{"id":293,"date":"2007-06-17T02:54:30","date_gmt":"2007-06-16T18:54:30","guid":{"rendered":"http:\/\/blog.smallken.ink\/2007\/06\/17\/293\/"},"modified":"2007-06-17T02:55:11","modified_gmt":"2007-06-16T18:55:11","slug":"%e4%bd%95%e8%ac%82-rsa-%e5%8a%a0%e5%af%86%e6%bc%94%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.smallken.site\/?p=293","title":{"rendered":"\u4f55\u8b02 RSA \u52a0\u5bc6\u6f14\u7b97\u6cd5?"},"content":{"rendered":"

RSA \u662f\u4e00\u7a2e\u975e\u5c0d\u7a31\u7684\u52a0\u5bc6\u6f14\u7b97\u6cd5\uff0c\u975e\u5c0d\u7a31\u662f\u56e0\u70ba\u5b83\u5229\u7528\u4e86\u5169\u628a\u4e0d\u540c\u7684\u9470\u5319\uff0c\u4e00\u628a\u53eb\u516c\u958b\u91d1\u9470\uff0c\u53e6\u4e00\u628a\u53eb\u79c1\u5bc6\u91d1\u9470\uff0c\u9019\u8ddf\u6211\u5011\u4e00\u822c\u8a8d\u77e5\u9470\u5319\u4e0d\u592a\u4e00\u6a23\uff0c\u5927\u5bb6\u5bb6\u88e1\u9762\u7684\u5927\u9580\u9396\u9580\u8ddf\u958b\u9580\u90fd\u7528\u540c\u4e00\u628a\u9470\u5319\u5427\uff01\u9019\u6c92\u554f\u984c\uff0c\u5c31\u5982 AES\u3001DES \u9019\u7a2e\u5c0d\u7a31\u7684\u52a0\u5bc6\u6f14\u7b97\u6cd5\u4e5f\u662f\u90fd\u4f7f\u7528\u540c\u4e00\u628a\u9470\u5319\u52a0\u5bc6\u53ca\u89e3\u5bc6\uff0c\u90a3 RSA \u70ba\u4ec0\u9ebc\u8981\u7528\u5169\u628a\u9470\u5319\u5462? \u5b83\u4e00\u628a\u7528\u4f86\u9396\u9580\uff0c\u53e6\u4e00\u628a\u662f\u7528\u4f86\u958b\u9580\u7684\uff0c\u4ea4\u63db\u4e5f\u662f\u53ef\u4ee5\uff0c\u53ea\u8981\u9396\u9580\u8ddf\u958b\u9580\u7528\u4e0d\u540c\u628a\u5c31\u53ef\u4ee5\u4e86\uff0c\u5594\uff0c\u9019\u9ebc\u9ebb\u7169\uff0c\u70ba\u4ec0\u9ebc\u5462?<\/p>\n

\u4e3b\u8981\u70ba\u4e86\u78ba\u4fdd\u7db2\u8def\u4e0a\u7684\u8cc7\u6599\u5b89\u5168\uff0c\u7db2\u8def\u4e0a\u6703\u6709\u4e09\u500b\u5f88\u91cd\u8981\u7684\u9700\u6c42\uff1a<\/p>\n

    \n
  1. \u4fdd\u5bc6\u6027:\u5927\u5bb6\u5728\u7db2\u8def\u4e0a\u50b3\u8cc7\u6599\u4e00\u5b9a\u8981\u4fdd\u5bc6\uff0c\u9019\u662f\u57fa\u672c\u4e0a\u9700\u8981\u7684\u3002<\/li>\n
  2. \u771f\u5be6\u9700\u6c42\u6027:\u4e5f\u5c31\u662f\u8aaa\u7576\u4f60\u6536\u5230\u4e00\u7b46\u8cc7\u6599\u5f8c\uff0c\u4f60\u600e\u9ebc\u80fd\u78ba\u5b9a\u8cc7\u6599\u662f\u6b63\u78ba\u7684?\u4e2d\u9593\u6c92\u6709\u88ab\u5225\u4eba\u7be1\u6539\u904e?\u4e5f\u5c31\u662f\u8981\u907f\u514d\u5176\u4ed6\u4eba”\u5047\u50b3\u8056\u65e8”\u3002<\/li>\n
  3. \u4e0d\u53ef\u5426\u8a8d\u6027:\u9019\u500b\u7279\u6027\u5c31\u662f\u6307\u985e\u4f3c\u865b\u64ec\u5370\u7ae0\u7684\u610f\u601d\uff0c\u9019\u4efd\u6587\u4ef6\u53ea\u8981\u7d93\u904e\u4f60\u7c3d\u540d\u84cb\u7ae0\u4e4b\u5f8c\uff0c\u4f60\u5c31\u4e0d\u53ef\u4ee5\u5426\u8a8d\u800d\u8cf4\uff0c\u7576\u7136\u9019\u8981\u6709\u4e00\u500b\u5f88\u597d\u7684\u6a5f\u5236\u624d\u80fd\u8b93\u4eba\u5fc3\u670d\u53e3\u670d\u3002<\/li>\n<\/ol>\n

