{"id":3711,"date":"2026-10-22T17:51:57","date_gmt":"2026-10-22T09:51:57","guid":{"rendered":"https:\/\/www.yqcsfz.com\/?p=3711"},"modified":"2026-10-22T17:51:57","modified_gmt":"2026-10-22T09:51:57","slug":"plinko-pir-%e6%95%99%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/www.chqs888.com\/?p=3711","title":{"rendered":"Plinko PIR \u6559\u7a0b &#8211;"},"content":{"rendered":"<p><em>\u7279\u522b\u611f\u8c22 Alex Hoover\u3001Keewoo Lee \u548c Ali \u7684\u53cd\u9988\u548c\u5ba1\u9605<\/em><\/p>\n<p>\u4e00\u79cd\u88ab\u4f4e\u4f30\u7684\u9690\u79c1\u5f62\u5f0f\uff0c\u662f ZK-SNARKs\u3001\u4f20\u7edf\u7248\u672c\u7684 FHE \u6216\u5176\u4ed6\u5e38\u88ab\u8ba8\u8bba\u7684\u65b9\u6cd5\u6240\u65e0\u6cd5\u5f88\u597d\u6ee1\u8db3\u7684\uff0c\u5c31\u662f <strong>\u79c1\u5bc6\u8bfb\u53d6<\/strong>\u3002\u7528\u6237\u5e0c\u671b\u4ece\u4e00\u4e2a\u5927\u578b\u6570\u636e\u5e93\u4e2d\u83b7\u53d6\u4fe1\u606f\uff0c\u800c\u4e0d\u900f\u9732\u4ed6\u4eec\u6b63\u5728\u9605\u8bfb\u7684\u5185\u5bb9\u3002\u4e00\u4e9b\u7528\u4f8b\u5305\u62ec\uff1a<\/p>\n<ul>\n<li>\u9690\u79c1\u4fdd\u62a4\u7684\u7ef4\u57fa\u767e\u79d1\uff08\u8fd9\u6837\u4f60\u53ef\u4ee5\u5728\u670d\u52a1\u5668\u751a\u81f3\u4e0d\u77e5\u9053\u4f60\u5728\u9605\u8bfb\u4ec0\u4e48\u7684\u60c5\u51b5\u4e0b\u5b66\u4e60\uff09<\/li>\n<li>\u9690\u79c1\u4fdd\u62a4\u7684 RAG \u6216 LLM \u641c\u7d22\uff08\u8fd9\u6837\u4f60\u7684\u672c\u5730 LLM \u53ef\u4ee5\u4ece\u4e92\u8054\u7f51\u83b7\u53d6\u6570\u636e\uff0c\u800c\u4e0d\u900f\u9732\u4f60\u5728\u67e5\u8be2\u4ec0\u4e48\uff09<\/li>\n<li>\u533a\u5757\u94fe\u6570\u636e\u8bfb\u53d6\uff08\u8fd9\u6837\u4f60\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u67e5\u8be2\u5916\u90e8 RPC \u8282\u70b9\u7684 dapp\uff0c\u800c\u8282\u70b9\u4e0d\u4f1a\u77e5\u9053\u4f60\u5728\u67e5\u8be2\u4ec0\u4e48\uff1b\u8bf7\u53c2\u89c1\u201c\u79c1\u5bc6\u8bfb\u53d6\u201d \u8fd9\u91cc\uff09<\/li>\n<\/ul>\n<p>\u6709\u4e00\u7c7b\u9690\u79c1\u534f\u8bae\u662f\u4e13\u95e8\u8bbe\u8ba1\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\uff0c\u79f0\u4e3a \u79c1\u5bc6\u4fe1\u606f\u68c0\u7d22 (PIR)\u3002\u4e00\u4e2a\u670d\u52a1\u5668\u6709\u4e00\u4e2a\u6570\u636e\u5e93 \\\\(D\\\\)\u3002\u4e00\u4e2a\u5ba2\u6237\u7aef\u6709\u4e00\u4e2a\u7d22\u5f15 \\\\(i\\\\)\u3002\u5ba2\u6237\u7aef\u5411\u670d\u52a1\u5668\u53d1\u9001\u4e00\u4e2a\u67e5\u8be2\uff0c\u670d\u52a1\u5668\u56de\u590d\u4e00\u4e2a\u7b54\u6848\uff0c\u4f7f\u5ba2\u6237\u7aef\u80fd\u591f\u91cd\u5efa \\\\(D[i]\\\\)\uff0c\u800c\u670d\u52a1\u5668\u5bf9 \\\\(i\\\\) \u4e00\u65e0\u6240\u77e5\u3002\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u5c06\u63cf\u8ff0\u6240\u6709 PIR \u534f\u8bae\u7684\u57fa\u672c\u539f\u7406\uff0c\u7136\u540e\u63cf\u8ff0 Plinko\uff0c\u4e00\u4e2a\u9ad8\u6548\u5b9e\u73b0\u8fd9\u4e00\u70b9\u7684\u534f\u8bae\u3002<\/p>\n<h2 id=\"pir\">PIR \u7684\u57fa\u672c\u539f\u7406<\/h2>\n<p>\u8981\u7406\u89e3\u66f4\u590d\u6742\u7684 PIR \u534f\u8bae\uff0c\u6700\u597d\u4ece\u201c\u7ecf\u5178\u53cc\u670d\u52a1\u5668 PIR\u201d\u5f00\u59cb\u3002\u7ecf\u5178\u53cc\u670d\u52a1\u5668 PIR \u5047\u8bbe\u5ba2\u6237\u7aef\u5411\u4e24\u4e2a\u670d\u52a1\u5668\u53d1\u51fa\u67e5\u8be2\uff0c\u5e76\u4e14\u5b83 \u4fe1\u4efb \u81f3\u5c11\u6709\u4e00\u4e2a\u662f\u8bda\u5b9e\u7684\u3002\u534f\u8bae\u7684\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491830948.