{"id":7181,"date":"2024-04-12T20:01:01","date_gmt":"2024-04-12T12:01:01","guid":{"rendered":""},"modified":"2024-04-12T20:01:01","modified_gmt":"2024-04-12T12:01:01","slug":"Oblivious Data Structures\u5b66\u4e60\u7b14\u8bb0","status":"publish","type":"post","link":"https:\/\/mushiming.com\/7181.html","title":{"rendered":"Oblivious Data Structures\u5b66\u4e60\u7b14\u8bb0"},"content":{"rendered":"

\n <\/path> \n<\/svg> <\/p>\n

Refence\uff1a<\/strong> Oblivious Data Structures*<\/sup>\uff08Xiao Shaun Wang1<\/sup>, Kartik Nayak1<\/sup>, Chang Liu1<\/sup>, T-H. Hubert Chan2<\/sup>,
Elaine Shi1<\/sup>, Emil Stefanov3<\/sup>, and Yan Huang4<\/sup>\uff09<\/p>\n

Introduction<\/h4>\n

\u2003Oblivious Data Structure\u5728\u6e10\u8fdb\u6027\u548c\u5b9e\u8df5\u4e2d\u6bd4\u8457\u540d\u7684O-RAM\u65b9\u6848\u597d\u3002
\u2003\u5bf9\u4e8e\u4e00\u4e9b\u5bf9\u8bbf\u95ee\u6a21\u5f0f\u6709\u9884\u89c1\u6027\u7684\u7b97\u6cd5\uff0c\u6709\u81ea\u5b9a\u4e49\u7684\u3001\u6e10\u8fdb\u7684\u3001\u66f4\u6709\u6548\u7684\u7ed3\u6784\u662f\u6709\u5229\u7684\u3002\u7b97\u6cd5\u7684\u8bbf\u95ee\u6a21\u5f0f\u56fe\u6709\u5b58\u50a8\u5355\u5143\u4f5c\u4e3a\u8282\u70b9\uff0c\u5e76\u4e14\u53ea\u6709\u5f53\u76f8\u5e94\u8282\u70b9\u4e4b\u95f4\u5b58\u5728\u6709\u5411\u8fb9\u65f6\uff0c\u4e24\u4e2a\u5355\u5143\u624d\u80fd\u88ab\u8fde\u7eed\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u4e00\u822c\u7684RAM\u7a0b\u5e8f\uff0c\u5b83\u4eec\u7684\u8bbf\u95ee\u6a21\u5f0f\u53ef\u4ee5\u662f\u4e00\u4e2a\u5b8c\u6574\u7684\u56fe\u3002\u901a\u7528\u6570\u636e\u7ed3\u6784\u5177\u6709\u66f4\u7a00\u758f\u7684\u8bbf\u95ee\u6a21\u5f0f\u56fe\uff0c\u4e0e\u5bf9\u6570\u636e\u8fdb\u884c\u4efb\u610f\u968f\u673a\u8bbf\u95ee\u7684\u901a\u7528RAM\u7a0b\u5e8f\u76f8\u6bd4\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\u6216\u5806\uff0c\u5185\u5b58\u8bbf\u95ee\u53ea\u80fd\u4ece\u4e00\u4e2a\u6811\u8282\u70b9\u5230\u76f8\u90bb\u7684\u8282\u70b9\uff0c\u56e0\u6b64\u901a\u8fc7\u4e0d\u9690\u85cf\u8bbf\u95ee\u6a21\u5f0f\u7684\u4e00\u4e9b\u516c\u5f00\u7684\u65b9\u9762\uff0c\u6211\u4eec\u5e94\u8be5\u80fd\u591f\u83b7\u5f97\u4e00\u4e9b\u6548\u7387(\u4e0eORAM\u76f8\u6bd4)\u3002\u5bf9\u4e8e\u7a00\u758f\u8bbf\u95ee\u56fe\u7684\u4e24\u79cd\u4e0d\u540c\u7684\u523b\u753b\uff0c\u4e0e\u4e00\u822cORAM\u65b9\u6848\u76f8\u6bd4\uff0cOblivious Data Structure\u83b7\u5f97\u4e86\u6e10\u8fd1\u6027\u80fd\u589e\u76ca\u3002<\/p>\n

