c31\u53ef\u4ee5\u7528\u81ea\u5df1\u7684\u79c1\u9470\u89e3\u5bc6\u3002\u7aca\u807d\u8005Eve\u5373\u4fbf\u7372\u5f97\u8a0a\u606f\uff0c\u4e5f\u7121\u6cd5\u53ea\u900f\u904eBob\u7684\u516c\u9470\u76f4\u63a5\u89e3\u5bc6\u6216\u63a8\u7b97\u79c1\u9470\u3002<\/p>\n

\u516c\u9470\u8207\u79c1\u9470\u7684\u7522\u751f\u65b9\u5f0f\u5982\u4e0b\uff1a\u7531\u4f7f\u7528\u8005\u9078\u64c7\u5169\u500b\u6975\u5927\u7684\u8cea\u6578\u200bp<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u548c\u200bq<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u8a08\u7b97\u5169\u8005\u7684\u7a4d\uff08\u200bN<\/span>=<\/span>p<\/span>q<\/span><\/span><\/span><\/span><\/span>\u200b\uff09\u5f8c\uff0c\u5229\u7528\u200bN<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u3001\u200bp<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u3001\u200bq<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u4f86\u7522\u751f\u516c\u9470\u548c\u79c1\u9470\u3002\u5176\u4e2dN<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u4f34\u96a8\u516c\u9470\u767c\u5e03\uff08\u52a0\u5bc6\u904e\u7a0b\u9700\u8981\u7528\u5230\uff09\uff0cp<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u548c\u200bq<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5247\u5728\u516c\u9470\u548c\u79c1\u9470\u7522\u751f\u5f8c\u92b7\u6bc0\u3002\u7406\u8ad6\u4e0a\uff0cEve\u82e5\u53ef\u4ee5\u5c07N<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u8cea\u56e0\u6578\u5206\u89e3\u6210p<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u548c\u200bq<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5c31\u53ef\u4ee5\u5f9e\u516c\u9470\u56de\u63a8\u79c1\u9470\uff1b\u4f46\u5be6\u969b\u4e0a\u4e4b\u6240\u4ee5\u5f88\u96e3\u9054\u6210\uff0c\u662f\u56e0\u70ba\u76ee\u524d\u4e26\u6c92\u6709\u4e00\u500b\u53ef\u4ee5\u5728\u6709\u9650\u6642\u9593\u5167\u5b8c\u6210\u5927\u6578\u8cea\u56e0\u6578\u5206\u89e3\u7684\u6f14\u7b97\u6cd5\uff0c\u56e0\u6b64\u53ea\u8981N<\/span><\/span><\/span><\/span><\/span><\/span>\u5920\u5927\uff0cRSA\u52a0\u5bc6\u662f\u5e7e\u4e4e\u4e0d\u53ef\u80fd\u88ab\u7834\u89e3\u7684\u3002<\/p>\n

\u5229\u7528\u67d0\u4e9b\u96e3\u4ee5\u53cd\u5411\u8a08\u7b97\u7684\u51fd\u6578\uff08\u4f8b\u5982\u96e3\u4ee5\u5f9e\u516c\u9470\u56de\u63a8\u79c1\u9470\uff09\uff0c\u6211\u5011\u5f97\u4ee5\u5229\u7528\u300c\u9677\u9580\u55ae\u5411\u51fd\u6578\u300d\uff08trapdoor one-way function\uff09\u9054\u5230\u52a0\u5bc6\u7684\u76ee\u7684\u3002\u7136\u800c\u4e00\u4e9b\u50b3\u7d71\u7684\u52a0\u5bc6\u6f14\u7b97\u6cd5\u56e0\u70ba\u91cf\u5b50\u96fb\u8166\u7684\u51fa\u73fe\u800c\u8b8a\u5f97\u4e0d\u518d\u53ef\u9760\uff0c\u4f8b\u5982\u9ebb\u7701\u7406\u5de5\u5b78\u9662\u6578\u5b78\u5bb6Peter Shor\u65bc1994\u5e74\u6240\u63d0\u51fa\u7684\u6f14\u7b97\u6cd5<\/a>\u4fbf\u53ef\u5728\u91cf\u5b50\u96fb\u8166\u4e0a\u7834\u89e3RSA\u52a0\u5bc6\u3002\u5bc6\u78bc\u5b78\u5bb6\u65bc\u662f\u958b\u59cb\u5c0b\u627e\u5f8c\u91cf\u5b50\u6642\u4ee3\u7684\u66ff\u4ee3\u65b9\u6848\uff0c\u4ee5\u4e0b\u7c21\u55ae\u4ecb\u7d39\u5176\u4e2d\u5169\u500b\u5019\u9078\u9078\u9805\u2500\u2500\u7db2\u683c\u52a0\u5bc6\uff08lattice-cryptography\uff09\u8207\u932f\u8aa4\u6821\u6b63\u78bc\uff08error correcting code\uff09\u3002<\/p>\n