    RSA \u5f88\u53b2\u5bb3\u7684\u5c31\u662f\u8aaa\u5b83\u90fd\u7b26\u5408\u4ee5\u4e0a\u9019\u4e09\u500b\u8981\u6c42\uff0c\u70ba\u4ec0\u9ebc\u6703\u7b26\u5408\u6211\u5011\u5148\u4e0d\u7ba1\uff0c\u6211\u5148\u4f86\u8aaa\u660e RSA \u7684\u6f14\u7b97\u6cd5\uff0c\u9019\u500b\u6f14\u7b97\u6cd5\u7c21\u55ae\u8b1b\u5c31\u662f\u4f7f\u7528\u4e86\u4e00\u500b\u5f88\u795e\u5947\u7684\u6578\u5b78\u7279\u6027\u4f86\u5b8c\u6210\uff0c\u800c\u4e14\u5f88\u795e\u5947\u5730\u525b\u597d\u90fd\u7b26\u5408\u4ee5\u4e0a\u4e09\u500b\u9700\u6c42\uff0c\u4f60\u4e00\u5b9a\u8981\u4e86\u89e3\u9019\u500b\u6578\u5b78\u7279\u6027\u662f\u4ec0\u9ebc\uff0c\u624d\u80fd\u9032\u4e00\u6b65\u77e5\u9053\u70ba\u4ec0\u9ebc\u9019\u6a23\u5c31\u6703\u9054\u5230\u52a0\u5bc6\u9700\u6c42\u3001\u771f\u5be6\u9700\u6c42\u3001\u4e0d\u53ef\u5426\u6027\u9700\u6c42\u3002<\/p>\n

    \u9019\u500b\u6578\u5b78\u7279\u6027\u5c31\u662f\u8aaa
    \n1.\u6709\u5169\u500b\u8cea\u6578\u5f88\u5927\u7684\u8cea\u6578 p \u8ddf q\uff0c\u8a08\u7b97\u5f97\u5230 n=pq\u3002
    \n2.\u63a5\u8457 z=(p-1)(q-1)\u3002
    \n3.\u63a5\u8457\u6211\u5011\u8981\u8a66\u8457\u627e\u4e00\u500b\u6578\u5b57 e\uff0ce \u8981\u6bd4 n \u5c0f\uff0c\u800c\u4e14 e \u8981\u8ddf z \u4e92\u70ba\u8cea\u6578\u3002
    \n4.\u518d\u4f86\u8981\u627e\u51fa\u53e6\u4e00\u500b\u6578\u5b57 d\uff0c\u5b83\u8981\u6eff\u8db3 ed-1 \u6070\u597d\u53ef\u4ee5\u88ab z \u6574\u9664\uff0c\u610f\u6307\u6c92\u6709\u9918\u6578\uff0c\u53e6\u4e00\u500b\u8aaa\u6cd5\u5c31\u662f\u8aaa ed mod z =1(mod\u662f\u53d6\u9918\u6578\u7684\u610f\u601d)\uff0c\u63db\u53e5\u8a71\u8aaa\uff0c\u5df2\u77e5 e\uff0c\u6211\u5011\u9078\u64c7 d\uff0c\u4f7f\u7528\u5f97\u7576 ed \u9664\u4ee5 z \u6642\u5f97\u5230\u9918\u6578 1\u3002<\/p>\n

