{"id":244688,"date":"2023-12-13T20:24:12","date_gmt":"2023-12-13T12:24:12","guid":{"rendered":"https:\/\/www.idc.net\/help\/244688\/"},"modified":"2023-12-13T20:24:12","modified_gmt":"2023-12-13T12:24:12","slug":"zk-%e8%af%81%e6%98%8e%e5%92%8c-zkevm-%e7%9a%84%e5%b7%a5%e4%bd%9c%e5%8e%9f%e7%90%86%ef%bc%88%e6%97%a0%e9%9c%80%e6%95%b0%e5%ad%a6%ef%bc%89","status":"publish","type":"post","link":"https:\/\/idc.net\/help\/244688\/","title":{"rendered":"ZK \u8bc1\u660e\u548c zkEVM \u7684\u5de5\u4f5c\u539f\u7406\uff08\u65e0\u9700\u6570\u5b66\uff09"},"content":{"rendered":"<p>\u96f6\u77e5\u8bc6 (ZK) \u8bc1\u660e\u6b63\u5728\u4e3a web3 \u7684\u6700\u65b0\u521b\u65b0\u63d0\u4f9b\u52a8\u529b\u3002\u5b83\u4eec\u5df2\u7ecf\u88ab\u7528\u4e8ePolygon \u7684 zkEVM[1]\u7b49\u4ea7\u54c1\u4e2d\uff0c\u4e3a\u4ee5\u592a\u574a\u5e26\u6765\u53ef\u9a8c\u8bc1\u7684\u53ef\u6269\u5c55\u6027\uff0c\u800cPolygon 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\u8bc1\u660e\u5982\u4f55\u5de5\u4f5c\uff1f<\/p>\n<p>\u4e3a\u4e86\u5728\u4e0d\u6cc4\u9732\u58f0\u660e\u672c\u8eab\u7684\u60c5\u51b5\u4e0b\u8bc1\u660e\u58f0\u660e\u7684\u6709\u6548\u6027\uff0c\u6d89\u53ca\u4e24\u65b9\uff1a<\/p>\n<p>1.&nbsp;\u8bc1\u660e\u8005\uff1a\u8bd5\u56fe\u8bc1\u660e\u67d0\u4e8b\u7684\u4eba\u3002<\/p>\n<p>2.&nbsp;\u9a8c\u8bc1\u8005\uff1a\u8bd5\u56fe\u9a8c\u8bc1\u58f0\u660e\u662f\u5426\u201c\u771f\u5b9e\u201d\u7684\u4eba\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u6709\u65f6\uff0c\u6d89\u53ca\u7b2c\u4e09\u65b9\uff08\u5373\u9881\u53d1\u8005\uff09\uff0c\u8be5\u7b2c\u4e09\u65b9\u5411\u8bc1\u660e\u8005\u6388\u4e88\u8bc1\u4e66\uff08\u4f8b\u5982\u8bb8\u53ef\u8bc1\uff09\uff0c\u9a8c\u8bc1\u8005\u5c06\u5176\u4f5c\u4e3a\u4fe1\u606f\u6765\u6e90\u4fe1\u4efb\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u4f8b\u5b50...\u6211\u60f3\u5411\u4e00\u4e2a\u7f51\u7ad9\u8bc1\u660e\u6211\u5df2\u5e74\u6ee1 18 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style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u5982\u679c\u6d77\u7ef5\u5b9d\u5b9d\u80fd\u8bc1\u660e\u4ed6\u7684\u540d\u5b57\uff0c\u6216\u8005\u6211\u80fd\u4ee5\u67d0\u79cd\u65b9\u5f0f\u8bc1\u660e\u6211\u5df2\u7ecf\u8d85\u8fc7 18 \u5c81\uff0c\u800c\u4e0d\u9700\u8981\u4ea4\u51fa\u90a3\u4e48\u591a\u654f\u611f\u4fe1\u606f\uff0c\u90a3\u5c31\u66f4\u597d\u4e86\u3002<\/p>\n<p>\u8fd9\u662f ZK \u8bc1\u660e\u5982\u4f55\u4e3a\u4e16\u754c\u63d0\u4f9b\u771f\u6b63\u4ef7\u503c\u7684\u4e00\u4e2a\u5178\u578b\u4f8b\u5b50\u3002\u6709\u4e86 ZK \u8bc1\u660e\uff0c\u6211\u73b0\u5728\u80fd\u591f\u5411\u9a8c\u8bc1\u8005\u8bc1\u660e\u6211\u7684\u90e8\u5206\u8eab\u4efd\uff08\u6216\u5176\u4ed6\u4efb\u4f55\u5185\u5bb9\uff09 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\u8bc1\u660e\u7531\u4ec0\u4e48\u7ec4\u6210\uff1f<\/h2>\n<p>\u6240\u4ee5\uff0c\u6211\u4eec\u60f3\u8981\u8bc1\u660e\u67d0\u4ef6\u4e8b\uff0c\u800c\u4e0d\u900f\u9732\u6211\u4eec\u5982\u4f55\u77e5\u9053\u90a3\u4ef6\u4e8b\uff0c\u6216\u8005\u90a3\u4ef6\u4e8b\u5230\u5e95\u662f\u4ec0\u4e48\u3002\u8fd9\u600e\u4e48\u53ef\u80fd\uff1f<\/p>\n<p>\u5728\u6211\u4eec\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u4e4b\u524d\uff0cZK \u8bc1\u660e\u5206\u4e3a\u4e24\u5927\u7c7b\uff1a<\/p>\n<ol>\n<li>1.&nbsp;\u4ea4\u4e92\u7684<\/li>\n<li>2.