\u7db2\u683c\u52a0\u5bc6<\/strong><\/p>\n

\u683c\u52a0\u5bc6\u662f\u5229\u7528\u9023\u91cf\u5b50\u96fb\u8166\u90fd\u7121\u6cd5\u6709\u6548\u89e3\u6c7a\u7684\u7db2\u683c\u554f\u984c\uff08Lattice problem\uff09<\/a>\u3002\u6240\u8b02\u7db2\u683c\uff0c\u662f\u7531\u4e00\u7d44\u4e92\u76f8\u7368\u7acb\u7684\u5411\u91cf\uff08\u7a31\u70ba\u300c\u57fa\u5e95\u300d\uff0cbasis\uff09\uff0c\u900f\u904e\u6574\u6578\u500d\u7684\u7dda\u6027\u7d44\u5408\u6240\u5f35\u958b\u7684\u7a7a\u9593\u3002\u4f8b\u5982\u4e0b\u5716\u4e2d\u6bcf\u500b\u7da0\u8272\u683c\u9ede\u90fd\u53ef\u4ee5\u57fa\u5e95\u5411\u91cf\u6574\u6578\u500d\u7684\u7dda\u6027\u7d44\u5408\u8868\u793a\u3002\u540c\u4e00\u7db2\u683c\u7684\u57fa\u5e95\u4e26\u4e0d\u552f\u4e00\uff0c\u5982\u4e0b\u5716\u7684\u7db2\u683c\u53ef\u4ee5\u4ee5\u200bb<\/span>1<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u8207\u200bb<\/span>2<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u70ba\u57fa\u5e95\uff0c\u4e5f\u53ef\u4ee5\u662f\u200bb<\/span>\u2032<\/span>1<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u8207 \u200bb<\/span>\u2032<\/span>2<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\uff0c\u7136\u800c\u67d0\u4e9b\u57fa\u5e95\u5411\u91cf\uff08\u5982\u5de6\u5716\uff0c\u53ef\u4f5c\u70ba\u79c1\u9470\uff09\u6bd4\u8f03\u5bb9\u6613\u63a8\u7b97\u51fa\u7db2\u683c\u9ede\u7684\u4f4d\u7f6e\uff0c\u4f8b\u5982\u5de6\u5716\u539f\u9edeO\u5230\u6a58\u8272\u7bad\u982d\u8655\u7684\u5411\u91cf\uff0c\u6211\u5011\u53ef\u4ee5\u5f88\u76f4\u89ba\u5730\u770b\u51fa\u662f1\u500db<\/span>1<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u82071\u500d\u200bb<\/span>2<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u548c\uff1b\u4f46\u5c0d\u65bc\u5176\u4ed6\u57fa\u5e95\u800c\u8a00\uff08\u5982\u53f3\u5716\u5e7e\u4e4e\u76f8\u4e92\u5e73\u884c\uff0c\u53ef\u4f5c\u70ba\u516c\u9470\uff09\uff0c\u9019\u9805\u4efb\u52d9\u4fbf\u6c92\u6709\u90a3\u9ebc\u7c21\u55ae\u4e86\uff01\u5c24\u5176\u5728\u5be6\u969b\u904b\u7528\u6642\uff0c\u7db2\u683c\u7a7a\u9593\u52d5\u8f12500\u500b\u7dad\u5ea6\u4ee5\u4e0a\u3002<\/p>\n