    \u5df2\u7d93\u4e82\u6389\u4e86\u5c0d\u4e0d\u5c0d? \u597d\u8907\u96dc\u5440\uff0ce \u8ddf d \u7684\u6578\u5b57\u7684\u78ba\u4e0d\u597d\u627e\uff0c\u9019\u88e1\u82092\u500b\u7b26\u5408\u7684\u4f8b\u5b50\uff0c\u4f60\u81ea\u5df1\u5957\u7528\u9a57\u8b49\u770b\u770b:
    \np=3, q=5, n=pq=15, z=(p-1)(q-1)=8, e=3, d=3
    \np=5, q=7, n=pq=35, z=(p-1)(q-1)=24, e=5, d=29<\/p>\n

    \u4e0d\u904e\u5982\u679c\u4f60\u5df2\u7d93\u627e\u5230\u9019\u4e9b\u8cc7\u6599\uff0c\u5e95\u4e0b\u5c31\u6703\u6709\u4e00\u500b\u5f88\u795e\u5947\u7684\u6578\u5b78\u7279\u6027\u4e86\uff0c\u5047\u8a2d m \u662f\u539f\u6587(plaintext)\uff0c\u6211\u5011\u4f7f\u7528\u4e86e,n \u9019\u4e00\u7d44\u6578\u5b57\u4f86\u52a0\u5bc6\uff0c\u5f97\u5230\u7d93\u904e\u52a0\u5bc6\u904e\u7684\u5bc6\u6587(ciphertext) c
    \nme <\/sup>mod n = c<\/p>\n

    \u6536\u5230\u5bc6\u6587 c \u4e4b\u5f8c\u6211\u5011\u518d\u4f7f\u7528 d,n \u9019\u4e00\u7d44\u6578\u5b57\u505a\u89e3\u5bc6\uff0c\u54a6\uff0c\u5f88\u795e\u5947\u5730\uff0c\u5b83\u6703\u56de\u5230\u5230\u539f\u4f86\u539f\u6587\u4e86<\/p>\n

    cd<\/sup> mod n = m<\/p>\n

    \u6240\u4ee5\u4efb\u4f55\u8cc7\u6599\u53ef\u4ee5\u4f7f\u7528 e,n \u9019\u7d44\u6578\u5b57\u52a0\u5bc6\uff0c\u4f7f\u7528 d,n \u9019\u7d44\u6578\u5b57\u89e3\u5bc6\uff0c\u89d2\u8272\u5c0d\u8abf\u4e5f\u53ef\u4ee5\uff0c\u4f7f\u7528 d,n \u9019\u7d44\u6578\u5b57\u52a0\u5bc6\uff0c\u4f7f\u7528 e,n \u9019\u7d44\u6578\u5b57\u89e3\u5bc6\u4e5f\u662fOK\uff0c\u6240\u4ee5 (e,n) \u8207 (d,n) \u5c31\u5f88\u50cf\u5169\u628a\u9470\u5319\uff0c\u4e00\u628a\u958b\uff0c\u53e6\u4e00\u628a\u5c31\u662f\u95dc\uff0c\u6211\u5011\u901a\u5e38\u5b9a\u7fa9\u5176\u4e2d\u4e00\u628a\u9470\u5319\u70ba\u516c\u959e\u91d1\u9470\uff0c\u53e6\u4e00\u628a\u5c31\u662f\u79c1\u5bc6\u91d1\u9470\uff0c\u516c\u958b\u91d1\u9470\u662f\u516c\u958b\u7684\uff0c\u4efb\u4f55\u4eba\u90fd\u53ef\u4ee5\u62ff\u5f97\u5230\u4f60\u7684\u516c\u958b\u91d1\u9470\uff0c\u4f46\u662f\u79c1\u5bc6\u91d1\u9470\u662f\u81ea\u5df1\u8981\u4fdd\u5b58\u597d\u7684\uff0c\u4eca\u5929\u67d0\u4eba\u8981\u50b3\u9001\u4e00\u4e32\u8cc7\u6599\u7d66\u4f60\uff0c\u4f8b\u5982”I love you”\uff0c\u4f46\u4ed6\u4e0d\u60f3\u8b93\u5176\u4ed6\u4eba\u770b\u5230\uff0c\u9019\u6642\u5019\u4ed6\u53ef\u4ee5\u62ff\u4f60\u7684\u516c\u958b\u91d1\u9470\u52a0\u5bc6\u904e\u518d\u50b3\u9001\u7d66\u4f60\uff0c\u7576\u4f60\u63a5\u6536\u5230\u4e4b\u5f8c\u518d\u4f7f\u7528\u4f60\u7684\u79c1\u5bc6\u91d1\u9470\u6253\u958b\u4f86\u770b\uff0c\u5c31\u7b97\u5728\u50b3\u9001\u904e\u7a0b\u4e2d\u5982\u679c\u88ab\u99ed\u5ba2\u64f7\u53d6\u5230\u4e86\uff0c\u99ed\u5ba2\u6c92\u6709\u4f60\u7684\u79c1\u5bc6\u91d1\u9470\u4e5f\u6253\u4e0d\u958b\u8cc7\u6599\uff0c\u6240\u4ee5\u4f7f\u7528\u4f60\u7684\u516c\u958b\u91d1\u9470\u52a0\u5bc6\u904e\u7684\u8cc7\u6599\uff0c\u5168\u4e16\u754c\u552f\u4e00\u53ea\u6709\u4f60\u81ea\u5df1\u80fd\u89e3\u5bc6\uff0c\u9019\u6a23\u5c31\u5de7\u5999\u5730\u9054\u5230\u5b89\u5168\u52a0\u5bc6\u7684\u6548\u679c\u4e86\u3002<\/p>\n