&nbsp;\u975e\u4ea4\u4e92\u5f0f<\/li>\n<\/ol>\n<p>\u5728 web3 \u4e2d\u6211\u4eec\u5173\u5fc3\u7684\u662f\u975e\u4ea4\u4e92\u6027\u7684\uff0c\u4f46\u8ba9\u6211\u4eec\u5feb\u901f\u4e86\u89e3\u4e00\u4e0b ZK \u4e0a\u4e0b\u6587\u4e2d\u7684\u201c\u4ea4\u4e92\u6027\u201d\u6307\u7684\u662f\u4ec0\u4e48\u3002<\/p>\n<h3>\u4ea4\u4e92\u5f0f ZK 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style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u4f60\u4e0d\u60f3\u544a\u8bc9\u4f60\u7684\u670b\u53cb\u5bc6\u7801\uff0c\u6240\u4ee5\u4f60\u8981\u8bc1\u660e\u4f60\u77e5\u9053\u5b83\uff1b\u9996\u5148\uff0c\u968f\u673a\u8fdb\u5165\u6d1e\u7a74\u7684\u4e00\u4fa7\uff1b\u5728\u4ed6\u4eec\u770b\u4e0d\u89c1\u7684\u60c5\u51b5\u4e0b\u3002<\/p>\n<p>\u6b64\u65f6\uff0c\u4f60\u7684\u670b\u53cb\u4e0d\u77e5\u9053\u4f60\u7ad9\u5728\u54ea\u4e00\u8fb9\u3002\u4f46\u4f5c\u4e3a\u6311\u6218\uff0c\u4ed6\u4eec\u4f1a\u558a\u51fa\u201cA\uff01\u201d \u6216\u201cB\uff01\u201d\uff1b\u8981\u6c42\u60a8\u4eceA\u4fa7\u6216B\u4fa7****\u9000\u51fa\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u4e2d\uff0c\u8fd9\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4e24\u79cd\u7ed3\u679c\uff1a<\/p>\n<ol>\n<li>1. \u4f60\u8fdb\u5165\u4e86A\u9762\uff0c\u6240\u4ee5\u4f60\u9700\u8981\u5bc6\u7801\u624d\u80fd\u901a\u8fc7\u5927\u95e8\u8fdb\u5165B\u9762\uff1a<\/li>\n<\/ol>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<ol>\n<li>2. \u60a8\u8fdb\u5165B\u9762\uff0c\u6240\u4ee5\u4e0d\u9700\u8981\u5bc6\u7801\uff1b\u4f60\u53ef\u4ee5\u76f4\u63a5\u9000\u51fa\uff1a<\/li>\n<\/ol>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u8fd9\u5c31\u662f\u6240\u8c13\u7684&nbsp;\u963f\u91cc\u5df4\u5df4\u6d1e\u7a74\u6545\u4e8b[4]\uff0c\u4f9b\u53c2\u8003\u3002<\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u56e0\u4e3a\u65e0\u8bba\u60a8\u662f\u5426\u9700\u8981\u5bc6\u7801\u6765\u6ee1\u8db3\u60a8\u670b\u53cb\u7684\u6311\u6218\uff0c\u8fd9\u90fd\u662f 50\/50 \u7684\u6bd4\u4f8b\uff1b\u56e0\u6b64\uff0c\u4ec5\u6267\u884c\u4e00\u6b21\u6b64\u6311\u6218\u4e0d\u8db3\u4ee5\u786e\u5b9a\u60a8\u77e5\u9053\u5bc6\u7801\u3002<\/p>\n<p>\u8fd9\u610f\u5473\u7740\u60a8\u9700\u8981\u5b8c\u6210\u66f4\u591a\u6b21\u6311\u6218\uff0c\u6b63\u786e\u9000\u51fa A \u4fa7\u6216 B \u4fa7\uff0c\u76f4\u5230\u60a8\u7684\u670b\u53cb\u6ee1\u610f\u4e3a\u6b62\uff1b\u6216\u8005\u5728\u7406\u8bba\u4e16\u754c\u4e2d\uff0c\u76f4\u5230\u4f60\u4e0d\u53ef\u80fd\u4f2a\u9020\u8bc1\u4eba\u7684\u77e5\u8bc6\uff08\u5bc6\u7801\uff09\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8fd9\u662f\u4ea4\u4e92\u5f0f\u7684\uff1b\u60a8\uff08\u8bc1\u660e\u8005\uff09\u548c\u60a8\u7684\u670b\u53cb\uff08\u9a8c\u8bc1\u8005\uff09\u6765\u56de\u4ea4\u4e92\u3002\u4f60\u7684\u670b\u53cb\u63d0\u51fa\u4e86\u4e00\u4e2a\u6311\u6218\uff0c\u4f60\u63d0\u51fa\u4e86\u4e00\u4e2a\u56de\u5e94\u3002\u91cd\u590d\u8fd9\u4e2a\u5faa\u73af\uff0c\u76f4\u5230\u9a8c\u8bc1\u8005\u6ee1\u610f\u4e3a\u6b62\uff0c\u6b64\u65f6\u9a8c\u8bc1\u8005\u5df2\u7ecf\u8bc1\u660e\u4e86\u8bc1\u4eba\u7684\u77e5\u8bc6\u3002<\/p>\n<p>\u8fd9\u6784\u6210\u4e86\u4ea4\u4e92\u5f0f ZK \u8bc1\u660e\u7684\u4e09\u4e2a\u90e8\u5206\uff1a<\/p>\n<ol>\n<li>1.&nbsp;\u89c1\u8bc1\u4eba\uff1a\u8bc1\u660e\u8005\u60f3\u8981\u8bc1\u660e\u5176\u4e86\u89e3\u7684\u79d8\u5bc6\u4fe1\u606f\u3002<\/li>\n<li>2.&nbsp;\u6311\u6218\uff1a\u53ea\u6709\u4e86\u89e3\u8bc1\u4eba\u7684\u4eba\u624d\u80fd\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff1b\u867d\u7136\u53ef\u80fd\u662f\u4e00\u4e2a\u5e78\u8fd0\u7684\u731c\u6d4b\u3002<\/li>\n<li>3.