\"\"<\/p>\n

\uff08\u5716\u7247\u4f86\u6e90\uff1a\u6539\u81eaC. Peikert, 2019.\uff09<\/p>\n<\/div>\n

\u7576Alice\u8981\u50b3\u9001\u8a0a\u606f\u6642\uff0c\u5148\u5c07\u8a0a\u606f\u8f49\u63db\u6210\u4f4d\u5143\u4e32\uff08bit string\uff09\uff0c\u63a5\u8457\u4ee5\u5411\u91cf\u4ee3\u8868\u6bcf\u500b\u4f4d\u5143\uff0c\u82e5\u8207\u6700\u9760\u8fd1\u7684\u683c\u5b50\u9ede\u7684\u5e7e\u4f55\u8ddd\u96e2\u5c0f\u65bc\u8207\u5468\u570d\u683c\u5b50\u9ede\u4e2d\u9593\u7684\u5e7e\u4f55\u8ddd\u96e2\uff0c\u5247\u4ee3\u88680\uff1b\u53cd\u4e4b\uff0c\u82e5\u8a72\u5411\u91cf\u4e0d\u9760\u8fd1\u4efb\u4f55\u4e00\u500b\u683c\u5b50\u9ede\uff0c\u4f4d\u65bc\u5468\u570d\u683c\u5b50\u9ede\u7684\u4e2d\u9593\uff0c\u5247\u4ee3\u88681\u3002Alice\u6839\u64daBob\u7684\u516c\u9470\uff0c\u5229\u7528\u9019\u7a2e\u65b9\u6cd5\u5c07\u8a0a\u606f\u52a0\u5bc6\u6210\u4e00\u7cfb\u5217\u7684\u7684\u5ea7\u6a19\uff0c\u4e26\u50b3\u9001\u7d66Bob\u3002Bob\u53ef\u4ee5\u900f\u904e\u81ea\u5df1\u8f03\u55ae\u7d14\u7684\u57fa\u5e95\u5411\u91cf\u4f86\u89e3\u5bc6\uff0c\u4f46Eve\u5373\u4fbf\u6709\u91cf\u5b50\u96fb\u8166\uff0c\u4e5f\u96e3\u4ee5\u900f\u904e\u8907\u96dc\u7684\u516c\u9470\u4f86\u89e3\u5bc6\u3002<\/p>\n

McEliece\u5bc6\u78bc\u7cfb\u7d71<\/strong><\/p>\n

\u53e6\u4e00\u7a2e\u5f8c\u91cf\u5b50\u52a0\u5bc6\u65b9\u5f0f\u5247\u662f\u932f\u8aa4\u6821\u6b63\u78bc\uff0c\u4f8b\u5982McEliece\u52a0\u5bc6\u7cfb\u7d71\u3002\u932f\u8aa4\u6821\u6b63\u78bc\u662f\u5728\u6b32\u50b3\u905e\u7684\u8a0a\u606f\u4e0a\u9644\u52a0\u7684\u591a\u9918\u8a0a\u606f\uff0c\u539f\u672c\u662f\u7528\u4f86\u907f\u514d\u539f\u59cb\u8a0a\u606f\u56e0\u610f\u5916\u5c0e\u81f4\u90e8\u4efd\u76840\u8b8a\u62101\uff0c\u62161\u8b8a\u62100\u800c\u5c0e\u81f4\u50b3\u905e\u932f\u8aa4\uff0c\u5e38\u898b\u7684\u65b9\u6cd5\u6709\u6f22\u660e\u78bc\uff08Hamming code\uff09\u7b49\u3002<\/p>\n