Applications<\/strong>
\u2003\u7a00\u677e\u8bbf\u95ee\u6a21\u5f0f\u56fe\u7684\u8fd9\u4e24\u79cd\u63cf\u8ff0\u4e3a\u5e38\u89c1\u7684\u5de5\u4f5c\u5f15\u8d77\u4e86\u4f17\u591a\u7684\u5e94\u7528\uff1a<\/p>\n

    \n
  1. \u5e38\u89c1\u7684\u6570\u636e\u7ed3\u6784\u3002\u4e00\u5957\u9ad8\u6548\u7684\u65e0\u5173\u6570\u636e\u7ed3\u6784\u5b9e\u73b0\uff0c\u5305\u62ec\u5e38\u7528\u7684map\/set\u3001priority_queue\u3001stack\u3001queue\u548cdeque\u3002<\/li>\n
  2. \u832b\u7136\u7684\u5185\u5b58\u5206\u914d\u5668\u3002\u4f7f\u7528ODS\u6846\u67b6\u6765\u8bbe\u8ba1\u4e00\u4e2a\u9ad8\u6548\u7684\u832b\u7136\u5185\u5b58\u5206\u914d\u5668\u3002\u832b\u7136\u5185\u5b58\u5206\u914d\u5668\u6bcf\u6b21\u64cd\u4f5c\u9700\u8981\u4f20\u8f93O(log3n)\u4f4d\u3002\u4e0e\u57fa\u7ebf\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5b9e\u73b0\u4e86\u6307\u6570\u8282\u7ea6\u3002\u5bf9\u4e8e\u832b\u7136\u5185\u5b58\u7684\u5206\u914d\uff0c\u832b\u7136\u5185\u5b58\u5206\u914d\u5668\u7b97\u6cd5\u53ef\u4ee5\u5728\u652f\u6301oram\u7684\u5b89\u5168\u5904\u7406\u5668\u4e0a\u4f7f\u7528\u3002<\/li>\n
  3. \u56fe\u7b97\u6cd5\u3002\u5728\u5177\u6709\u4f4e\u500d\u7ef4\u6570\u56fe\u7684\u64cd\u4f5c\u4e0a\u5b9e\u73b0\u6e10\u8fdb\u6027\u6539\u8fdb\uff0c\u5305\u62ec\u968f\u673a\u6f2b\u6b65\u548c\u6700\u5927\u6d41\u3002\u6211\u4eec\u8003\u8651\u4e86FordFulkerson[15]\u6700\u5927\u6d41\u91cf\u7b97\u6cd5\u7684\u4e00\u79cdOblivious\u53d8\u4f53\uff0c\u8be5\u7b97\u6cd5\u5728\u6bcf\u6b21\u8fed\u4ee3\u4e2d\u4f7f\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff0c\u5728\u6b8b\u5dee\u7f51\u7edc\u4e2d\u627e\u5230\u4e00\u6761\u589e\u5e7f\u8def\u5f84\u3002\u6211\u4eec\u8fd8\u8003\u8651\u4e86\u5e73\u9762\u56fe\u4e0a\u7684\u6700\u77ed\u8def\u5f84\u8ddd\u79bb\u67e5\u8be2\u3002\u6211\u4eec\u5229\u7528\u5e73\u9762\u5206\u9694\u5668\u5b9a\u7406\u6765\u521b\u5efa\u4e00\u4e2a\u56fe\u6570\u636e\u7ed3\u6784\uff0c\u4f7f\u5176oblivious\u3002<\/li>\n<\/ol>\n

    Techniques<\/strong>
    \u2003\u4ee5\u4e0b\u4e24\u4e2a\u4e3b\u8981\u7684\u6280\u672f\u6765\u6784\u9020\u7a00\u758f\u8bbf\u95ee\u6a21\u5f0f\u56fe\u7684\u832b\u7136\u6570\u636e\u7ed3\u6784\u3002<\/p>\n