&nbsp;Response\uff1a\u8bc1\u660e\u8005\u5bf9\u6311\u6218\u7684\u54cd\u5e94\uff1b\u5305\u542b\uff08\u5e0c\u671b\uff09\u6b63\u786e\u7684\u7b54\u6848\u3002<\/li>\n<\/ol>\n<p>\u91cd\u590d\u6b65\u9aa42\u548c3\uff0c\u76f4\u5230\u9a8c\u8bc1\u8005\u6ee1\u610f\u4e3a\u6b62\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u6700\u7ec8\uff0c\u4e00\u65e6\u9a8c\u8bc1\u8005\u6ee1\u610f\uff0c\u5faa\u73af\u5c31\u4f1a\u4e2d\u65ad\uff1b\u9a8c\u8bc1\u8005\u4e0d\u4f1a\u4ea7\u751f\u53e6\u4e00\u4e2a\u6311\u6218\uff0c\u800c\u662f\u627f\u8ba4\u8bc1\u660e\u8005\u4e86\u89e3\u8bc1\u4eba\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u867d\u7136\u8fd9\u4e2a\u8fc7\u7a0b\u6709\u6548\uff0c\u4f46\u5b83\u9700\u8981\u8bc1\u660e\u8005\u548c\u9a8c\u8bc1\u8005\u4e4b\u95f4\u8fdb\u884c\u591a\u8f6e\u901a\u4fe1\uff1b\u8fd9\u662f\u4f4e\u6548\u7684\uff0c\u5e76\u4e14\u5728\u533a\u5757\u94fe\u73af\u5883\u4e2d\u6548\u679c\u4e0d\u4f73\u3002<\/p>\n<p>\u4ea4\u4e92\u5f0f\u8bc1\u660e\u8fd8\u6709\u53e6\u4e00\u4e2a\u5f88\u5927\u7684\u9650\u5236\uff1b\u5373\u4f7f\u9a8c\u8bc1\u8005\u6ee1\u610f\u540e\uff0c\u8be5\u8bc1\u636e\u4e5f\u65e0\u6cd5\u7528\u4e8e\u72ec\u7acb\u9a8c\u8bc1[5]\uff1b\u8fd9\u610f\u5473\u7740\u53ea\u6709\u9a8c\u8bc1\u5b83\u7684\u4e00\u65b9\u624d\u80fd\u4fe1\u4efb\u5b83\uff0c\u800c\u4e0d\u662f\u5176\u4ed6\u4efb\u4f55\u4eba\u3002<\/p>\n<p>\u7531\u4e8e\u8fd9\u4e9b\u539f\u56e0\uff0c\u8fdb\u884c\u4e86\u975e\u4ea4\u4e92\u5f0f ZK \u8bc1\u660e\u3002<\/p>\n<h3>\u975e\u4ea4\u4e92\u5f0f ZK \u8bc1\u660e<\/h3>\n<p>\u975e\u4ea4\u4e92\u5f0f ZK \u8bc1\u660e\u53ea\u9700\u8981\u4ece\u8bc1\u660e\u8005\u5230\u9a8c\u8bc1\u8005\u7684\u4e00\u8f6e\u901a\u4fe1\u3002\u8bc1\u660e\u8005\u4f7f\u7528\u4e00\u79cd\u7b97\u6cd5\u6765\u8ba1\u7b97 ZK \u8bc1\u660e\u5e76\u5c06\u5176\u53d1\u9001\u7ed9\u9a8c\u8bc1\u8005\uff0c\u9a8c\u8bc1\u8005\u4e5f\u4f7f\u7528\u53e6\u4e00\u79cd\u7b97\u6cd5\u6765\u68c0\u67e5\u5b83\u3002<\/p>\n<p>\u975e\u4ea4\u4e92\u5f0f ZK \u8bc1\u660e\u7684\u53e6\u4e00\u4e2a\u597d\u5904\u662f\u5b83\u4eec\u4e5f\u53ef\u4f9b\u5176\u4ed6\u4efb\u4f55\u4eba\u9a8c\u8bc1\uff1b\u8fd9\u610f\u5473\u7740\u5b83\u4e0d\u4ec5\u53ef\u4ee5\u4ece\u9a8c\u8bc1\u8005\u7684 POV \u4e2d\u5f97\u5230\u8bc1\u660e\uff0c\u800c\u4e14\u53ef\u4ee5\u4f9b\u6bcf\u4e2a\u4eba\u9a8c\u8bc1\u81ea\u5df1\uff1b\u9002\u5408\u533a\u5757\u94fe\u3002<\/p>\n<p>\u8fd9\u4e9b\u80fd\u591f\u8bc1\u660e\u4fe1\u606f\u548c\u9a8c\u8bc1\u8bc1\u636e\u7684\u201c\u7b97\u6cd5\u201d\u662f\u4ec0\u4e48\uff1f\u55ef\uff0c\u7b54\u6848\u662f\uff1b\u8fd9\u53d6\u51b3\u4e8e\u3002[\u5b83\u4eec\u7684\u6570\u91cf\u76f8\u5f53\u591a](https:\/\/en.wikipedia.org\/wiki\/Zero-knowledge_proof#:~:text=The most popular interactive or,Delegation (VPD)%2C and Succinct)\uff0c\u4f46\u5728\u533a\u5757\u94fe\u73af\u5883\u4e2d\u901a\u5e38\u4f7f\u7528\u4e24\u79cd ZKP \u7cfb\u7edf\uff1bZK-SNARK \u548c ZK-STARK\u3002<\/p>\n<h3>\u4ec0\u4e48\u662f ZK-SNARK\uff1f<\/h3>\n<p>ZK-SNARK \u7684\u610f\u601d\u662f\u96f6\u77e5\u8bc6\u7b80\u6d01\u975e\u4ea4\u4e92\u5f0f\u77e5\u8bc6\u8bba\u8bc1\u3002<\/p>\n<p>\u2022&nbsp;ZK\uff1a\u5e0c\u671b\u73b0\u5728\u4f60\u80fd\u731c\u5230\u8fd9\u610f\u5473\u7740\u4ec0\u4e48\uff08\u96f6\u77e5\u8bc6\uff09\u3002<\/p>\n<p>\u2022&nbsp;\u7b80\u6d01\uff1a\u5b83\u4eec\u5f88\u5c0f\uff0c\u5e76\u4e14\u53ef\u4ee5\u88ab\u9a8c\u8bc1\u8005\u5feb\u901f\u9a8c\u8bc1\u3002<\/p>\n<p>\u2022&nbsp;\u975e\u4ea4\u4e92\u5f0f\uff1a\u6211\u4eec\u4e4b\u524d\u8ba8\u8bba\u8fc7\u8fd9\u4e00\u70b9\u3002\u8bc1\u660e\u8005\u548c\u9a8c\u8bc1\u8005\u4e4b\u95f4\u53ea\u9700\u8981\u4e00\u8f6e\u901a\u4fe1\u3002<\/p>\n<p>\u2022&nbsp;\u8bba\u636e\uff1a\u7406\u8bba\u4e0a\u6765\u8bf4\uff0c\u201c\u6b3a\u9a97\u201d\u7cfb\u7edf\u7684\u53ef\u80fd\u6027\u6781\u5c0f\u3002<\/p>\n<p>\u2022&nbsp;\uff08\u7684\uff09\u77e5\u8bc6\uff1a\u5982\u679c\u4e0d\u8bbf\u95ee\u79d8\u5bc6\u4fe1\u606f\uff08\u89c1\u8bc1\u4eba\uff09\uff0c\u5c31\u65e0\u6cd5\u6784\u5efa\u77e5\u8bc6\u3002<\/p>\n<p>\u4ed6\u4eec\u4f7f\u7528\u4e00\u79cd\u79f0\u4e3a\u692d\u5706\u66f2\u7ebf\u914d\u5bf9[6]\u7684\u52a0\u5bc6\u539f\u8bed\u4f5c\u4e3a\u521b\u5efa\u548c\u9a8c\u8bc1\u8fd9\u4e9b\u8bc1\u660e\u7684\u65b9\u6cd5\uff08\u6211\u4eec\u4e0d\u4f1a\u5728\u8fd9\u91cc\u8ba8\u8bba\u6570\u5b66\uff09\u3002<\/p>\n<p>\u5173\u4e8e ZK-SNARK \u9700\u8981\u6ce8\u610f\u7684\u4e00\u4ef6\u5173\u952e\u4e8b\u60c5\u662f\uff0c\u5728\u521d\u59cb\u8bbe\u7f6e\u9636\u6bb5\uff0c\u8bc1\u660e\u8005\u548c\u9a8c\u8bc1\u8005\u5fc5\u987b\u540c\u610f\u4f7f\u7528\u201c\u5171\u4eab\u5bc6\u94a5\u201d\uff0c\u5373\u516c\u5171\u53c2\u8003\u5b57\u7b26\u4e32 (CRS)\u3002\u4efb\u4f55\u6709\u6743\u8bbf\u95ee\u6b64\u5171\u4eab\u5bc6\u94a5\u7684\u4eba\u90fd\u53ef\u4ee5\u9a8c\u8bc1\u8fd9\u4e9b\u8bc1\u660e\u3002<\/p>\n<p>\u8fd9\u4e2a\u5171\u4eab\u5bc6\u94a5\u4f7f ZK-SNARK \u6210\u4e3a\u53ef\u80fd\uff1b\u5c3d\u7ba1\u8fd9\u4e5f\u53ef\u4ee5\u8bf4\u662f\u5b83\u4eec\u6700\u5927\u7684\u7f3a\u70b9\uff0c\u56e0\u4e3a\u5b83\u521b\u5efa\u4e86\u6240\u8c13\u7684\u201c\u53ef\u4fe1\u73af\u5883\u201d\u3002<\/p>\n<p>\u7528\u4e8e\u521b\u5efa CRS \u7684\u503c\uff08\u6709\u65f6\u79f0\u4e3a\u201c\u6709\u6bd2\u5e9f\u7269\u201d\uff09\u9700\u8981\u5728 CRS \u751f\u6210\u540e\u9500\u6bc1\u3002\u5982\u679c\u4e0d\u662f\uff0c\u6574\u4e2a\u7cfb\u7edf\u5c31\u4f1a\u9762\u4e34\u98ce\u9669\uff1b\u56e0\u4e3a\u4e0d\u8bda\u5b9e\u7684\u8bc1\u660e\u8005\u80fd\u591f\u8ba1\u7b97\u51fa\u9519\u8bef\u7684\u8bc1\u660e\uff1b\u56e0\u6b64\uff0c\u7528\u6237\u5fc5\u987b\u76f8\u4fe1\u4ef7\u503c\u5df2\u88ab\u7834\u574f\u3002<\/p>\n<p>\u5173\u4e8e ZK SNARK \u8fd8\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5b83\u4eec\u4e0d\u5177\u6709\u201c\u6297\u91cf\u5b50\u6027\u201d\u3002\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u5c06\u6765\u5f88\u5bb9\u6613\u53d7\u5230\u91cf\u5b50\u8ba1\u7b97\u673a\u7684\u653b\u51fb\uff1b\u5c3d\u7ba1\u5b83\u4eec\u5c06\u6765\u53ef\u80fd\u4f1a\u5347\u7ea7\u4ee5\u5177\u6709\u6297\u91cf\u5b50\u6027\u3002<\/p>\n<h3>\u4ec0\u4e48\u662f ZK-STARK\uff1f<\/h3>\n<p>ZK-STARK \u7684\u610f\u601d\u662f\u96f6\u77e5\u8bc6\u53ef\u6269\u5c55\u900f\u660e\u77e5\u8bc6\u8bba\u8bc1\u3002<\/p>\n<p>\u2022&nbsp;\u53ef\u6269\u5c55\uff1a\u5b83\u4eec\u4e0d\u662f\u201c\u7b80\u6d01\u201d\u7684\uff0c\u800c\u662f\u53ef\u6269\u5c55\u7684\uff1b\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u6bd4 ZK-SNARK \u66f4\u6709\u6548\u5730\u751f\u6210\u548c\u9a8c\u8bc1\u66f4\u591a\u89c1\u8bc1\u4eba\u7684\u8bc1\u660e\u3002<\/p>\n<p>\u2022&nbsp;\u900f\u660e\uff1a\u65e0\u9700\u53ef\u4fe1\u8bbe\u7f6e\u3002\u4ed6\u4eec\u4f9d\u9760\u53ef\u516c\u5f00\u9a8c\u8bc1\u7684\u968f\u673a\u6027\u6765\u751f\u6210\u5171\u4eab\u5bc6\u94a5\u3002<\/p>\n<p>\u8fd9\u79cd\u900f\u660e\u5ea6\u7684\u63d0\u9ad8\u901a\u5e38\u9700\u8981\u6743\u8861\u751f\u6210\u6bd4 ZK-SNARK \u5927\u5c0f\u5927\u5f97\u591a\u7684\u8bc1\u660e\uff1b\u9664\u975e\u5904\u7406\u975e\u5e38\u5927\u7684\u6570\u636e\u96c6\u3002[\u8bc1\u660e\u7684\u5927\u5c0f\u4ece 288 \u5b57\u8282\u589e\u52a0\u5230\u51e0\u767e KB](https:\/\/vitalik.ca\/general\/2017\/11\/09\/starks_part_1.html#:~:text=the size of a proof goes up from 288 bytes to a few hundred kilobytes)\u3002<\/p>\n<p>\u4ed6\u4eec\u4e0d\u4f7f\u7528\u692d\u5706\u66f2\u7ebf\uff0c\u800c\u662f\u4f7f\u7528\u591a\u9879\u5f0f[7]\uff1b\u6211\u7edd\u5bf9\u6ca1\u6709\u8d44\u683c\u544a\u8bc9\u4f60\u3002Vitalik \u9488\u5bf9\u8be5\u4e3b\u9898\u63a8\u51fa\u4e86\u4e00\u4e2a\u7531\u4e09\u90e8\u5206\u7ec4\u6210\u7684\u7cfb\u5217\uff1a1[8]&nbsp;,&nbsp;2[9]&nbsp;,&nbsp;3[10]\u3002<\/p>\n<p>ZK STARK \u89e3\u51b3\u4e86\u6211\u4eec\u4e0e ZK-SNARK \u8ba8\u8bba\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u5b83\u4eec\uff1a<\/p>\n<ol>\n<li>1. \u4e0d\u9700\u8981\u201c\u53ef\u4fe1\u73af\u5883\u201d\u3002<\/li>\n<li>2. \u4f3c\u4e4e\u662f\u540e\u91cf\u5b50\u5b89\u5168\u7684\uff1b\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u5c06\u6765\u4e0d\u4f1a\u5bb9\u6613\u53d7\u5230\u91cf\u5b50\u8ba1\u7b97\u673a\u7684\u653b\u51fb\u3002<\/li>\n<\/ol>\n<p>ZK-STARKS \u6bd4 ZK-SNARK \u66f4\u65b0\uff0cVitalik \u79f0\u5b83\u4eec\u4e3a\u201c[\u66f4\u65b0\u3001\u66f4\u95ea\u4eae\u7684\u8868\u5f1f](https:\/\/vitalik.ca\/general\/2017\/11\/09\/starks_part_1.html#:~:text=a newer%2C shinier cousin)\u201d\uff01\ud83e\udd20 \u6240\u4ee5\uff0c\u5feb\u901f\u56de\u987e\u4e00\u4e0b\uff1a<\/p>\n<table style=\"width: 100%;border-collapse: collapse\">\n<tbody>\n<tr>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p><\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>ZK-SNARK<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>ZK-STARK<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u5c3a\u5bf8<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u7b80\u6d01\u3001\u53ef\u5feb\u901f\u9a8c\u8bc1<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u66f4\u5927\uff0c\u4f46\u5728\u8bc1\u660e\u66f4\u5927\u7684\u8bc1\u4eba\u65f6\u53ef\u4ee5\u66f4\u6709\u6548\u5730\u6269\u5c55<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u5b89\u5168<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u9700\u8981\u53ef\u4fe1\u7684\u73af\u5883<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u4e0d\u9700\u8981\u53ef\u4fe1\u73af\u5883<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u540e\u91cf\u5b50<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u5c3d\u7ba1\u53ef\u4ee5\u5347\u7ea7\uff0c\u4f46\u4e0d\u5b89\u5168<\/p>\n<\/td>\n<td style=\"vertical-align: top;min-width: auto;margin: 4px 8px;padding: 4px 8px;cursor: default\">\n<p>\u5b89\u5168\u7684<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>zkEVM \u5982\u4f55\u5de5\u4f5c\uff1f<\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u96f6\u77e5\u8bc6\u8bc1\u660e\u7684\u5de5\u4f5c\u539f\u7406\u4ee5\u53ca web3 \u4e16\u754c\u4e2d\u51fa\u73b0\u7684\u4e24\u79cd\u5e38\u89c1\u7684 ZKP \u5f62\u5f0f\uff0c\u8ba9\u6211\u4eec\u6765\u63a2\u8ba8\u4e00\u4e0b\u7531 ZKP \u652f\u6301\u7684\u6700\u65b0\u521b\u65b0\u4e4b\u4e00\uff1bzkEVM\uff08\u96f6\u77e5\u8bc6\u4ee5\u592a\u574a\u865a\u62df\u673a\uff09\u3002<\/p>\n<p>zkEVM \u6709\u51e0\u79cd\u4e0d\u540c\u7684\u5f62\u5f0f\uff1b\u6b63\u5982 Vitalik \u5728\u4ed6\u7684\u535a\u5ba2\u6587\u7ae0\u201c\u4e0d\u540c\u7c7b\u578b\u7684 