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe\" \/><\/p>\n<ul>\n<li>\u5ba2\u6237\u7aef\u60f3\u77e5\u9053 \\\\(D[i]\\\\)\uff0c\u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\u662f \\\\(D[8]\\\\)\u3002<\/li>\n<li>\u5ba2\u6237\u7aef\u751f\u6210\u4e00\u4e2a\u968f\u673a\u7684\u7d22\u5f15\u5b50\u96c6\uff0c\u5e73\u5747\u7ea6\u4e3a\u4e00\u534a\uff08\u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\\\\([1, 5, 6, 10, 15]\\\\)\uff09\u3002<\/li>\n<li>\u5ba2\u6237\u7aef\u5c06\u8be5\u5b50\u96c6\u53d1\u9001\u7ed9\u4e00\u4e2a\u670d\u52a1\u5668\uff0c\u7136\u540e\u5c06\u4e00\u4e2a <em>\u4fee\u6539\u8fc7\u7684\u5b50\u96c6<\/em> \u53d1\u9001\u7ed9\u53e6\u4e00\u4e2a\u670d\u52a1\u5668\uff0c\u5176\u4e2d \\\\(D[i]\\\\) \u7684\u6210\u5458\u8d44\u683c\u88ab\u7ffb\u8f6c\uff08\u5373\uff0c\u5982\u679c\u4e0d\u5728\u5219\u6dfb\u52a0\uff0c\u5982\u679c\u5728\u5219\u79fb\u9664\uff09\u3002<\/li>\n<li>\u6bcf\u4e2a\u670d\u52a1\u5668\u8ba1\u7b97\u5b83\u88ab\u8be2\u95ee\u7684 \\\\(D[i]\\\\) \u4e2d\u503c\u7684 XOR\uff0c\u5e76\u8fd4\u56de\u7ed3\u679c\u3002<\/li>\n<li>\u5ba2\u6237\u7aef\u5bf9\u8fd9\u4e24\u4e2a\u503c\u8fdb\u884c XOR \u8fd0\u7b97\uff0c\u4ece\u800c\u5f97\u5230 \\\\(D[i]\\\\) \u7684\u503c\u3002<\/li>\n<\/ul>\n<p>\u5173\u952e\u601d\u60f3\u662f\u6bcf\u4e2a\u670d\u52a1\u5668\u63a5\u6536\u5230\u7684\u770b\u8d77\u6765\u50cf\u662f\u4e00\u4e2a\u5b8c\u5168\u968f\u673a\u7684\u7d22\u5f15\u5b50\u96c6\u3002\u7531\u4e8e\u6df7\u5408 \\\\(i\\\\) \u7684\u4fee\u6539\u662f\u6dfb\u52a0\u503c\u548c\u79fb\u9664\u503c\u7684\u53ef\u80fd\u6027\u76f8\u540c\uff0c\u56e0\u6b64\u6ca1\u6709\u4efb\u4f55\u8f7b\u5fae\u7684\u504f\u5dee\u3002\u8fd9\u4e24\u4e2a\u670d\u52a1\u5668\u7ed9\u51fa\u7684\u5b50\u96c6\u7684 XOR \u548c\u51e0\u4e4e\u76f8\u540c\uff0c\u4f46\u5728\u4e00\u4e2a\u5730\u65b9\u4e0d\u540c\uff1a\u4e00\u4e2a\u5305\u542b \\\\(D[i]\\\\)\uff0c\u800c\u53e6\u4e00\u4e2a\u4e0d\u5305\u542b\u3002\u5ba2\u6237\u7aef\u83b7\u53d6\u8fd9\u4e24\u4e2a\u503c\uff0c\u5e76\u8ba1\u7b97\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u4ece\u800c\u5f97\u5230 \\\\(D[i]\\\\)\u3002<\/p>\n<p>\u8fd9\u81ea\u7136\u53ef\u4ee5\u63a8\u5e7f\u5230\u201c\u5927\u4e8e\u4e00\u4e2a\u6bd4\u7279\u7684\u5355\u5143\u201d\uff1b\u4f60\u53ef\u4ee5\u8ba9\u6bcf\u4e2a \\\\(D[i]\\\\) \u4f8b\u5982\u6709 1000 \u4e2a\u6bd4\u7279\uff0c\u534f\u8bae\u5b8c\u5168\u76f8\u540c\u3002<\/p>\n<p>\u8be5\u534f\u8bae\u6709\u4e09\u4e2a\u4e3b\u8981\u5f31\u70b9\uff1a<\/p>\n<ol>\n<li>\u4f60\u5fc5\u987b\u4fe1\u4efb\u4e24\u4e2a\u670d\u52a1\u5668\u4e2d\u7684\u4e00\u4e2a\u662f\u8bda\u5b9e\u7684\u3002<\/li>\n<li>\u5ba2\u6237\u7aef\u7684\u901a\u4fe1\u5f00\u9500\u7b49\u4e8e\u5355\u5143\u7684\u6570\u91cf\uff08\u5982\u679c\u5355\u5143\u5f88\u5927\uff0c\u8fd9\u53ef\u80fd\u8fdc\u5c0f\u4e8e\u6570\u636e\u7684\u603b\u5927\u5c0f\uff0c\u4f46\u4ecd\u7136\u662f\u5f88\u591a\uff09\u3002<\/li>\n<li>\u670d\u52a1\u5668\u5fc5\u987b\u5bf9\u534a\u4e2a\u603b\u6570\u636e\u8fdb\u884c XOR \u8fd0\u7b97\u4ee5\u54cd\u5e94\u5355\u4e2a\u67e5\u8be2\u3002<\/li>\n<\/ol>\n<p>\u6709\u4e24\u79cd\u5bf9\u7ecf\u5178\u53cc\u670d\u52a1\u5668 PIR \u7684\u4fee\u6539\u662f\u4f17\u6240\u5468\u77e5\u7684\uff0c\u53ef\u4ee5\u89e3\u51b3\uff081\uff09\u3002<\/p>\n<p>\u4e00\u79cd\u7b56\u7565\u662f <strong>\u5e26\u9884\u5904\u7406\u7684 PIR<\/strong>\u3002\u6ce8\u610f\uff0c\u5728\u4e0a\u8ff0\u534f\u8bae\u4e2d\uff0c\u4f60\u53ef\u4ee5\u5728\u751a\u81f3\u4e0d\u77e5\u9053\u8981\u67e5\u8be2\u54ea\u4e2a \\\\(i\\\\) \u4e4b\u524d\u8ba1\u7b97\u4e24\u4e2a\u968f\u673a\u6837\u672c\u96c6\u4e4b\u4e00\u3002\u4f60\u751f\u6210\u6210\u5343\u4e0a\u4e07\u7684\u8fd9\u4e9b\u968f\u673a\u67e5\u8be2\u3002\u4f60\u6709\u4e00\u4e2a\u521d\u59cb\u9636\u6bb5\uff0c\u5728\u8fd9\u4e2a\u9636\u6bb5\u4f60\u4e0b\u8f7d\uff08\u4f46\u4e0d\u9700\u8981\u5b58\u50a8\uff09\u6574\u4e2a\u6587\u4ef6 \\\\(D\\\\)\uff0c\u5e76\u5728\u672c\u5730\u8ba1\u7b97\u8fd9\u4e9b\u968f\u673a\u7d22\u5f15\u96c6\u7684 XOR \u548c\u3002\u57fa\u672c\u4e0a\uff0c\u4f60\u5145\u5f53\u4e86\u4e24\u4e2a\u670d\u52a1\u5668\u4e4b\u4e00\u2014\u2014\u4ee5\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6ee1\u8db3\u4e86 1-of-2 \u7684\u4fe1\u4efb\u5047\u8bbe\uff0c\u56e0\u6b64\u4f60\u4e0d\u9700\u8981\u4fe1\u4efb\u53e6\u4e00\u4e2a\u670d\u52a1\u5668\u3002\u8fd9\u79cd\u65b9\u6cd5\u786e\u5b9e\u9700\u8981\u5927\u91cf\u7684\u524d\u671f\u5e26\u5bbd\uff0c\u4f46\u4f60\u53ef\u4ee5\u63d0\u524d\u5b8c\u6210\uff0c\u6216\u8005\u5728\u540e\u53f0\u8fdb\u884c\uff0c\u5e76\u4f7f\u7528\u4e00\u79cd\u6548\u7387\u8f83\u4f4e\u7684 