\u5176\u4e2d\uff0c\u82e5\u932f\u8aa4\u6821\u6b63\u78bc\u7684\u7522\u751f\u65b9\u5f0f\u662f\u900f\u904e\u4e00\u500b\u7dda\u6027\u8b8a\u63db\uff08\u200bx<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>\u21a6<\/span>G<\/span><\/span><\/span>x<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\uff09\uff0c\u6211\u5011\u7a31\u4e4b\u70ba\u7dda\u6027\u7684\u932f\u8aa4\u6821\u6b63\u78bc\u3002\u5176\u4e2d\uff0c\u200bx<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u662f\u8a0a\u606f\uff0c\u53ef\u4ee5\u5beb\u6210\u4e00\u500b\u5411\u91cf\uff0c\u800c\u77e9\u9663\u200bG<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u5247\u7a31\u70ba\u9019\u500b\u932f\u8aa4\u6821\u6b63\u78bc\u7684\u751f\u6210\u5668\uff08generator\uff09\u3002\u7576\u7136\uff0c\u200bG<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u5fc5\u9808\u6eff\u8db3\u4e00\u4e9b\u689d\u4ef6\u624d\u80fd\u5728\u89e3\u5bc6\u6642\u7372\u5f97\u552f\u4e00\u4e14\u6b63\u78ba\u7684\u8a0a\u606f\u3002<\/p>\n

\u57281970\u5e74\u4ee3\uff0c\u5bc6\u78bc\u5b78\u5bb6\u8b49\u660e\u9019\u985e\u7684\u65b9\u6cd5\u540c\u6642\u5177\u6709\u52a0\u5bc6\u7684\u529f\u80fd\u3002McEliece\u52a0\u5bc6\u7cfb\u7d71\u5c31\u662f\u4e00\u7a2e\u5229\u7528\u932f\u8aa4\u6821\u6b63\u78bc\u7684\u7279\u6027\u4f86\u52a0\u5bc6\u7684\u7cfb\u7d71\u3002Bob\u9996\u5148\u5148\u751f\u6210\u4e00\u500b\u6700\u591a\u5141\u8a31\u200bk<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u500b\u932f\u8aa4\u7684\u6821\u6b63\u78bc\u751f\u6210\u5668\u200bG<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001\u4e00\u500b\u5b58\u5728\u53cd\u77e9\u9663\u7684\u96a8\u6a5f\u77e9\u9663\u200b\u200b<\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u4ee5\u53ca\u4e00\u500b\u96a8\u6a5f\u7684\u7f6e\u63db\u77e9\u9663\uff08permutation matrix\uff09\u200bP<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u3002\u63a5\u8457\uff0c\u5b83\u8a08\u7b97\u200bG<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>=<\/span>S<\/span>G<\/span>P<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\uff0c\u4e26\u5c07\u200b(<\/span>G<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>,<\/span>t<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u516c\u4f48\u4f5c\u70ba\u516c\u9470\uff0c\u200b(<\/span>S<\/span><\/span><\/span>,<\/span>G<\/span><\/span><\/span>,<\/span>P<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b\u5247\u4f5c\u70ba\u79c1\u9470\u3002Alice\u52a0\u5bc6\u8a0a\u606f\u200bm<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u6642\uff0c\u5247\u8a08\u7b97\u200bc<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>\u2032<\/span><\/span>=<\/span>G<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>m<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\uff0c\u4e26\u96a8\u6a5f\u9078\u64c7\u200bk<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u500b\u200bc<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u7684\u4f4d\u5143\u6539\u8b8a\u5176\u503c\uff0c\u6700\u5f8c\u767c\u9001\u8a0a\u606f\u3002\u5982\u6b64Bob\u6536\u5230\u8a0a\u606f\u6642\uff0c\u53ef\u4ee5\u900f\u904e\u200bP<\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u200bS<\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u4ee5\u53ca\u539f\u672c\u6821\u6b63\u89e3\u5bc6\u6cd5\u56de\u63a8\u539f\u59cb\u7684\u8a0a\u606f\u3002Eve\u5247\u56e0\u70ba\u516c\u9470\u200bG<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u7d93\u904e\u5169\u500b\u96a8\u6a5f\u77e9\u9663\u200bS<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u3001\u200bP<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u6253\u4e82\u800c\u96e3\u4ee5\u56de\u63a8\u79c1\u9470\u200bG<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\uff0c\u4e5f\u5c31\u96e3\u4ee5\u63a8\u7b97\u200bG<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6240\u5c0d\u61c9\u7684\u89e3\u5bc6\u65b9\u5f0f\u800c\u7372\u5f97\u539f\u59cb\u8a0a\u606f\u3002<\/p>\n