      \n
    • Pointer-based technique \u57fa\u4e8e\u6307\u9488\u7684\u65b9\u6cd5.<\/strong> \u9002\u7528\u4e8e\u6709\u9650\u5236\u5ea6\u7684\u6709\u6839\u6811\u3002\u6bcf\u4e2a\u7236\u8282\u70b9\u4e3a\u5176\u5b50\u8282\u70b9\u5b58\u653e\u6307\u9488\u5e76\u4e14\u50a8\u5b58\u5b50\u8282\u70b9\u7684\u4f4d\u7f6e\u6807\u8bb0\u3002\u8fd9\u6837\u5f53\u83b7\u53d6\u7236\u8282\u70b9\u65f6\uff0c\u7acb\u5373\u83b7\u53d6\u5176\u5b50\u8282\u70b9\u7684\u4f4d\u7f6e\u6807\u8bb0\uff0c\u4ece\u800c\u6d88\u9664\u4e86\u6267\u884c\u4f4d\u7f6e\u56fe(position map)\u67e5\u627e\u7684\u9700\u8981(\u56e0\u6b64\u6709\u4e86\u5bf9\u6570\u56e0\u5b50\u7684\u6539\u8fdb)\u3002<\/li>\n
    • Locality-based technique \u57fa\u4e8e\u4f4d\u7f6e\u7684\u6280\u672f.<\/strong> \u9002\u7528\u4e8e\u5177\u6709\u4f4e\u500d\u7ef4\u5ea6\u7684\u8bbf\u95ee\u6a21\u5f0f\u56fe\u3002\u56fe\u4e2d\u7684\u8282\u70b9\u88ab\u5212\u5206\u4e3a\u96c6\u7fa4\uff0c\u8fd9\u6837\u6bcf\u4e2a\u96c6\u7fa4\u7684\u6307\u9488\u53ea\u6307\u5411O(1)dim<\/sup>\u7684\u76f8\u90bb\u96c6\u7fa4\uff0c\u5176\u4e2ddim\u662f\u500d\u7ef4\u7684\u4e0a\u754c\u3002\u76f4\u89c9\u4e0a\uff0c\u6bcf\u4e2a\u96c6\u7fa4\u5305\u542bO(log N)\u4e2a\u8282\u70b9\uff0c\u5e76\u4e14\u53ef\u4ee5\u652f\u6301O(log 1\/dim<\/sup> N)\u4e2a\u8282\u70b9\u8bbf\u95ee\u3002\u6b63\u5982\u6211\u4eec\u5c06\u8981\u770b\u5230\u7684\uff0c\u6bcf\u4e2a\u96c6\u7fa4\u7684\u5927\u5c0f\u4e3a\u03a9(log2<\/sup>N)\u4f4d\uff0c\u56e0\u6b64\u6bcf\u4e2a\u96c6\u7fa4\u53ef\u4ee5\u5728Path ORAM\u4e2d\u88ab\u5b58\u50a8\u4e3a\u4e00\u4e2a\u5757block\uff0c\u5e26\u5bbd\u589e\u52a0\u5230O(log N)\u3002<\/li>\n<\/ul>\n