PIR \u5f62\u5f0f\u6765\u56de\u7b54\u5728\u5b8c\u6210\u4e4b\u524d\u6536\u5230\u7684\u4efb\u4f55\u67e5\u8be2\u3002<\/p>\n<p>\u53e6\u4e00\u79cd\u7b56\u7565\u662f <strong>\u5355\u670d\u52a1\u5668 PIR<\/strong>\u3002\u57fa\u672c\u4e0a\uff0c\u4f60\u4f7f\u7528\u67d0\u79cd\u53d8\u4f53\u7684\u540c\u6001\u52a0\u5bc6\uff08\u901a\u5e38\u6bd4\u5b8c\u5168\u7684 FHE \u66f4\u7b80\u5355\uff09\u6765\u52a0\u5bc6\u4f60\u7684\u67e5\u8be2\uff0c\u4ee5\u4fbf\u670d\u52a1\u5668\u53ef\u4ee5\u5728\u4f60\u7684\u52a0\u5bc6\u67e5\u8be2\u4e0a\u8fdb\u884c\u8ba1\u7b97\uff0c\u4ece\u800c\u7ed9\u4f60\u4e00\u4e2a\u52a0\u5bc6\u7684\u7b54\u6848\u3002\u8fd9\u5728\u670d\u52a1\u5668\u7aef\u7684\u8ba1\u7b97\u5f00\u9500\u5f88\u9ad8\uff0c\u56e0\u6b64\u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\u636e\u96c6\u6765\u8bf4\u5c1a\u4e0d\u53ef\u884c\u3002\u8fd9\u79cd\u7b56\u7565\u53ef\u4ee5\u4e0e\u5e26\u9884\u5904\u7406\u7684 PIR \u7ed3\u5408\u4f7f\u7528\uff0c\u56e0\u6b64\u7406\u8bba\u4e0a\u4f60\u53ef\u4ee5\u901a\u8fc7\u5728\u670d\u52a1\u5668\u7aef\u8fdb\u884c\u540c\u6001\u52a0\u5bc6\u7684\u8fc7\u7a0b\u6765\u907f\u514d\u521d\u59cb\u4e0b\u8f7d\u3002<\/p>\n<p>Plinko \u89e3\u51b3\u4e86\uff082\uff09\u548c\uff083\uff09\u2014\u2014\u6216\u8005\u81f3\u5c11\uff0c\u5b83\u5c06\u901a\u4fe1\u5f00\u9500\u548c\u670d\u52a1\u5668\u7aef\u8ba1\u7b97\u5f00\u9500\u4ece \\\\(O(N)\\\\) \u964d\u4f4e\u5230 \\\\(O(\\\\sqrt{N})\\\\)\uff0c\u5176\u4e2d \\\\(N\\\\) \u662f\u5355\u5143\u7684\u6570\u91cf\u3002\u5b83\u4f7f\u7528\u9884\u5904\u7406\u7b56\u7565\u6765\u6d88\u9664\u4fe1\u4efb\u5047\u8bbe\u3002\u7406\u8bba\u4e0a\uff0c\u4f60\u53ef\u4ee5\u5728 FHE \u4e2d\u8fdb\u884c\u9884\u5904\u7406\uff1b\u76ee\u524d\u8fd9\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898\uff0c\u5c1a\u672a\u6709\u6548\u5730\u505a\u5230\u8fd9\u4e00\u70b9\u3002<\/p>\n<p>\u5728 Plinko \u7684\u672f\u8bed\u4e2d\uff0c\u6709\uff1a<\/p>\n<ul>\n<li>\u4e00\u4e2a <strong>\u8bbe\u7f6e\u9636\u6bb5<\/strong>\uff0c\u5ba2\u6237\u7aef\u5904\u7406\u6240\u6709\u6570\u636e\u4e00\u6b21\uff08\u4f46\u53ea\u8bb0\u4f4f\u5c11\u91cf\u7684\u201c<strong>\u63d0\u793a<\/strong>\u201d\uff09<\/li>\n<li>\u4e00\u4e2a <strong>\u67e5\u8be2\u673a\u5236<\/strong>\uff0c\u5ba2\u6237\u7aef\u5411\u670d\u52a1\u5668\u53d1\u51fa\u67e5\u8be2\uff0c\u5e76\u5c06\u7b54\u6848\u4e0e\u6b63\u786e\u7684\u63d0\u793a\u7ed3\u5408\u4ee5\u8ba1\u7b97\u6240\u9700\u7684\u503c\u3002<\/li>\n<\/ul>\n<p>\u5982\u679c\u6570\u636e\u96c6\u53d1\u751f\u53d8\u5316\uff0c\u5ba2\u6237\u7aef\u4e5f\u6709\u4e00\u79cd\u7b80\u5355\u7684\u65b9\u6cd5\u6765\u66f4\u65b0\u63d0\u793a\u3002\u73b0\u5728\uff0c\u8ba9\u6211\u4eec\u8fdb\u5165\u534f\u8bae\uff01<\/p>\n<h2 id=\"\">\u8bbe\u7f6e\u9636\u6bb5<\/h2>\n<p>\u5c06\u6570\u636e\u5e93\u89c6\u4e3a\u4e00\u4e2a\u6b63\u65b9\u5f62\uff0c\u5177\u6709 \\\\(\\\\sqrt{N}\\\\) \u884c\u548c \\\\(\\\\sqrt{N}\\\\) \u5217\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491835704.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe1\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe1\" \/><\/p>\n<p>\u5ba2\u6237\u7aef\u751f\u6210\u4e00\u4e2a\u968f\u673a\u4e3b\u79cd\u5b50 \\\\(S\\\\)\u3002\u5bf9\u4e8e\u6bcf\u4e00\u884c \\\\(i\\\\)\uff0c\u5ba2\u6237\u7aef\u4f7f\u7528\u4e3b\u79cd\u5b50\u751f\u6210\u4e00\u884c\u79cd\u5b50 \\\\(S_i\\\\)\u3002\u5ba2\u6237\u7aef\u751f\u6210\u5927\u7ea6 \\\\(128 * \\\\sqrt{N}\\\\)<strong>\u63d0\u793a<\/strong>\u3002\u6bcf\u4e2a\u63d0\u793a\u7684\u751f\u6210\u65b9\u5f0f\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u968f\u673a\uff08\u6216\u66f4\u786e\u5207\u5730\u8bf4\uff0c\u901a\u8fc7\u5bf9\u4e3b\u79cd\u5b50\u8fdb\u884c\u54c8\u5e0c\u4f2a\u968f\u673a\uff09\u9009\u62e9 \\\\(\\\\frac{\\\\sqrt{N}}{2} + 1\\\\) \u884c<\/li>\n<li>\u5982\u679c\u6211\u4eec\u6b63\u5728\u8ba1\u7b97\u7b2c \\\\(j\\\\) \u4e2a\u63d0\u793a\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u884c \\\\(r_i\\\\)\uff0c\u4f7f\u7528\u54c8\u5e0c \\\\(H(S_{r_i}, j)\\\\) \u751f\u6210\u4e00\u4e2a\u968f\u673a\u5217 \\\\(c_i\\\\)\u3002\u56e0\u6b64\u6211\u4eec\u5f97\u5230 \\\\(\\\\frac{\\\\sqrt{N}}{2} + 1\\\\) \u5bf9 \\\\((r_i, c_i)\\\\)<\/li>\n<li>\u5bf9\u8fd9\u4e9b\u5bf9\u8fdb\u884c XOR \u8fd0\u7b97\uff0c\u5e76\u4fdd\u5b58\u8be5\u4f4d<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491839860.