ZK-EVM[11]&nbsp;\u201d\u4e2d\u6982\u8ff0\u7684\u90a3\u6837\u3002\u6211\u5c06\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\u5f15\u7528\u7684\u662fPolygon zkEVM[12]\u3002<\/p>\n<p>zkEVM \u7684\u76ee\u6807\u662f\u63d0\u9ad8\u4ee5\u592a\u574a\u533a\u5757\u94fe\u7684\u53ef\u6269\u5c55\u6027\uff0c\u540c\u65f6\u4fdd\u6301\u5b89\u5168\u3001\u53bb\u4e2d\u5fc3\u5316\u548cEVM[13]\u517c\u5bb9\u3002<\/p>\n<p>\u7ec6\u8282\u5f88\u590d\u6742\uff0c\u4f46\u6838\u5fc3\u539f\u7406\u4e0e\u6211\u4eec\u5230\u76ee\u524d\u4e3a\u6b62\u8ba8\u8bba\u7684\u76f8\u540c\u3002\u4e0e\u6240\u6709 ZKP \u7cfb\u7edf\u4e00\u6837\uff0c\u6709\uff1a<\/p>\n<p>1.&nbsp;\u8bc1\u660e\u8005\uff1a\u751f\u6210\u4ee3\u8868\u7528\u6237\u63d0\u4ea4\u7684\u4e00\u6279\u4ea4\u6613\u771f\u5b9e\u6027\u7684\u6709\u6548\u6027\u8bc1\u660e\u3002<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u9996\u5148\uff0c\u5b83\u521b\u5efa\u591a\u4e2a ZK-STARK \u8bc1\u660e\u3002<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u5b83\u4f7f\u7528STARK Recursion[14]\u5c06 ZK-STARK \u6346\u7ed1\u5728\u4e00\u8d77\uff0c\u4ee5\u521b\u5efa\u5355\u4e2a ZK-STARK\u3002<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u8fd9\u4e2a ZK-STARK \u5f88\u5927\uff0c\u56e0\u6b64\u5b83\u901a\u8fc7CIRCOM \u7ec4\u4ef6[15]\u8f93\u51fa\u5230 SNARK \u6784\u5efa\u5668\u3002<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u987e\u540d\u601d\u4e49\uff0cSNARK \u6784\u5efa\u5668\u751f\u6210 ZK-SNARK \u6709\u6548\u6027\u8bc1\u660e\uff1b\u8fd9\u6709\u52a9\u4e8e\u5c06 Gas \u6210\u672c\u4ece 5M \u964d\u4f4e\u5230 350K\u3002<\/p>\n<p>2.&nbsp;\u9a8c\u8bc1\u8005\uff1aPolygonZkEVM\u90e8\u7f72\u5728\u4ee5\u592a\u574a\u4e0a\u7684\u667a\u80fd\u5408\u7ea6\u662f ZK \u8bc1\u660e\u7684\u9a8c\u8bc1\u8005\u3002<\/p>\n<h3>zkEVM \u4e2d\u7684\u6570\u636e\u6d41<\/h3>\n<p>\u4e0b\u9762\u662f Polygon zkEVM \u4e2d\u6570\u636e\u7684\u7b80\u5316\u6d41\u7a0b\u56fe\u3002<\/p>\n<p>\u6211\u5c06\u5176\u5206\u6210\u6309\u65f6\u95f4\u987a\u5e8f\u6392\u5217\u7684\u90e8\u5206\uff0c\u4ee5\u5e2e\u52a9\u5176\u66f4\u5bb9\u6613\u7406\u89e3\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<h4>\u63d0\u4ea4\u4ea4\u6613<\/h4>\n<p>\u4f5c\u4e3a\u7528\u6237\uff0c\u60a8\u53ef\u4ee5\u50cf\u5e73\u5e38\u4f7f\u7528\u4efb\u4f55\u5176\u4ed6 EVM \u94fe\uff08\u4f8b\u5982\u4ee5\u592a\u574a\uff09\u4e00\u6837\u63d0\u4ea4\u4ea4\u6613\uff1b\u901a\u8fc7\u7b7e\u7f72\u4ea4\u6613\u5e76\u901a\u8fc7 JSON RPC \u53d1\u9001\u5b83\u4eec\u3002<\/p>\n<p>\u8fd0\u884c zkEVM \u8f6f\u4ef6\u7684\u5b9a\u5e8f\u5668\u8282\u70b9\u4f1a\u9009\u53d6\u8fd9\u4e9b\u4ea4\u6613\u5e76\u51b3\u5b9a\u8981\u5904\u7406\u54ea\u4e9b\u4ea4\u6613\uff0c\u5e76\u5236\u5b9a\u4e00\u4e9b\u6fc0\u52b1\u673a\u5236\u6765\u6b63\u786e\u5904\u7406\u8fd9\u4e9b\u4ea4\u6613\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<h4>\u6279\u91cf\u4ea4\u6613<\/h4>\n<p>\u6392\u5e8f\u5668\u5c06\u4ea4\u6613\u6279\u91cf\u5408\u5e76\u4e3a\u4e00\u4e2a\uff0c\u5e76\u5c06\u5b83\u4eec\u63d0\u4ea4\u5230PolygonZkEvm\u667a\u80fd\u5408\u7ea6\uff0c\u8be5\u667a\u80fd\u5408\u7ea6\u5b58\u50a8\u5728\u4ee5\u592a\u574a\u4e3b\u7f51\u4e0a\uff08\u4ee5\u53ca\u4ee5\u592a\u574a Goerli \u6d4b\u8bd5\u7f51\u4e0a\u7684\u4e00\u4e2a\u5355\u72ec\u5b9e\u4f8b\uff09\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u8fd9\u4e9b\u6279\u6b21\u76ee\u524d\u4e0d\u4e00\u5b9a\u6b63\u786e\u6216\u7ecf\u8fc7\u9a8c\u8bc1\u3002<\/p>\n<h4>\u9a8c\u8bc1\u4ea4\u6613<\/h4>\n<p>\u4f7f\u7528 