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alt=\"\"\/><\/figure>\n\n\n\n<p><strong>\u540c\u6001\u52a0\u5bc6<\/strong><\/p>\n\n\n\n<p>\u540c\u6001\u52a0\u5bc6\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u52a0\u5bc6\u6280\u672f\u3002\u52a0\u5bc6\u662f\u5982\u4f55\u5c06\u660e\u6587\u8fdb\u884c\u53d8\u6362\uff0c\u53d8\u6210\u5bc6\u6587\u7684\u4e00\u4e2a\u8fc7\u7a0b\u3002\u540c\u6001\u52a0\u5bc6\u662f\u4ec0\u4e48\u610f\u601d\u5462\uff1f\u5b83\u7684\u672c\u8d28\u5c31\u662f\u8bf4\u6211\u53ef\u4ee5\u5bf9\u5bc6\u6587\u505a\u8ba1\u7b97\u3002\u5bc6\u6587\u672c\u8eab\u5b83\u662f\u4e00\u4e2a\u65e0\u5e8f\u3001\u5185\u5bb9\u968f\u673a\u5206\u5e03\u7684\u4e00\u4e32\u201ccode\u201d\uff0c\u56e0\u6b64\u5bf9\u5bc6\u6587\u8ba1\u7b97\u662f\u6bd4\u8f83\u96be\u7684\u4e8b\u60c5\uff0c\u4f46\u662f\u540c\u6001\u52a0\u5bc6\u5c31\u53ef\u4ee5\u5b9e\u73b0\u3002<strong>\u540c\u6001\u52a0\u5bc6\u7684\u610f\u601d\u662f\uff0c\u5bf9\u4e24\u4e2a\u5bc6\u6587\u8fdb\u884c\u64cd\u4f5c\u7684\u7ed3\u679c\uff0c\u7b49\u4e8e\u5bf9\u8fd9\u4e24\u4e2a\u5bc6\u6587\u5bf9\u5e94\u7684\u660e\u6587m1\u3001m2\u8fdb\u884c\u64cd\u4f5c\u540e\u518d\u52a0\u5bc6\u7684\u7ed3\u679c\u3002<\/strong>\u4e3e\u4e2a\u4f8b\u5b50\u3002\u5047\u8bbeAlice\u5e0c\u671b\u5de5\u5320\u5e2e\u5979\u628a\u4e24\u4e2a\u91d1\u5757\u52a0\u5de5\u6210\u624b\u956f\u3002\u5728\u8fd9\u4e2a\u52a0\u5de5\u8fc7\u7a0b\u4e2d\uff0c\u5979\u5e0c\u671b\u5de5\u5320\u65e0\u6cd5\u628a\u8fd9\u4e2a\u91d1\u5757\u7684\u788e\u7247\u6536\u96c6\u8d77\u6765\u3002\u56e0\u6b64\u5de5\u5320\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u7279\u6b8a\u7684\u88c5\u7f6e\u3002\u8fd9\u4e2a\u88c5\u7f6e\u662f\u900f\u660e\u7684\u5e76\u4e14\u5e26\u4e86\u4e00\u628a\u9501\uff08\u4ec5\u6709Alice\u53ef\u4ee5\u6253\u5f00\u8fd9\u628a\u9501\u62ff\u5230\u88c5\u7f6e\u5185\u90e8\u7684\u7269\u4f53\uff09\uff0c\u5e76\u4e14\u56fa\u5b9a\u4e86\u4e00\u4e2a\u624b\u5957\uff0c\u5de5\u5320\u53ef\u4ee5\u5c06\u53cc\u624b\u653e\u5230\u624b\u5957\u91cc\uff0c\u9694\u7740\u88c5\u7f6e\u8fdb\u884c\u7cbe\u7ec6\u7684\u52a0\u5de5\uff0c\u4f46\u662f\u6234\u7740\u624b\u5957\uff0c\u5e76\u4e14\u624b\u5957\u65e0\u6cd5\u79bb\u5f00\u88c5\u7f6e\uff0c\u5de5\u5320\u5b9e\u9645\u4e0a\u65e0\u6cd5\u89e6\u78b0\u5230\u4efb\u4f55\u7684\u91d1\u5757\u548c\u91d1\u5757\u788e\u7247\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u91cc\uff0c\u88c5\u7f6e\u91cc\u7684\u4e24\u4e2a\u91d1\u5757\u53ef\u4ee5\u770b\u6210\u539f\u59cb\u5bc6\u6587Encrypt(m1)\u548cEncrypt(m2)\uff0c\u5de5\u5320\u6240\u505a\u7684\u4e8b\u60c5\uff0c\u5c31\u597d\u50cf\u662f\u4ed6\u5728\u76d2\u5b50\u7684\u906e\u6321\u4e0b\u5728\u64cd\u4f5c\u5bc6\u6587\uff0c\u800