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe2\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe2\" \/><\/p>\n<p>\u7528\u4e8e\u8ba1\u7b97 \\\\(c_i\\\\) \u503c\u7684\u201c\u54c8\u5e0c\u201d <em>\u53ef\u4ee5<\/em> \u662f\u5e38\u89c4\u54c8\u5e0c\uff0c\u4f46\u8fd9\u4f1a\u5bfc\u81f4\u67e5\u8be2\u9636\u6bb5\u7684\uff08\u53ef\u5bb9\u5fcd\u4f46\u663e\u8457\u7684\uff09\u4f4e\u6548\u3002\u56e0\u6b64\uff0cPlinko \u66f4\u503e\u5411\u4e8e\u4e00\u79cd\u79f0\u4e3a\u201c\u53ef\u9006 PRF\u201d\u7684\u7279\u6b8a\u7c7b\u578b\u54c8\u5e0c\u3002\u5b83\u5b9e\u73b0\u7684\u6838\u5fc3\u5c5e\u6027\u662f\uff0c\u7ed9\u5b9a \\\\(S_i\\\\) \u548c \\\\(c_i\\\\)\uff0c\u4f60\u53ef\u4ee5\u8f7b\u677e\u6062\u590d\u6240\u6709\u5bfc\u81f4\u8be5 \\\\(c_i\\\\) \u7684 \\\\(j\\\\) \u503c\u3002\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u4efb\u4f55\u5355\u5143 \\\\((r_i, c_i)\\\\)\uff0c\u4f60\u53ef\u4ee5\u8f7b\u677e\u627e\u5230\u201c\u5305\u542b\u201d\u8be5\u5355\u5143\u7684\u6240\u6709\u63d0\u793a\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u8bbe\u7f6e\u9636\u6bb5\u8fd8\u751f\u6210\u4e00\u4e9b\u201c\u5907\u4efd\u63d0\u793a\u201d\u3002\u8fd9\u4e9b\u63d0\u793a\u7684\u6784\u9020\u65b9\u5f0f\u4e0e\u5e38\u89c4\u63d0\u793a\u76f8\u4f3c\uff0c\u4f46\u5bf9\u4e8e\u6bcf\u4e2a\u7d22\u5f15 \\\\(j\\\\)\uff0c\u4f60\u9009\u62e9 \\\\(\\\\frac{\\\\sqrt{N}}{2}\\\\) \u884c\uff0c\u5e76\u8ba1\u7b97\u4e00\u5bf9\u63d0\u793a\uff1a\u4e00\u4e2a\u662f\u9488\u5bf9\u6240\u9009\u7684\u884c\u5b50\u96c6\uff0c\u53e6\u4e00\u4e2a\u662f\u9488\u5bf9\u5176 <em>\u8865\u96c6<\/em>\uff08\u5373\u672a\u9009\u62e9\u7684 \\\\(\\\\frac{\\\\sqrt{N}}{2}\\\\) \u884c\uff09\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491842766.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe3\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe3\" \/><\/p>\n<p>\u6574\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u201c\u6d41\u5f0f\u201d\u8fdb\u884c\uff0c\u65e0\u9700\u5ba2\u6237\u7aef\u5728\u4efb\u4f55\u65f6\u5019\u5b58\u50a8\u4efb\u4f55\u6570\u636e\uff0c\u9664\u4e86\u63d0\u793a\u672c\u8eab\u3002\u603b\u7684\u6765\u8bf4\uff0c\u5ba2\u6237\u7aef\u9700\u8981\u4e0b\u8f7d\u6574\u4e2a\u6570\u636e\u96c6\u5e76\u5b58\u50a8\u5927\u7ea6 \\\\(64 \\\\*\\\\sqrt{N}\\\\) \u4e2a\u5355\u5143\u7684\u6570\u636e\uff0c\u4ee5\u53ca\u6bcf\u4e2a\u5907\u4efd\u63d0\u793a \\\\(\\\\sqrt{N}\\\\) \u4e2a\u5355\u5143\uff08\u5ba2\u6237\u7aef\u9700\u8981\u4e3a\u6bcf\u4e2a\u5c06\u8981\u53d1\u51fa\u7684\u67e5\u8be2\u51c6\u5907\u4e00\u4e2a\u5907\u4efd\u63d0\u793a\uff09\u3002<\/p>\n<p>\u5982\u679c\u9700\u8981\uff0c\u8be5\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u5728 FHE \u4e2d\u8fdb\u884c\uff0c\u8fd9\u610f\u5473\u7740\u5ba2\u6237\u7aef\u53ea\u9700\u4e0b\u8f7d\u63d0\u793a\uff0c\u4f46\u670d\u52a1\u5668\u9700\u8981\u5bf9\u6574\u4e2a\u6570\u636e\u96c6\u8fdb\u884c FHE \u5904\u7406\uff1b\u8fd9\u5f53\u7136\u662f\u6602\u8d35\u7684\uff0c\u4f18\u5316\u8fd9\u4e00\u70b9\u4ecd\u7136\u662f\u4e00\u4e2a\u6301\u7eed\u7684\u95ee\u9898\u3002<\/p>\n<h2 id=\"-1\">\u67e5\u8be2\u9636\u6bb5<\/h2>\n<p>\u5047\u8bbe\u4f60\u5bf9\u7279\u5b9a\u5750\u6807 \\\\((x, y)\\\\) \u611f\u5174\u8da3\u3002\u9996\u5148\uff0c\u4f60\u53d1\u73b0\u4e00\u4e2a\u63d0\u793a\u7d22\u5f15 \\\\(j\\\\)\uff0c\u8be5\u7d22\u5f15\u751f\u6210\u4e00\u4e2a\u5305\u542b \\\\((x, y)\\\\) \u7684\u63d0\u793a\u3002\u8fd9\u65f6\uff0c\u201c\u53ef\u9006 