      Problem Definition<\/h4>\n

      \u2003\u6570\u636e\u7ed3\u6784D\u662f\u4e00\u4e2a\u652f\u6301\u7279\u5b9a\u7c7b\u578b\u64cd\u4f5c(insert,del,or lookup)\u7684\u6570\u636e\u96c6\u5408\u3002\u6bcf\u4e2a\u64cd\u4f5c\u90fd\u7531\u4e00\u4e9b\u64cd\u4f5c\u6570\u53c2\u6570\u5316(\u4f8b\u5982\uff0c\u8981\u67e5\u627e\u7684\u952e)\u3002ODS\u7684\u76ee\u6807\u662f\u786e\u4fdd\u4efb\u610f\u4e24\u4e2a\u5305\u542bk\u4e2a\u64cd\u4f5c\u7684\u5e8f\u5217\uff0c\u4ed6\u4eec\u7684\u8bbf\u95ee\u6a21\u5f0f\u5fc5\u987b\u662f\u4e0d\u53ef\u533a\u5206\u7684\u3002\u8fd9\u610f\u5473\u7740\u8bbf\u95ee\u6a21\u5f0f(\u5305\u62ec\u8bbf\u95ee\u6b21\u6570)\u4e0d\u5e94\u8be5\u6cc4\u9732\u64cd\u4f5c\u7801(\u64cd\u4f5c\u7c7b\u578b)\u548c\u64cd\u4f5c\u6570(key\u548cdata)\u7684\u4fe1\u606f\u3002
      Definition 1<\/strong>(Oblivious data structure)\u6211\u4eec\u8ba4\u4e3a\u6570\u636e\u7ed3\u6784D\u662f\u832b\u7136\u7684\uff0c\u8bbe\u5b58\u5728\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u6a21\u62df\u5668S\uff0c\u8fd9\u6837\u5bf9\u4e8e\u4efb\u610f\u591a\u9879\u5f0f\u957f\u5ea6\u5e8f\u5217\u7684\u6570\u636e\u7ed3\u6784\u64cd\u4f5c o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> =( (op1<\/sub>,arg1<\/sub>),(op2<\/sub>,arg2<\/sub>),\u2026,(opM<\/sub>,argM<\/sub>) )
      \u2003\u2003\u2003\u2003addressesD<\/sub>( o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)== S(L( o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> ))
      \u5176\u4e2daddressesD<\/sub>( o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)\u662f\u7531\u832b\u7136\u6570\u636e\u7ed3\u6784\u5728\u4e00\u7cfb\u5217\u64cd\u4f5c o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u671f\u95f4\u4ea7\u751f\u7684\u7269\u7406\u5730\u5740\uff1b\u5e76\u4e14L( o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> )\u79f0\u4e3a\u6cc4\u9732\u51fd\u6570\u3002\u901a\u5e38\u6211\u4eec\u8ba4\u4e3aL( o p s \u20d7 \\vec{ops} <\/span><\/span><\/span>o<\/span>p<\/span>s<\/span><\/span><\/span><\/span>
      \n \n <\/path> \n <\/svg><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> ) = M\uff0c\u5373\u64cd\u4f5c\u6570\u7684\u6570\u91cf\u88ab\u6cc4\u9732\u4e86\uff0c\u4f46\u6ca1\u6709\u5176\u4ed6\u7684\u3002
      \u2003\u76f4\u89c2\u5730\u8bf4\uff0c\u8fd9\u4e2a\u5b9a\u4e49\u8868\u793a\u7531\u4e00\u7cfb\u5217\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\u4ea7\u751f\u7684\u8bbf\u95ee\u6a21\u5f0f\u5e94\u8be5\u53ea\u663e\u793a\u64cd\u4f5c\u7684\u603b\u6570\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u591a\u9879\u5f0f\u65f6\u95f4\u6a21\u62df\u5668S\u53ea\u77e5\u9053\u64cd\u4f5c\u7684\u603b\u6b21\u6570\uff0c\u5c31\u53ef\u4ee5\u6a21\u62df\u7269\u7406\u5730\u5740\uff0c\u8fd9\u6837\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u8bc6\u522b\u5668\u5c31\u65e0\u6cd5\u533a\u5206\u88ab\u9057\u5fd8\u7684\u6570\u636e\u7ed3\u6784\u751f\u6210\u7684\u6a21\u62df\u5730\u5740\u548c\u771f\u5b9e\u5730\u5740\u3002
      \u2003\u8bf7\u6ce8\u610f\uff0c\u76f4\u63a5\u4f7f\u7528\u6807\u51c6ORAM\u53ef\u80fd\u4e0d\u80fd\u6ee1\u8db3\u6211\u4eec\u7684\u5b9a\u4e49\uff0c\u56e0\u4e3a\u4fe1\u606f\u53ef\u80fd\u4f1a\u901a\u8fc7\u8bbf\u95ee\u7684\u6570\u91cf\u6cc4\u9732\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u67d0\u4e9b\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\u6bd4\u5176\u4ed6\u64cd\u4f5c\u9700\u8981\u66f4\u591a\u7684\u5185\u5b58\u8bbf\u95ee;\u4f8b\u5982\uff0cAVL\u6811\u7684\u5220\u9664\u53ef\u80fd\u4f1a\u5f15\u8d77\u65cb\u8f6c\u64cd\u4f5c\uff0c\u56e0\u6b64\u4f1a\u6bd4\u67e5\u627e\u64cd\u4f5c\u5f15\u8d77\u66f4\u591a\u7684\u5185\u5b58\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u6211\u4eec\u4f7f\u7528\u6807\u51c6\u7684ORAM\uff0c\u4e5f\u53ef\u80fd\u9700\u8981\u586b\u5145\u6765\u9690\u85cf\u6b63\u5728\u6267\u884c\u7684\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\u3002<\/p>\n

      Building Block: Non-Recursive Position-based ORAM(\u6784\u5efa\u5757:\u975e\u9012\u5f52\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM)<\/h5>\n