\u5c55\u671b<\/strong><\/p>\n

\u5927\u591a\u6578\u7684\u5f8c\u91cf\u5b50\u52a0\u5bc6\u6f14\u7b97\u6cd5\u90fd\u662f\u4f7f\u7528\u66f4\u9577\u7684\u91d1\u9470\uff0c\u6216\u8005\u5c0b\u627e\u6bd4\u73fe\u4eca\u6f14\u7b97\u6cd5\u6240\u9700\u7684\u8a08\u7b97\u91cf\u9084\u591a\u7684\u6f14\u7b97\u6cd5\uff0c\u4f86\u9632\u6b62\u91cf\u5b50\u96fb\u8166\u7684\u7834\u89e3\u3002\u7136\u800c\uff0c\u8377\u862d\u62c9\u5fb7\u5821\u5fb7\u5927\u5b78\u7684\u5bc6\u78bc\u5b78\u5bb6Simona Samardjiska\u8207\u4ed6\u7684\u5718\u968a\u5247\u6b63\u5728\u767c\u5c55\u57fa\u65bc\u4e8c\u6b21\u65b9\u7a0b\u7d44\u800c\u4e0d\u9700\u8981\u66f4\u9577\u7684\u91d1\u9470\u7684\u6f14\u7b97\u6cd5\uff0c\u672a\u4f86\u6216\u53ef\u61c9\u7528\u65bc\u7db2\u9801\u7684\u96fb\u5b50\u7c3d\u8b49\u3002<\/p>\n

\u7136\u800c\uff0c\u76ee\u524d\u4e26\u6c92\u6709\u4eba\u8b49\u660e\u4ee5\u4e0a\u7684\u65b9\u6cd5\u5c0d\u65bc\u91cf\u5b50\u96fb\u8166\u662f\u5b8c\u5168\u7121\u6cd5\u7834\u89e3\uff0c\u751a\u81f3\u5c0d\u65bc\u50b3\u7d71\u96fb\u8166\u4e5f\u662f\uff08\u4f8b\u5982\u82e5\u6709\u4eba\u80fd\u63d0\u51fa\u65b0\u7684\u3001\u66f4\u6709\u6548\u7387\u7684\u6f14\u7b97\u6cd5\uff0c\u5c31\u6709\u53ef\u80fd\u7834\u89e3\u76f8\u95dc\u7684\u52a0\u5bc6\u65b9\u5f0f\uff09\u3002\u56e0\u6b64\uff0c\u5fae\u8edf\u7684\u5bc6\u78bc\u5b78\u5bb6Brian LaMacchia\u8a8d\u70ba\uff1a\u76ee\u524d\u767c\u5c55\u7684\u5f8c\u91cf\u5b50\u6f14\u7b97\u6cd5\u61c9\u6703\u66ab\u6642\u8207\u73fe\u4eca\u7684\u6f14\u7b97\u6cd5\u540c\u6642\u4f7f\u7528\uff0c\u800c\u975e\u5b8c\u5168\u53d6\u4ee3\u3002\u7f8e\u570b\u570b\u5bb6\u6a19\u6e96\u6280\u8853\u7814\u7a76\u6240\uff08National Institute of Standards and Technology\uff0cNIST\uff09\u6700\u5feb\u53ef\u80fd\u57282022\u5e74\u6642\u516c\u4f48\u4e8c\u5230\u4e09\u7a2e\u6a19\u6e96\u7684\u52a0\u5bc6\u6f14\u7b97\u6cd5\u4ee5\u53ca\u6578\u4f4d\u7c3d\u8b49\u3002NIST\u7684\u6578\u5b78\u5bb6Sustim Moody\u8868\u793a\uff0c\u82e5\u6709\u4eba\u6210\u529f\u5730\u7834\u89e3\u67d0\u7a2e\u52a0\u5bc6\u7cfb\u7d71\uff0c\u6211\u5011\u4ecd\u6709\u5176\u4ed6\u6f14\u7b97\u6cd5\u53ef\u4f9b\u4f7f\u7528\u3002LaMacchia\u5247\u8868\u793a\uff0c\u904e\u53bb30\u5e74\u4f86\uff0c\u5bc6\u78bc\u5b78\u6b77\u7d93\u56db\u5230\u4e94\u6b21\u7684\u91cd\u5927\u8b8a\u9769\uff0c\u300c\u7136\u800c\u9019\u6b21\u5728\u6027\u8cea\u4e0a\u5b8c\u5168\u4e0d\u540c\uff0c\u4e14\u8907\u96dc\u7684\u591a\u3002\u300d<\/p>\n