PRF\u201d\u673a\u5236\u53d1\u6325\u4e86\u4f5c\u7528\uff1a\u5b83\u8ba9\u4f60\u5728\u77e5\u9053 \\\\(S_x\\\\) \u548c \\\\(y\\\\) \u7684\u60c5\u51b5\u4e0b\u7acb\u5373\u53cd\u5411\u8fd0\u884c\u8be5\u51fd\u6570\uff0c\u4ee5\u8ba1\u7b97\u6240\u6709\u6ee1\u8db3 \\\\(H(S_x, j) = y\\\\) \u7684 \\\\(j\\\\)\u3002\u7136\u800c\uff0c\u5982\u679c\u4f60\u60f3\u907f\u514d\u8fd9\u79cd\u590d\u6742\u6027\uff0c\u4f60\u53ef\u4ee5\u7b80\u5355\u5730\u8bbe\u7f6e \\\\(H(S_x, j) = sha256(S_x, \\\\lfloor \\\\frac{j}{16}\\\\rfloor)[j \\\\% 16: (j \\\\% 16) + 2]\\\\)\uff0c\u7136\u540e\u6bcf\u6b21\u5e73\u5747\u8ba1\u7b97 \\\\(\\\\frac{\\\\sqrt{N}}{16}\\\\) \u4e2a\u54c8\u5e0c\u3002<\/p>\n<p>\u7136\u540e\uff0c\u4f60\u786e\u5b9a\u63d0\u793a\u751f\u6210\u7684 \\\\(\\\\frac{\\\\sqrt{N}}{2} + 1\\\\) \u884c\u3002\u4f60 <em>\u53bb\u6389<\/em> \u884c \\\\(x\\\\)\u3002\u7136\u540e\u4f60\u5411\u670d\u52a1\u5668\u53d1\u9001\u4e00\u4e2a\u5305\u542b\u4ee5\u4e0b\u5185\u5bb9\u7684\u6d88\u606f\uff1a<\/p>\n<ul>\n<li>\\\\([(r_1, c_1), (r_2, c_2) \u2026(r_{\\\\frac{\\\\sqrt{N}}{2}}, c_{\\\\frac{\\\\sqrt{N}}{2}})]\\\\)\uff1a\u8be5\u63d0\u793a\u4e2d\u5305\u542b\u7684\u70b9\u96c6\uff0c\u9664\u4e86\u4f60\u60f3\u8981\u7684\u70b9<\/li>\n<li>\\\\([(x_1, y_1), (x_2, y_2) \u2026(x_{\\\\frac{\\\\sqrt{N}}{2}}, y_{\\\\frac{\\\\sqrt{N}}{2}})]\\\\)\uff1a\u6240\u6709 <em>\u5176\u4ed6<\/em> \u884c\u7684\u96c6\u5408\uff08\u5305\u62ec\u4f60\u60f3\u8981\u7684\u884c\uff09\uff0c\u6bcf\u4e00\u884c\u90fd\u6709\u4e00\u4e2a\u968f\u673a\u9009\u62e9\u7684\u5217<\/li>\n<\/ul>\n<p>\u4f60\u4ee5\u968f\u673a\u987a\u5e8f\u53d1\u9001\u8fd9\u4e9b\uff0c\u56e0\u6b64\u670d\u52a1\u5668\u4e0d\u77e5\u9053\u54ea\u4e2a\u662f\u54ea\u4e2a\u3002\u5c31\u670d\u52a1\u5668\u800c\u8a00\uff0c\u4f60\u53ea\u662f\u5411\u5b83\u53d1\u9001\u4e86\u4e00\u7ec4\u968f\u673a\u70b9\uff0c\u6bcf\u884c\u4e00\u4e2a\uff0c\u884c\u4ee5\u4efb\u610f\u65b9\u5f0f\u5206\u6210\u4e24\u534a\u3002\u670d\u52a1\u5668\u5bf9\u8fd9\u4e24\u7ec4\u5355\u5143\u8fdb\u884c XOR \u8fd0\u7b97\uff0c\u5e76\u56de\u590d\u4e24\u4e2a\u8f93\u51fa\u3002<\/p>\n<p>\u7136\u540e\uff0c\u5ba2\u6237\u7aef\u5728\u672c\u5730\u5c06\u5176\u63d0\u793a\u4e0e\u670d\u52a1\u5668\u8fd4\u56de\u7684\uff08\u975e\u5783\u573e\uff09\u503c\u8fdb\u884c XOR \u8fd0\u7b97\uff0c\u4ece\u800c\u5f97\u51fa\u7b54\u6848\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491846352.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe4\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe4\" \/><\/p>\n<p>\u670d\u52a1\u5668\u57fa\u4e8e \\\\(\\\\sqrt{N}\\\\) \u4e2a\u5355\u5143\u8fdb\u884c\u8ba1\u7b97\uff0c\u5e76\u5c06\u8be5\u6570\u636e\u8fd4\u56de\u7ed9\u5ba2\u6237\u7aef\u3002\u670d\u52a1\u5668\u5bf9\u5ba2\u6237\u7aef\u60f3\u8981\u54ea\u4e2a\u5355\u5143\u4e00\u65e0\u6240\u77e5\uff08\u524d\u63d0\u662f\u5ba2\u6237\u7aef\u4e0d\u91cd\u590d\u4f7f\u7528\u63d0\u793a\uff09\uff0c\u56e0\u4e3a\u5ba2\u6237\u7aef\u7ed9\u670d\u52a1\u5668\u63d0\u4f9b\u4e86\u63d0\u793a\u4e2d\u6bcf\u4e2a\u70b9\u7684\u6240\u6709\u70b9 <em>\u9664\u4e86<\/em> \u5b83\u5b9e\u9645\u60f3\u8981\u7684\u70b9\u3002\u800c\u4e14\u5728\u4e0d\u77e5\u9053\u751f\u6210\u8fd9\u4e9b\u5b50\u96c6\u7684\u54c8\u5e0c\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u670d\u52a1\u5668\u800c\u8a00\uff0c\u6240\u6709\u884c\u548c\u5217\u7684\u9009\u62e9\u770b\u8d77\u6765\u90fd\u662f\u5b8c\u5168\u968f\u673a\u7684\u3002<\/p>\n<h2 id=\"-2\">\u5907\u4efd\u67e5\u8be2<\/h2>\n<p>\u4e3a\u4e86\u907f\u514d\u91cd\u590d\u4f7f\u7528\u63d0\u793a\uff08\u4ece\u800c\u6cc4\u9732\u6570\u636e\uff09\uff0c\u5f53\u5ba2\u6237\u7aef\u53d1\u51fa\u67e5\u8be2\u65f6\uff0c\u5b83\u4f1a\u4e22\u5f03\u6240\u4f7f\u7528\u7684\u63d0\u793a\uff0c\u5e76\u5c06\u4e00\u4e2a\u5907\u4efd\u63d0\u793a\u201c\u63d0\u5347\u201d\u4e3a\u5e38\u89c4\u63d0\u793a\u3002\u8bf7\u8bb0\u4f4f\uff0c\u6bcf\u4e2a\u201c\u5907\u4efd\u63d0\u793a\u201d\u662f\u4e00\u5bf9\u63d0\u793a\uff0c\u4e00\u4e2a\u57fa\u4e8e\u968f\u673a\u5b50\u96c6\u7684\u884c\uff0c\u53e6\u4e00\u4e2a\u57fa\u4e8e\u5176\u8865\u96c6\u3002\u7b97\u6cd5\u5f88\u7b80\u5355\uff1a<\/p>\n<ul>\n<li>\u53d6\u51fa\u4ece\u4e0d\u5305\u542b\u4f60\u67e5\u8be2\u7684\u884c\u7684\u884c\u5b50\u96c6\u751f\u6210\u7684\u63d0\u793a\u503c<\/li>\n<li>\u5c06\u4f60\u67e5\u8be2\u7684\u503c\u8fdb\u884c