      \"Oblivious
      Figure1:\u9759\u6001\u832b\u7136\u4e8c\u53c9\u67e5\u627e\u6811.<\/strong> \u5de6\u8fb9\u4e8c\u903b\u8f91\u4e8c\u53c9\u67e5\u627e\u6811\uff0c\u53f3\u8fb9\u662f\u5982\u4f55\u5c06\u8fd9\u4e9b\u8282\u70b9\u975e\u9012\u5f52\u7684\u5b58\u50a8\u5728\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM\u4e0a\u3002\u6bcf\u4e2a\u4f4d\u7f6e\u6807\u8bb0\u6307\u5b9a\u5230\u6811\u4e2d\u53f6\u7ed3\u70b9\u7684\u8def\u5f84\u3002\u6bcf\u4e2a\u7236\u7c7b\u90fd\u6307\u5411\u5176\u5b50\u7c7b\u7684\u4f4d\u7f6e\u6807\u7b7e\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u7701\u53bb\u67e5\u627eposition map\u7684\u9700\u8981\uff0c\u4ece\u800c\u4e0e\u901a\u7528ORAM\u76f8\u6bd4\u8282\u7701\u4e86O(log N)\u56e0\u5b50\u3002<\/p>\n

      Oblivious Data Structure(\u832b\u7136\u6570\u636e\u7ed3\u6784)<\/h5>\n

      Node format.<\/strong> \u5728ODS\u8fd9\u4e2a\u6570\u636e\u7ed3\u6784\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u90fd\u7531\u6807\u8bc6\u7b26id\u548c\u5b83\u7684\u4f4d\u7f6e\u6807\u7b7epos\u6765\u6807\u8bc6\uff0c\u8282\u70b9\u8fd8\u5b58\u50a8\u4e86\u5b83\u6240\u6709\u5b50\u8282\u70b9\u7684\u4f4d\u7f6e\u6807\u7b7e\u3002\u56e0\u6b64\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u683c\u5f0f\u4e3anode := (data,id,pos,childrenPos)<\/strong> ,\u7279\u522b\u5730\uff0cchildrenPos\u662f\u4ece\u6bcf\u4e2a\u5b50id\u6620\u5c04\u5230\u5b83\u7684\u4f4d\u7f6e\u6807\u8bb0\u3002\u8bb0\u4e3achildrenPos[idc<\/sub>]<\/strong> \u8868\u793a\u4ee5idc<\/sub>\u6807\u8bc6\u7684\u5b50\u7c7b\u7684\u4f4d\u7f6e\u6807\u7b7e\u3002
      \u2003\u6240\u6709\u8282\u70b9\u5c06\u88ab(\u52a0\u5bc6\u5e76)\u5b58\u50a8\u5728\u670d\u52a1\u5668\u4e0a\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM(\u975e\u9012\u5f52)\u4e2d\u3002\u5ba2\u6237\u7aef\u53ea\u5b58\u50a8\u6811\u6839\u7684\u4f4d\u7f6e\u6807\u8bb0\u548c\u6807\u8bc6\u7b26\u3002<\/p>\n