 <\/p>\n

\u7de8\u8b6f\u4f86\u6e90<\/strong><\/p>\n

A. Cho, \u201cCryptographers scramble to protect the internet from attackers armed with quantum computers<\/a>\u201c,\u00a0Science<\/em>, 2019.<\/p>\n

\u53c3\u8003\u8cc7\u6599<\/strong><\/p>\n

    \n
  1. D. Bernstein & T. Lange,\u201cPost-quantum cryptography<\/a>\u201d,\u00a0Nature<\/em>, 2017.<\/li>\n
  2. A. Fenyes, \u201cMatrix Algebra and Error-Correcting Codes<\/a>\u201c, Math.toronto.edu, 2015.<\/li>\n
  3. N. Wolchover, \u201cThe Tricky Encryption that could Stump Quantum Computers<\/a>\u201c,\u00a0WIRED<\/em>, 2015.<\/li>\n
  4. C. Peikert,\u00a0Lattice-based cryptography<\/i><\/a>. Oxford Post-Quantum Cryptography Workshop, 2019.<\/li>\n<\/ol>\n<\/div>\n
    \n
    Facebook<\/span><\/a>Twitter<\/span><\/a>Line<\/span><\/a>Email<\/span><\/a>\u5206\u4eab<\/span><\/a><\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    \u96d6\u7136\u8ddd\u96e2\u5546\u696d\u6216\u65e5\u5e38\u4f7f\u7528\u4ecd\u6709\u4e00\u6bb5\u8ddd\u96e2\uff0c\u4f46\u91cf\u5b50\u96fb\u8166\u7684\u51fa\u73fe\u5a01\u8105\u4e86\u73fe\u4eca\u88ab\u5ee3\u6cdb\u4f7f\u7528\u7684RSA\u52a0\u5bc6\u6f14\u7b97\u6cd5\uff0c\u56e0\u6b64\u5bc6\u78bc\u5b78\u5bb6\u627e\u5230\u4e86\u6578\u7a2e\u53ef\u80fd\u6210\u70ba\u4e0b\u4e00\u4ee3\u52a0\u5bc6\u65b9\u5f0f\u7684\u9078\u64c7\uff0c\u4f8b\u5982\u7db2\u683c\u52a0\u5bc6\u8207McEliece\u5bc6\u78bc\u7cfb\u7d71\u3002<\/p>\n","protected":false},"author":21,"featured_media":38381,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3772,3293],"tags":[5702,5703,2972],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2022\/01\/hacker.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/38380"}],"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\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38380"}],"version-history":[{"count":1,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/38380\/revisions"}],"predecessor-version":[{"id":38382,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/38380\/revisions\/38382"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/38381"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38380"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=38380"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=38380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}