XOR \u8fd0\u7b97<\/li>\n<\/ul>\n<p>\u73b0\u5728\uff0c\u4f60\u6709\u4e00\u7ec4 \\\\(\\\\frac{\\\\sqrt{N}}{2}+ 1\\\\) \u884c\uff0c\u6bcf\u884c\u90fd\u6709\u4e00\u4e2a\u968f\u673a\u9009\u62e9\u7684\u5217\u7684 XOR\uff1a\u683c\u5f0f\u4e0e\u5e38\u89c4\u63d0\u793a\u5b8c\u5168\u76f8\u540c\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491851798.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe5\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe5\" \/><\/p>\n<h2 id=\"-3\">\u66f4\u65b0\u6570\u636e\u96c6<\/h2>\n<p>\u5047\u8bbe\u6570\u636e\u4e2d\u7684\u4e00\u4e2a\u503c\u66f4\u65b0\u4e86\u3002\u90a3\u4e48\uff0c\u4f60\u53ef\u4ee5\u627e\u5230\u6240\u6709\u5305\u542b\u8be5\u503c\u7684\u63d0\u793a\uff0c\u5e76\u7b80\u5355\u5730\u8fdb\u884c\u76f4\u63a5\u66f4\u65b0\uff1a\u5c06\u65e7\u503c\u548c\u65b0\u503c\u7684 XOR \u6df7\u5408\u5728\u4e00\u8d77\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491854452.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe6\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe6\" \/><\/p>\n<p>\u8fd9\u5c31\u662f\u6574\u4e2a\u534f\u8bae\uff01<\/p>\n<h2 id=\"-4\">\u5177\u4f53\u6548\u7387<\/h2>\n<p>\u5728\u6e10\u8fd1\u610f\u4e49\u4e0a\uff0cPlinko \u4e2d\u7684\u4e00\u5207\u90fd\u662f \\\\(O(\\\\sqrt{N})\\\\)\uff1a\u5ba2\u6237\u7aef\u9700\u8981\u5b58\u50a8\u7684\u63d0\u793a\u5927\u5c0f\u3001\u6bcf\u4e2a\u67e5\u8be2\u4f20\u8f93\u7684\u6570\u636e\uff08<em>\u6280\u672f\u4e0a<\/em> \u662f \\\\(O(\\\\sqrt{N} *log(N))\\\\)\uff09\u4ee5\u53ca\u670d\u52a1\u5668\u7aef\u7684\u8ba1\u7b97\u6210\u672c\u3002\u4f46\u5c06\u8fd9\u4e00\u5207\u653e\u5728\u73b0\u5b9e\u5de5\u4f5c\u8d1f\u8f7d\u7684\u80cc\u666f\u4e0b\u662f\u6709\u5e2e\u52a9\u7684\u3002\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u4f7f\u7528\u6211\u6700\u719f\u6089\u7684\u73b0\u5b9e\u5de5\u4f5c\u8d1f\u8f7d\uff1a\u4ee5\u592a\u574a\u3002<\/p>\n<p>\u5047\u8bbe\u4f60\u6b63\u5728\u67e5\u8be2\u4e00\u4e2a\u5305\u542b 100 \u4ebf\u4e2a\u503c\u7684\u6570\u636e\u96c6\uff0c\u6bcf\u4e2a\u503c\u4e3a 32 \u5b57\u8282\u3002\u8fd9\u662f\u5bf9\u4ee5\u592a\u574a\u72b6\u6001\u6811\u7684\u4e00\u4e2a\u76f8\u5f53\u597d\u7684\u63cf\u8ff0\uff0c\u51e0\u5e74\u540e\u5b83\u5c06\u7531\u4e8e\u89c4\u6a21\u7684\u6269\u5927\u800c\u53d8\u5f97\u663e\u8457\u66f4\u5927\u3002\u6211\u4eec\u4f7f\u7528 \u5e03\u8c37\u9e1f\u54c8\u5e0c \u5c06\u952e\u503c\u5b58\u50a8\u8f6c\u6362\u4e3a Plinko \u5904\u7406\u7684\u201c\u6241\u5e73\u201d\u67e5\u627e\u8868\u3002<\/p>\n<p>\u4e3a\u4e86\u5305\u542b Merkle \u5206\u652f\uff0c\u4e00\u79cd\u7b80\u5355\u7684\u65b9\u6cd5\uff08\u5c3d\u7ba1\u4e0d\u662f\u6700\u4f18\u7684\u65b9\u6cd5\uff09\u662f\u5c06\u5b83\u4eec\u5355\u72ec\u89c6\u4e3a\u5bf9\u8f83\u5c0f\u6570\u636e\u5e93\u7684\u67e5\u8be2\uff1b\u5982\u679c\u5b83\u662f\u4e00\u4e2a \u4e8c\u53c9\u6811\uff0c\u90a3\u4e48\u7b2c\u4e00\u5c42\u662f\u5168\u5c3a\u5bf8\uff0c\u7b2c\u4e8c\u5c42\u662f\u534a\u5c3a\u5bf8\uff0c\u7b2c\u4e09\u5c42\u662f\u56db\u5206\u4e4b\u4e00\u5c3a\u5bf8\uff0c\u7b49\u7b49\uff1b\u56e0\u4e3a PIR \u6210\u672c\u90fd\u4e0e\u5e73\u65b9\u6839\u6210\u6b63\u6bd4\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u7684\u603b\u6210\u672c\u5c06\u88ab\u4e58\u4ee5 \\\\(1 + 1 + \\\\frac{1}{\\\\sqrt{2}} +\\\\frac{1}{2} + \\\\frac{1}{2\\\\sqrt{2}} + \u2026 = 3 + \\\\sqrt{2} \\\\approx4.414\\\\)\u3002\u4ee5\u592a\u574a\u7684\u72b6\u6001\u6811\uff08\u76ee\u524d\uff09\u662f\u4e00\u4e2a \u6548\u7387\u8f83\u4f4e\u7684\u516d\u53c9\u6811\uff0c\u4f46\u4f60\u53ef\u4ee5\u901a\u8fc7 ZK \u8bc1\u660e\u4e0e\u4e8c\u53c9\u6811\u7684\u7b49\u4ef7\u6027\uff0c\u4ee5\u83b7\u5f97\u4eca\u5929\u4e8c\u53c9\u6811\u7684\u6548\u7387\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491856401.