ZKP\uff0cPolygonZkEVM\u667a\u80fd\u5408\u7ea6\u5728\u6b64\u8bbe\u7f6e\u4e2d\u5145\u5f53\u9a8c\u8bc1\u8005\u3002\u5b83\u60f3\u8981\u9a8c\u8bc1\u521a\u521a\u6536\u5230\u7684\u6279\u6b21\u662f\u5426\u6709\u6548\uff1b\u5b83\u901a\u8fc7\u5c06\u6279\u6b21\u53d1\u9001\u5230\u805a\u5408\u5668\u8282\u70b9\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<h4>\u751f\u6210\u548c\u9a8c\u8bc1 ZK \u8bc1\u660e\/\u6709\u6548\u6027\u8bc1\u660e<\/h4>\n<p>\u667a\u80fdPolygonZkEVM\u5408\u7ea6\u5c06\u521a\u521a\u6536\u5230\u7684\u6279\u6b21\u53d1\u9001\u5230\u805a\u5408\u5668\u8282\u70b9\uff0c\u8be5\u8282\u70b9\u662f\u53e6\u4e00\u53f0\u8fd0\u884c zkEVM \u8f6f\u4ef6\u5e76\u4e0e ZK \u8bc1\u660e\u5668\u901a\u4fe1\u7684\u673a\u5668\u3002\u6d41\u7a0b\u5982\u4e0b\uff1a<\/p>\n<p>\u2022&nbsp;\u805a\u5408\u5668\u4ece\u667a\u80fd\u5408\u7ea6\u63a5\u6536\u6279\u6b21<\/p>\n<p>\u2022&nbsp;\u805a\u5408\u5668\u5c06\u6279\u6b21\u53d1\u9001\u5230 ZK Prover<\/p>\n<p>\u2022&nbsp;ZK Prover \u521b\u5efa\u591a\u4e2a ZK-STARK -&gt; \u5355\u4e2a ZK-STARK -&gt; \u4e00\u4e2a ZK-SNARK<\/p>\n<p>\u2022&nbsp;ZK-SNARK\uff08\u6709\u6548\u6027\u8bc1\u660e\uff09\u88ab\u53d1\u9001\u56de\u805a\u5408\u5668<\/p>\n<p>\u2022&nbsp;\u805a\u5408\u5668\u5c06\u6709\u6548\u6027\u8bc1\u660e\u53d1\u9001\u56dePolygonZkEVM\u667a\u80fd\u5408\u7ea6<\/p>\n<p>\u2022&nbsp;\u667a\u80fdPolygonZkEVM\u5408\u7ea6\u9a8c\u8bc1\u6709\u6548\u6027\u8bc1\u660e<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u5982\u679c\u6709\u6548\u6027\u8bc1\u660e\u6709\u6548\uff0c\u5219\u63a5\u53d7\u3002<\/p>\n<p style=\"text-indent: 2em\">\u2022&nbsp;\u5982\u679c\u65e0\u6548\uff0c\u5219\u62d2\u7edd\u5b83\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<h4>\u9605\u8bfb ZK EVM<\/h4>\n<p>\u4e3a\u4e86\u4f7f ZK EVM \u53d1\u6325\u4f5c\u7528\uff0c\u53bb\u4e2d\u5fc3\u5316\u5e94\u7528\u7a0b\u5e8f\uff08dApp\uff09\u9700\u8981\u4ece\u4e2d\u8bfb\u53d6\u4fe1\u606f\uff1b\u8fd9\u5c31\u662f\u540c\u6b65\u5668\u53d1\u6325\u4f5c\u7528\u7684\u5730\u65b9\u3002<\/p>\n<p>\u5b83\u4ece\u4ee5\u592a\u574a\u667a\u80fd\u5408\u7ea6\u4e2d\u8bfb\u53d6\u4e8b\u4ef6\uff0c\u5b58\u50a8\u6765\u81ea\u805a\u5408\u5668\u7684 ZK \u6709\u6548\u6027\u8bc1\u660e\u548c\u4ece\u6392\u5e8f\u5668\u63d0\u4ea4\u7684\u6279\u6b21\u7684\u77e5\u8bc6\u3002<\/p>\n<p style=\"text-align:center\"><span>\u56fe\u7247<\/span><\/p>\n<p>\u8fd9\u6837\uff0c\u5e94\u7528\u7a0b\u5e8f\u5c31\u53ef\u4ee5\u901a\u8fc7 JSON RPC \u8f7b\u677e\u83b7\u53d6\u6c47\u603b\u72b6\u6001\u7684\u89c6\u56fe\u3002<\/p>\n<h2>\u603b\u7ed3<\/h2>\n<p>\u96f6\u77e5\u8bc6\u8bc1\u660e\u662f\u5bc6\u7801\u5b66\u7684\u73b0\u5b9e\u5e94\u7528\uff0c\u53ef\u4ee5\u6210\u4e3a\u66f4\u52a0\u6ce8\u91cd\u9690\u79c1\u7684\u672a\u6765\u7684\u57fa\u7840\uff1b\u5728Polygon ID[16]\u7b49\u4ea7\u54c1\u4e2d\u5f97\u5230\u4e86\u8bc1\u660e\u3002<\/p>\n<p>\u5728\u533a\u5757\u94fe\u7684\u80cc\u666f\u4e0b\uff0cZKP \u88ab\u7528\u6765\u63d0\u9ad8Polygon \u7684 zkEVM[17]\u7b49\u4ea7\u54c1\u4e2d\u4ee5\u592a\u574a\u7684\u53ef\u6269\u5c55\u6027\uff0c\u901a\u8fc7\u63d0\u4f9b\u4e00\u79cd\u9a8c\u8bc1\u6279\u91cf\u4ea4\u6613\u7684\u65b0\u65b9\u6cd5\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u6211\u4eec\u4eca\u5929\u5728\u5176\u4ed6\u6c47\u603b\u89e3\u51b3\u65b9\u6848\u4e2d\u770b\u5230\u7684\u5178\u578b\u7684\u5b89\u5168\u6027\u6216 