      \u2003\u6ce8\u610f\u4e00\u65e6\u4e00\u4e2a\u8282\u70b9\u88ab\u670d\u52a1\u5668\u83b7\u53d6\uff0c\u4ed6\u7684\u4f4d\u7f6e\u6807\u8bb0\u5c31\u4f1a\u66b4\u9732\u7ed9\u670d\u52a1\u5668\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4e3a\u8fd9\u4e2a\u8282\u70b9\u751f\u6210\u4e00\u4e2a\u65b0\u7684\u4f4d\u7f6e\u6807\u8bb0\u3002\u540c\u65f6\uff0c\u8fd9\u4e2a\u4f4d\u7f6e\u6807\u8bb0\u4e5f\u5e94\u8be5\u5728\u4ed6\u7236\u8282\u70b9\u7684\u5b50\u7c7b\u4f4d\u7f6e\u5217\u8868\u4e2d\u66f4\u65b0\u3002\u6211\u4eec\u7684\u5173\u952e\u601d\u60f3\u662f\u4f9d\u8d56O(logN)\u5927\u5c0f\u7684\u5ba2\u6237\u7aef\u7f13\u5b58\uff0c\u8fd9\u6837\u5728\u6574\u4e2a\u63d2\u5165\u64cd\u4f5c\u4e2d\uff0c\u4e0e\u6b64\u64cd\u4f5c\u6709\u5173\u7684\u6240\u6709\u8282\u70b9\u90fd\u88ab\u83b7\u53d6\u4e00\u6b21\u3002\u5728\u8fd9\u4e9b\u9636\u6bb5\u88ab\u4ece\u670d\u52a1\u5668\u83b7\u53d6\u548c\u5220\u9664\u540e\uff0c\u4ed6\u4eec\u5c06\u88ab\u50a8\u5b58\u5728\u5ba2\u6237\u7aef\u7f13\u5b58\u4e2d\u3002\u8fd9\u6837\u5ba2\u6237\u7aef\u53ef\u4ee5\u5728\u5199\u56de\u4ed6\u4eec\u4e4b\u524d\u5728\u672c\u5730\u5bf9\u8fd9\u4e9b\u8282\u70b9\u8fdb\u884c\u66f4\u65b0\u3002\u8fd9\u4e9b\u66f4\u65b0\u53ef\u80fd\u5305\u62ec\u63d2\u5165\u3001\u5220\u9664\u3001\u548c\u4fee\u6539\u56fe\u7ed3\u6784(\u5982AVL\u6811\u793a\u4f8b\u4e2d\u7684\u65cb\u8f6c)\u3002\u6700\u540e\uff0c\u5728\u64cd\u4f5c\u7ed3\u675f\u65f6\uff0c\u672c\u5730\u7f13\u5b58\u7684\u6240\u6709\u8282\u70b9\u5c06\u88ab\u5199\u56de\u670d\u52a1\u5668\u3002\u5728\u56de\u5199\u4e4b\u524d\uff0c\u6240\u6709\u88ab\u83b7\u53d6\u7684\u8282\u70b9\u5fc5\u987b\u88ab\u968f\u673a\u5206\u914d\u65b0\u7684\u4f4d\u7f6e\u6807\u7b7e\uff0c\u4ed6\u4eec\u7684\u7236\u8282\u70b9\u5fc5\u987b\u88ab\u9002\u5f53\u7684\u4fee\u6539\uff0c\u4ee5\u6307\u5411\u5b50\u8282\u70b9\u7684\u65b0\u4f4d\u7f6e\u6807\u7b7e\u3002<\/p>\n

      B ODS\u6570\u636e\u7ed3\u6784\u548c\u6846\u67b6<\/h4>\n
      B.1\u5185\u5b58\u62bd\u8c61<\/h5>\n

      \u2003\u5185\u5b58\u4e3a\u5b58\u50a8\u4e0a\u8ff0\u6570\u636e\u7ed3\u6784\u56fe\u4e2d\u7684\u8282\u70b9\u63d0\u4f9b\u4e86\u7a7a\u95f4\u3002\u8be5\u56fe\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9(id, data)\u90fd\u662f\u4e00\u4e2a\u539f\u5b50\u5b58\u50a8\u5355\u5143\uff0c\u5176\u4e2did\u53ef\u4ee5\u89c6\u4e3a\u8282\u70b9\u5728\u5185\u5b58\u4e2d\u7684\u5730\u5740\u3002\u6211\u4eec\u5b9a\u4e49\u4e86\u4ee5\u4e0b\u56db\u79cd\u7c7b\u578b\u7684\u5185\u5b58\u64cd\u4f5c\uff1a
      \u2003 \u2003 \u2003 \u2003 Read(id), Write(id,data*<\/sup>), Insert(id,data*<\/sup>), Del(id)
      \u2003\u4efb\u4f55\u7684\u6570\u636e\u7ed3\u6784\u7b97\u6cd5\u53ef\u4ee5\u7528\u8fd9\u56db\u4e2a\u7c7b\u578b\u7684\u5185\u5b58\u64cd\u4f5c\u4ee5\u53ca\u5185\u5b58\u64cd\u4f5c\u4e4b\u95f4\u7684\u8ba1\u7b97\u6b65\u9aa4(\u4f8b\u5982\uff0c\u952e\u503c\u7684\u6bd4\u8f83)\u6765\u8868\u793a\u3002
      \u2003\u8bf7\u6ce8\u610f\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6807\u51c6\u7684\u901a\u7528\u7684ORAM\u901a\u5e38\u53ea\u652f\u6301read(id)\u548cwrite(id,data*<\/sup> )\u64cd\u4f5c\uff0c\u4f46\u4e0d\u652f\u6301insert(id,data*<\/sup> )\u548cdel(id)\u3002\u9644\u52a0\u7684insert(id,data*<\/sup>)\u548cdel(id)\u64cd\u4f5c\u662f\u4e3a\u4e86\u65b9\u4fbf\u8868\u793a\u52a8\u6001\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\uff0c\u5982\u63d2\u5165\u548c\u5220\u9664\u3002<\/p>\n