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe7\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe7\" \/><\/p>\n<p>\u4f46\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u63d0\u4f9b\u6ca1\u6709 Merkle \u5206\u652f\u7684\u539f\u59cb\u6210\u672c\u3002\u8fd9\u610f\u5473\u7740\u4e00\u4e2a 100000\u00d7100000 \u7684\u7f51\u683c\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5355\u5143\u4e3a 32 \u5b57\u8282\uff08256 \u4f4d\uff09\u3002\u5ba2\u6237\u7aef\u9700\u8981\u5b58\u50a8 100000\u00d7128 \u7684\u63d0\u793a\uff0c\u5373 100000 \u00d7 128 \u00d7 32 \u5b57\u8282 ~= <strong>390 MB<\/strong>\uff0c\u52a0\u4e0a\u4e00\u4e9b\u989d\u5916\u7684\u5907\u4efd\u63d0\u793a\u3002<\/p>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u67e5\u8be2\uff0c\u5ba2\u6237\u7aef\u9700\u8981\u5411\u670d\u52a1\u5668\u53d1\u9001\u884c\u7684\u5206\u533a\uff0c\u5206\u4e3a\u4e24\u90e8\u5206\uff0c\u4ee5\u53ca 100000 \u4e2a\u5217\u7d22\u5f15\u3002\u6211\u4eec<em>\u53ef\u4ee5<\/em> \u975e\u5e38\u806a\u660e\u5730\u505a\u5f97\u6bd4\u8fd9\u7a0d\u597d\uff0c\u4f46\u5982\u679c\u6211\u4eec\u5929\u771f\u5730\u505a\uff0c\u884c\u5206\u533a\u662f 100000 \u4f4d\uff0812.2 kB\uff09\uff0c\u5217\u7d22\u5f15\u662f 100000 * ceil(log2(100000)) = 1.7m \u4f4d = 202.7 kB\u3002\u8fd9\u4e24\u8005\u52a0\u8d77\u6765\u6bcf\u4e2a\u67e5\u8be2\u4e3a <strong>215 kB<\/strong>\u3002<\/p>\n<p>\u5982\u679c\u5f15\u5165 Merkle \u5206\u652f\uff0c\u63d0\u793a\u6210\u672c\u5c06\u98d9\u5347\u81f3\u7ea6 <strong>1.68 GB<\/strong>\u3002\u901a\u8fc7\u5de7\u5999\u7684\u5de5\u4f5c\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u53ef\u4ee5\u907f\u514d\u6bcf\u4e2a\u67e5\u8be2\u7684\u901a\u4fe1\u6210\u672c\u589e\u52a0 4.414 \u500d\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u8c03\u6574 PIR\uff0c\u4f7f\u5f97\u6211\u4eec\u5bf9\u8868\u793a\u6811\u7684\u4e0d\u540c\u5c42\u7ea7\u7684\u6570\u636e\u96c6\u4f7f\u7528\u76f8\u540c\uff08\u6216\u66f4\u786e\u5207\u5730\u8bf4\uff0c\u7c7b\u4f3c\u7684\uff09\u67e5\u8be2\u7d22\u5f15\u3002<\/p>\n<p>\u670d\u52a1\u5668\u7aef\u7684\u6210\u672c\u6d89\u53ca\u8bfb\u53d6\u548c XOR 100000 \u4e2a\u5355\u5143\uff0c\u6216\u6bcf\u4e2a\u67e5\u8be2 3.05MB\uff1bXOR \u662f\u5fae\u4e0d\u8db3\u9053\u7684\uff0c\u4f46\u8bfb\u53d6\u8d1f\u8f7d\u662f\u663e\u8457\u7684\u3002\u6dfb\u52a0 Merkle \u5206\u652f\u7406\u8bba\u4e0a\u4f1a\u5c06\u5176\u589e\u52a0\u5230\u7ea6 13.4 MB\uff0c\u5c3d\u7ba1\u5b9e\u9645\u589e\u52a0\u7684\u6210\u672c\u53ef\u80fd\u5fae\u4e0d\u8db3\u9053\uff0c\u56e0\u4e3a\u5de7\u5999\u7684\u5de5\u7a0b\u53ef\u4ee5\u786e\u4fdd\u5339\u914d\u7684\u503c\u59cb\u7ec8\u5728\u540c\u4e00\u9875\u9762\u4e2d\uff08\u5185\u5b58\u9875\u9762\u901a\u5e38\u4e3a 4096 \u5b57\u8282\uff09\u3002<\/p>\n<p>\u6211\u4eec\u8c03\u6574\u8fd9\u4e9b\u6570\u5b57\u7684\u4e3b\u8981\u5de5\u5177\u662f <strong>\u4f7f\u77e9\u5f62\u4e0d\u5e73\u8861\uff08\u5bbd\u5ea6\u548c\u9ad8\u5ea6\u4e0d\u540c\uff09<\/strong>\uff1a\u6211\u4eec\u53ef\u4ee5\u5c06\u63d0\u793a\u5b58\u50a8\u589e\u52a0 2 \u500d\uff0c\u4ee5\u5c06\u67e5\u8be2\u5927\u5c0f\u51cf\u5c11 2 \u500d\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u6743\u8861\uff1a\u5b58\u50a8\u751a\u81f3 10 GB \u7684\u63d0\u793a\u5e76\u4e0d\u56f0\u96be\uff0c\u4f46\u7279\u522b\u662f\u5982\u679c\u8282\u70b9\u6bcf 200 \u6beb\u79d2\u53d1\u9001\u591a\u4e2a\u67e5\u8be2\uff0c\u6bcf\u4e2a\u67e5\u8be2 215 kB \u7684\u5927\u5c0f\u662f\u6211\u4eec\u4e0d\u592a\u80fd\u63a5\u53d7\u7684\u3002<\/p>\n<p>\u5728\u641c\u7d22\u5f15\u64ce\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u8c61\u7684\u5927\u5c0f\u4f1a\u5927\u5f97\u591a\uff08\u4f8b\u5982\uff0c\u6bcf\u4e2a\u6587\u672c\u7f51\u9875 