EVM \u517c\u5bb9\u6027\u635f\u5931\u3002<\/p>\n<p>\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u4ecb\u7ecd\u4e86\uff1a<\/p>\n<ul>\n<li>\u2022 ZK \u8bc1\u660e\u662f\u4ec0\u4e48\uff0c\u4ee5\u53ca\u4e3a\u4ec0\u4e48\u5b83\u4eec\u5f88\u91cd\u8981\u3002<\/li>\n<li>\u2022 ZK \u8bc1\u660e\u5982\u4f55\u5de5\u4f5c\uff0c\u5305\u62ec ZK-SNARK \u548c ZK-STARK\u3002<\/li>\n<li>\u2022&nbsp;\u8fd9\u4e9b\u8bc1\u660e\u5982\u4f55\u5728\u533a\u5757\u94fe\u4e16\u754c\u4e2d\u4f7f\u7528\u3002<\/li>\n<\/ul>\n<p>\u5982\u679c\u60a8\u60f3\u4e86\u89e3\u5982\u4f55\u5e94\u7528\u8fd9\u4e9b\u6982\u5ff5\uff0c\u6211\u4e4b\u524d\u6709\u4e00\u7bc7\u535a\u5ba2\u6587\u7ae0\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728 Polygon zkEVM \u4e0a\u6784\u5efa\u60a8\u7684\u7b2c\u4e00\u4e2a\u667a\u80fd\u5408\u7ea6\u548c\u53bb\u4e2d\u5fc3\u5316\u5e94\u7528\u7a0b\u5e8f\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<p>https:\/\/blog.jarrodwatts.com\/the-ultimate-guide-to-building-on-polygon-zkevm<\/p>\n<blockquote style=\"line-height: 1.75;margin-top: 5px;margin-bottom: 5px;padding-left: 1em;margin-left: 0px\">\n<p>\u539f\u6587\uff1ahttps:\/\/blog.jarrodwatts.com\/how-zk-proofs-and-zkevms-work<\/p>\n<\/blockquote>\n<h4>\u5f15\u7528\u94fe\u63a5<\/h4>\n<p>[1]&nbsp;Polygon \u7684 zkEVM:&nbsp;https:\/\/polygon.technology\/polygon-zkevm<\/p>\n<p>[2]&nbsp;Polygon ID:&nbsp;https:\/\/polygon.technology\/polygon-id<\/p>\n<p>[3]&nbsp;\u65af\u8482\u82ac:&nbsp;https:\/\/twitter.com\/0ceans404<\/p>\n<p>[4]&nbsp;\u963f\u91cc\u5df4\u5df4\u6d1e\u7a74\u6545\u4e8b:&nbsp;https:\/\/en.wikipedia.org\/wiki\/Zero-knowledge_proof#The_Ali_Baba_cave<\/p>\n<p>[5]&nbsp;\u7528\u4e8e\u72ec\u7acb\u9a8c\u8bc1:&nbsp;https:\/\/ethereum.org\/en\/zero-knowledge-proofs\/#non-interactive-zero-knowledge-proofs<\/p>\n<p>[6]&nbsp;\u692d\u5706\u66f2\u7ebf\u914d\u5bf9:&nbsp;https:\/\/medium.com\/@VitalikButerin\/exploring-elliptic-curve-pairings-c73c1864e627<\/p>\n<p>[7]&nbsp;\u591a\u9879\u5f0f:&nbsp;https:\/\/vitalik.ca\/general\/2017\/11\/09\/starks_part_1.html<\/p>\n<p>[8]&nbsp;1:&nbsp;https:\/\/vitalik.ca\/general\/2017\/11\/09\/starks_part_1.html<\/p>\n<p>[9]&nbsp;2:&nbsp;https:\/\/vitalik.ca\/general\/2017\/11\/22\/starks_part_2.html<\/p>\n<p>[10]&nbsp;3:&nbsp;https:\/\/vitalik.ca\/general\/2018\/07\/21\/starks_part_3.html<\/p>\n<p>[11]&nbsp;\u4e0d\u540c\u7c7b\u578b\u7684 ZK-EVM:&nbsp;https:\/\/vitalik.ca\/general\/2022\/08\/04\/zkevm.html<\/p>\n<p>[12]&nbsp;Polygon zkEVM:&nbsp;https:\/\/polygon.technology\/polygon-zkevm<\/p>\n<p>[13]&nbsp;EVM:&nbsp;https:\/\/ethereum.org\/en\/developers\/docs\/evm\/<\/p>\n<p>[14]&nbsp;\u5b83\u4f7f\u7528STARK Recursion:&nbsp;https:\/\/zkevm.polygon.technology\/docs\/zkProver\/overview\/#stark-recursion-component<\/p>\n<p>[15]&nbsp;CIRCOM \u7ec4\u4ef6:&nbsp;https:\/\/zkevm.polygon.technology\/docs\/zkProver\/overview\/#circom-library<\/p>\n<p>[16]&nbsp;\u5728Polygon ID:&nbsp;https:\/\/polygon.technology\/polygon-id<\/p>\n<p>[17]&nbsp;Polygon \u7684 zkEVM:&nbsp;https:\/\/polygon.technology\/polygon-zkevm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u96f6\u77e5\u8bc6 (ZK) \u8bc1\u660e\u6b63\u5728\u4e3a web3 \u7684\u6700\u65b0\u521b\u65b0\u63d0\u4f9b\u52a8\u529b\u3002\u5b83\u4eec\u5df2\u7ecf\u88ab\u7528\u4e8ePolygon \u7684 zkEVM[1] 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