      B.2 ODS\u67b6\u6784<\/h5>\n

      \u2003ODS \u5ba2\u6237\u7aef.<\/strong> \u5728\u666e\u901a\u7684\u3001\u975e\u832b\u7136\u7684\u6570\u636e\u7ed3\u6784\u4e2d\uff0c\u5185\u5b58\u64cd\u4f5c\u76f4\u63a5\u8fdb\u5165\u5185\u5b58\uff0c\u4ece\u800c\u901a\u8fc7\u8bbf\u95ee\u6a21\u5f0f\u6cc4\u9732\u4fe1\u606f\u3002\u5728\u832b\u7136\u6570\u636e\u7ed3\u6784\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4e00\u4e2a\u4e13\u95e8\u8bbe\u8ba1\u7684\u201c\u832b\u7136\u5185\u5b58\u201d\u66ff\u6362\u5185\u5b58\uff0c\u79f0\u4e3aODS\u5ba2\u6237\u7aef\u3002\u8fd9\u4e2aODS\u5ba2\u6237\u7aef\u7684\u89d2\u8272\u7c7b\u4f3c\u4e8eORAM\u5ba2\u6237\u7aef;\u4ece\u6570\u636e\u7ed3\u6784\u7a0b\u5e8f\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5b83\u63d0\u4f9b\u4e86\u4e0e\u5185\u5b58\u5b8c\u5168\u76f8\u540c\u7684\u63a5\u53e3(\u5373\u652f\u6301\u524d\u9762\u63d0\u5230\u7684\u56db\u79cd\u64cd\u4f5c)\u3002\u5728\u5185\u90e8\uff0cODS\u5ba2\u6237\u673a\u5c06\u903b\u8f91\u5185\u5b58\u8bf7\u6c42\u8f6c\u6362\u4e3a\u4e00\u7cfb\u5217\u6df7\u6dc6\u7684\u5185\u5b58\u8bbf\u95ee\uff0c\u5e76\u5c06\u6df7\u6dc6\u7684\u7269\u7406\u5730\u5740\u663e\u793a\u7ed9\u4e0d\u53d7\u4fe1\u4efb\u7684\u670d\u52a1\u5668\u3002
      \u2003\u663e\u7136\uff0c\u4e00\u79cd\u7b80\u5355\u4f46\u4f4e\u6548\u7684\u65b9\u6cd5\u662f\u7b80\u5355\u5730\u4f7f\u7528\u901a\u7528ORAM\u5ba2\u6237\u673a\u4f5c\u4e3aODS\u5ba2\u6237\u673a\u3002\u4f46\u662f\uff0c\u6211\u4eec\u5c06\u6784\u9020\u4e00\u4e2a\u5b9a\u5236\u7684ODS\u5ba2\u6237\u673a\uff0c\u5b83\u5c06\u5e26\u6765\u6e10\u8fd1\u7684\u52a0\u901f\u3002
      \u2003**\u4e0d\u53d7\u4fe1\u4efb\u7684\u670d\u52a1\u5668.**\u4e0d\u53d7\u4fe1\u4efb\u7684\u670d\u52a1\u5668\u652f\u6301getphys addr\u548cputphys addr, data\u7684\u7b80\u5355\u63a5\u53e3\u3002\u670d\u52a1\u5668\u4e0d\u5e94\u8be5\u4ece\u88ab\u8bbf\u95ee\u7684\u7269\u7406\u5730\u5740\u5e8f\u5217\u4e2d\u83b7\u5f97\u4efb\u4f55\u4fe1\u606f\u3002<\/p>\n

      B.3 \u52a8\u6001\u8bbf\u95ee<\/h5>\n

      \u2003 \u6bcf\u4e2a(\u52a8\u6001)\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n