10 kB\uff09\uff0c\u4f46\u67e5\u8be2\u7684\u6570\u91cf\u53ef\u80fd\u8f83\u5c11\u3002\u56e0\u6b64\uff0c\u67e5\u8be2\u590d\u6742\u5ea6\u76f8\u5bf9\u8f83\u4f4e\uff0c\u4f46\u63d0\u793a\u5927\u5c0f\u4f1a\u5f88\u5927\u3002\u4e3a\u4e86\u5f25\u8865\u8fd9\u4e00\u70b9\uff0c\u53ef\u80fd\u6709\u610f\u4e49\u7684\u662f\u5728 <em>\u53e6\u4e00\u4e2a\u65b9\u5411<\/em> \u4f7f\u77e9\u5f62\u4e0d\u5e73\u8861\u3002<\/p>\n<h2 id=\"plinko\">\u8d85\u8d8a Plinko\uff1a\u4e0e\u66ff\u4ee3\u65b9\u6848\u7684\u6bd4\u8f83<\/h2>\n<p>Plinko \u7684\u4e00\u4e2a\u73b0\u6709\u66ff\u4ee3\u65b9\u6848\u662f TreePIR\u3002TreePIR \u901a\u8fc7\u4f7f\u7528\u201c\u53ef\u7a7f\u900f\u7684\u4f2a\u968f\u673a\u51fd\u6570\u201d\uff08puncturable PRF\uff09\u6765\u5de5\u4f5c\uff1a\u4e00\u79cd\u54c8\u5e0c\u51fd\u6570\uff0c\u60a8\u53ef\u4ee5\u63d0\u4f9b\u4e00\u4e2a\u5bc6\u94a5\uff0c\u4f7f\u5176\u80fd\u591f\u5728\u6240\u6709\u70b9\u4e0a\u8fdb\u884c\u8bc4\u4f30\uff0c<em>\u9664\u4e86<\/em> \u4e00\u4e2a\u9009\u5b9a\u7684\u70b9\u3002\u8fd9\u4f7f\u60a8\u80fd\u591f\u751f\u6210\u67e5\u8be2\u5217\u7684\u8868\u793a\uff08\u201c\u4ece\u79cd\u5b50 \\\\(S\\\\) \u751f\u6210\u7684\u503c\uff0c<em>\u9664\u4e86<\/em> \u7b2c \\\\(j\\\\) \u4e2a\u503c\u201d\uff09\uff0c\u5176\u5927\u5c0f\u4e3a\u5bf9\u6570\u7ea7\u522b\u2014\u2014\u6bd4\u76f4\u63a5\u63d0\u4f9b\u6574\u4e2a\u5217\u8868\u8981\u7d27\u51d1\u5f97\u591a\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/static.aicoinstorge.com\/attachment\/article\/20251125\/176411491860333.jpg\" title=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe8\" alt=\"Plinko PIR \u6559\u7a0b &#8211;\u63d2\u56fe8\" \/><\/p>\n<p>\u5b8c\u6574\u7684\u65b9\u6cd5\u6bd4\u4e0a\u9762\u7684\u56fe\u793a\u66f4\u4e3a\u5de7\u5999\u3002\u8be5\u56fe\u4e2d\u7684\u60f3\u6cd5\u63ed\u793a\u4e86\u88ab\u6392\u9664\u7684\u7d22\u5f15 01100\uff0c\u8fdd\u53cd\u4e86\u9690\u79c1\u3002TreePIR \u901a\u8fc7\u63d0\u4f9b\u9ec4\u8272\u503c <em>\u800c\u4e0d<\/em> \u63ed\u793a\u5b83\u4eec\u5728\u6811\u4e2d\u7684\uff08\u6c34\u5e73\uff09\u4f4d\u7f6e\u6765\u5de5\u4f5c\u3002\u53ef\u4ee5\u901a\u8fc7\u4e3a\u6bcf\u4e2a\u9ec4\u8272\u503c\u9009\u62e9\u5de6\u4fa7\u548c\u53f3\u4fa7\u4f4d\u7f6e\u6765\u751f\u6210 \\\\(2^{log_2(\\\\sqrt{N})} = \\\\sqrt{N}\\\\) \u79cd\u53ef\u80fd\u7684\u53f6\u5b50\u503c\u96c6\u5408\uff0c\u56e0\u6b64\u53ef\u4ee5\u751f\u6210 \\\\(\\\\sqrt{N}\\\\) \u79cd\u53ef\u80fd\u7684\u5217\u96c6\u5408\u3002\u670d\u52a1\u5668\u6709\u4e00\u4e2a \\\\(O(\\\\sqrt{N} * log(N))\\\\) \u65f6\u95f4\u7b97\u6cd5\uff0c\u53ef\u4ee5\u540c\u65f6\u8ba1\u7b97\u6bcf\u79cd\u53ef\u80fd\u6392\u5217\u7684\u6240\u9009\u5355\u5143\u7684 XOR \u548c\u3002\u5ba2\u6237\u7aef\u77e5\u9053\u8fd9\u4e9b\u548c\u4e2d\u54ea\u4e2a\u5bf9\u5e94\u4e8e\u5b83\u5b9e\u9645\u9700\u8981\u7684\u96c6\u5408\u3002\u5b83\u4f7f\u7528\u5355\u670d\u52a1\u5668 PIR 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<strong>\u754c\u9650<\/strong>\u3002\u7136\u800c\uff0c\u5b9e\u9645\u4e0a\uff0c\u5927\u591a\u6570\u8fd9\u4e9b\u754c\u9650\u90fd\u6709\u9644\u5e26\u6761\u4ef6\uff0c\u56e0\u6b64\u201c\u771f\u5b9e\u201d\u7684\u4e0b\u9650\u8981\u5c11\u5f97\u591a\u3002\u4f8b\u5982\uff0c\u5982\u679c\u60a8\u6709\u6df7\u6dc6\uff0c\u60a8\u53ef\u4ee5\u4f7f\u8fd9\u4e9b\u534f\u8bae\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u4ec5\u9700\u5e38\u91cf\u7684\u5b9e\u65f6\u901a\u4fe1\u5f00\u9500\u2014\u2014\u4f46\u5f53\u7136\uff0c\u4eca\u5929\uff0c\u8fd9\u6837\u7684\u534f\u8bae\u4ecd\u7136\u79bb\u5b9e\u7528\u6027\u76f8\u5f53\u8fdc\u3002\u66f4\u96be\u51cf\u5c11\u7684\u662f\u670d\u52a1\u5668\u7aef\u7684\u8ba1\u7b97\u3002\u56e0\u4e3a\u5b83\u201c\u53ea\u662f\u201d XOR\uff0c\u6240\u4ee5 Plinko \u4e2d\u7684\u5de5\u4f5c\u8d1f\u8f7d\u5df2\u7ecf\u4e0d\u7b97\u5927\u3002\u4f46\u5982\u679c\u6211\u4eec\u60f3\u8981\u6d88\u9664\u5ba2\u6237\u7aef\u7684 \\\\(O(N)\\\\) 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