cEncrypt(m1+m2)\u5c31\u662f\u88c5\u7f6e\u91cc\u7684\u624b\u956f\uff0cAlice\u901a\u8fc7\u89e3\u9501\u83b7\u5f97\u4e86\u624b\u956f\uff0c\u5373m1+m2\u3002<\/p>\n\n\n\n<p>\u540c\u6001\u52a0\u5bc6\u9700\u8981\u89e3\u51b3\u7684\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\u662f\u53ef\u4ee5\u652f\u6301\u4efb\u610f\u7c7b\u578b\u7684\u8ba1\u7b97\u3002\u4efb\u610f\u7684\u610f\u601d\u662f\u6307\u52a0\u6cd5\u548c\u4e58\u6cd5\uff0c\u56e0\u4e3a\u6240\u6709\u7684\u8ba1\u7b97\u7a0b\u5e8f\u62bd\u8c61\u4e3a\u7b97\u672f\u7535\u8def\u8868\u793a\u90fd\u53ef\u4ee5\u7528\u52a0\u6cd5\u548c\u4e58\u6cd5\u5b9e\u73b0\u3002\u4f20\u7edf\u7684\u8054\u90a6\u5b66\u4e60\u7528\u7684\u4e00\u822c\u662f\u52a0\u6cd5\u540c\u6001\u52a0\u5bc6\u7cfb\u7edf\uff0c\u800c\u8457\u540d\u7684\u5546\u7528\u5bc6\u7801\u7b97\u6cd5RSA\u5c31\u662f\u4e00\u4e2a\u4e58\u6cd5\u540c\u6001\u52a0\u5bc6\u7b97\u6cd5\u3002\u6700\u5389\u5bb3\u7684\u662f\u5168\u540c\u6001\u52a0\u5bc6\uff0c\u6307\u7684\u662f\u5bf9\u4e8e\u65e2\u652f\u6301\u52a0\u6cd5\u64cd\u4f5c\u53c8\u652f\u6301\u4e58\u6cd5\u64cd\u4f5c\uff0c\u5e76\u4e14\u8ba1\u7b97\u6b21\u6570\u6ca1\u6709\u9650\u5236\u7684\u52a0\u5bc6\u7b97\u6cd5\u3002\u8fd9\u79cd\u65b9\u6848\u7279\u522b\u975e\u5e38\u5c11\uff0c\u76f4\u52302009\u5e74\u7b2c\u4e00\u4e2a\u5168\u540c\u6001\u52a0\u5bc6\u65b9\u6848\u88abGentry\u7b49\u4eba\u63d0\u51fa\u6765\u3002\u73b0\u4ee3\u7684\u5168\u540c\u6001\u52a0\u5bc6\u7cfb\u7edf\uff0c\u4e00\u822c\u57fa\u4e8e\u683c\u7406\u8bba\u7b49\u57fa\u7840\u5de5\u5177\uff0c\u53ef\u4ee5\u5bf9\u6297\u91cf\u5b50\u653b\u51fb\u3002<\/p>\n\n\n\n<p><strong>\u5b89\u5168\u591a\u65b9\u8ba1\u7b97<\/strong><\/p>\n\n\n\n<p>\u5b89\u5168\u591a\u65b9\u8ba1\u7b97\uff08MPC\uff09\u662f\u7531\u56fe\u7075\u5956\u83b7\u5f97\u8005\uff0c\u4e2d\u56fd\u79d1\u5b66\u9662\u9662\u58eb\u59da\u671f\u667a\u5148\u751f\u6700\u65e9\u63d0\u51fa\u6765\u7684\u3002\u59da\u5148\u751f\u5f53\u65f6\u63d0\u51fa\u4e86\u4e00\u4e2a\u767e\u4e07\u5bcc\u7fc1\u95ee\u9898\uff0c\u4e24\u4e2a\u5bcc\u7fc1\u975e\u5e38\u6709\u94b1\uff0c\u4ed6\u4eec\u4e92\u76f8\u4e4b\u95f4\u8981\u6bd4\u8f83\u8c01\u66f4\u5bcc\u6709\uff0c\u4f46\u662f\u53c8\u4e0d\u60f3\u544a\u8bc9\u5bf9\u65b9\u81ea\u5df1\u5177\u4f53\u7684\u8d22\u5bcc\u6570\uff0c\u540c\u65f6\u4ed6\u4eec\u4e0d\u5e0c\u671b\u4f9d\u6258\u4e00\u4e2a\u53ef\u4fe1\u7684\u7b2c\u4e09\u65b9\u6765\u5b8c\u6210\u95ee\u9898\u7684\u56de\u7b54\u3002\u4e8b\u5b9e\u4e0a\uff0cMPC\u8981\u89e3\u51b3\u7684\u5c31\u662f\u591a\u4e2a\u53c2\u4e0e\u65b9\u5728\u4e0d\u6cc4\u9732\u9690\u79c1\u6570\u636e\u7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zk-STARKs, 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