        \n
      • \u4e00\u4e2a\u5355\u72ec\u7684 ODS. Start \u8c03\u7528\u3002<\/strong> \u4e3a\u8be5\u64cd\u4f5c\u7684\u5f00\u59cb\u505a\u51c6\u5907\u3002<\/li>\n
      • \u4e00\u4e2a ODS.Access \u5e8f\u5217\u8c03\u7528ODS\u3002<\/strong> \u8fd9\u5c06\u544a\u8bc9ODS\u8981\u4ece\u670d\u52a1\u5668\u83b7\u53d6\u548c\u5220\u9664\u54ea\u4e9b\u8282\u70b9\uff0c\u4ee5\u53ca\u8981\u5bf9\u8fd9\u4e9b\u8282\u70b9\u8fdb\u884c\u54ea\u4e9b\u672c\u5730\u66f4\u65b0\u3002\u8fd9\u4e9b\u8282\u70b9(\u6700\u591a\u4e3aO(log N))\u5728\u6267\u884cODS.Finalize\u8c03\u7528\u4e4b\u524d\u4fdd\u5b58\u5728ODS\u5ba2\u6237\u673a\u7684\u7f13\u5b58\u4e2d\u3002
        \u2003 ODS.Access\u8c03\u7528\u5e95\u5c42\u7684\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM\u751f\u6210\u7684ReadAndRemove\u64cd\u4f5c\uff0c\u56e0\u6b64\u670d\u52a1\u5668\u89c2\u5bdf\u5230\u7684\u7269\u7406\u8bbf\u95ee\u662f\u832b\u7136\u7684\u3002\u5e76\u4e0d\u662f\u6bcf\u4e2aODS.Access\u8c03\u7528\u90fd\u5c06\u751f\u6210\u4e00\u4e2aReadAndRemove\u64cd\u4f5c\uff0c\u56e0\u4e3a\u7f13\u5b58\u4e2d\u7684\u8282\u70b9\u53ef\u4ee5\u76f4\u63a5\u8fd4\u56de\u3002(\u53ea\u6709\u5728ODS.Access\u7b97\u6cd5\u76848\uff0c17\uff0c25\u884c\u751f\u6210ReadAndRemove\u64cd\u4f5c\uff0c\u5176\u4ed6\u6240\u6709\u64cd\u4f5c\u7531\u7f13\u5b58\u63d0\u4f9b) \u4f46\u662f\uff0c\u56e0\u4e3a\u5728ODS.Finalize\u4e4b\u540e\uff0c\u8fd9\u6837\u7684\u7f13\u5b58\u547d\u4e2d\/\u9519\u8fc7\u884c\u4e3a\u4e0d\u4f1a\u6cc4\u9732\u4fe1\u606f\uff0cODS\u5ba2\u6237\u7aef\u6267\u884c\u586b\u5145\u4ee5\u786e\u4fdd\u6bcf\u4e00\u4e2a\u64cd\u4f5c\u90fd\u4f1a\u4ea7\u751f\u5bf9\u5e95\u5c42\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM\u7684\u76f8\u540c\u6570\u91cf\u7684ReadAndRemove\u548cAdd\u8c03\u7528\u3002<\/li>\n
      • \u4e00\u4e2a\u5355\u4e00\u7684ODS.Finalize\u8c03\u7528ODS\u3002<\/strong> \u6b64\u65f6\uff0cODS\u5ba2\u6237\u673a\u6267\u884c\u4e09\u4e2a\u4efb\u52a1:1)\u4e3a\u6bcf\u4e2a\u7f13\u5b58\u8282\u70b9\u751f\u6210\u65b0\u7684pos\uff0c\u5e76\u6839\u636e\u6bcf\u4e2a\u8282\u70b9\u7684(id, pos)\u66f4\u65b0\u6240\u6709\u7f13\u5b58\u8282\u70b9\u7684childrenPos(lines 1 - 3 in ODS.Finalize); 2)\u901a\u8fc7\u5bf9\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM (line 7 in ODS.Finalize)\u8fdb\u884cAdd\u8c03\u7528\uff0c\u5c06\u7f13\u5b58\u7684\u8282\u70b9\u5199\u56de\u670d\u52a1\u5668; 3)\u6267\u884c\u586b\u5145\uff0c\u4ee5\u786e\u4fdd\u6bcf\u4e2a\u6570\u636e\u7ed3\u6784\u64cd\u4f5c\u4ea7\u751f\u76f8\u540c\u6570\u91cf\u7684ReadAndRemove(\u7b2c4\u884cODS.Finalize)\u548cAdd\u64cd\u4f5c(\u7b2c9\u884cODS.Finalize)\u5230\u5e95\u5c42\u57fa\u4e8e\u4f4d\u7f6e\u7684ORAM\u3002
        \"Oblivious<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"Oblivious Data Structures\u5b66\u4e60\u7b14\u8bb0Introduction\u2003ObliviousDataStructure\u5728\u6e10\u8fdb\u6027\u548c\u5b9e\u8df5\u4e2d\u6bd4\u8457\u540d\u7684O-RAM\u65b9\u6848\u597d","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/7181"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=7181"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/7181\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=7181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=7181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=7181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}