    \u597d\uff0c\u4f46\u662f\u4f60\u6709\u6c92\u6709\u60f3\u904e\uff0c\u516c\u958b\u91d1\u9470\u662f\u6bcf\u500b\u4eba\u90fd\u53ef\u4ee5\u62ff\u5230\u7684\uff0c\u90a3\u6709\u6c92\u6709\u8fa6\u6cd5\u7531\u516c\u958b\u91d1\u9470\u4f86\u8a08\u7b97\u51fa\u4f60\u7684\u79c1\u5bc6\u91d1\u9470\u662f\u4ec0\u9ebc? \u4e5f\u5c31\u662f\u8aaa\u6709\u6c92\u6709\u53ef\u80fd\u5f9e\u5df2\u77e5 e,n \u9019\u7d44\u6578\u5b57\uff0c\u7b97\u51fa d,n \u9019\u7d44\u6578\u5b57\u5462? \u7b54\u6848\u662f\u53ef\u4ee5\u7684!<\/strong>\u5f9e n \u7684\u8cea\u56e0\u6578\u5206\u89e3\u958b\u59cb\u627e\u3002<\/p>\n

    \u54c7\uff0c\u90a3\u4e0d\u662f\u767d\u5e79\u4e86Orz….\uff0c\u4e26\u4e0d\u6703\uff0c\u56e0\u70ba\u8cea\u56e0\u6578\u5206\u89e3\u5c0d\u96fb\u8166\u7684\u8a08\u7b97\u4e0a\u4f86\u8b1b\u5f88\u8907\u96dc\uff0c\u4e5f\u5c31\u662f\u8981\u82b1\u5f88\u4e45\u7684\u6642\u9593\u4f86\u505a\uff0c\u5c31\u7b97\u662f\u8d85\u7d1a\u96fb\u8166\u4f86\u8dd1\u4e5f\u8981\u8dd1\u500b\u4e00\u5169\u5e74\uff0c\u6cc1\u4e14 p,q \u662f\u4e00\u500b\u5920\u5927\u7684\u8cea\u6578\uff0c\u9019\u500b\u52a0\u5bc6\u7d50\u679c\u4e26\u4e0d\u662f\u7b97\u4e0d\u51fa\u4f86\uff0c\u800c\u8981\u82b1\u5f88\u9577\u7684\u6642\u9593\uff0c\u7b49\u5230\u8dd1\u51fa\u7d50\u679c\u4f86\u6642\u5df2\u7d93\u904e\u4e86\u6642\u6548\u6027\u4e86<\/p>\n

    \u57fa\u672c\u4e0a\u4e0a\u9762\u5df2\u7d93\u63d0\u5230\u4e86\u7b2c\u4e00\u500b\u9700\u6c42\uff0c\u4fdd\u5bc6\u7684\u9700\u6c42\uff0c\u90a3\u7b2c\u4e8c\u500b\u9700\u6c42\u662f\u771f\u5be6\u7684\u9700\u6c42\uff0c\u5982\u4f55\u4f86\u78ba\u5b9a\u539f\u6587\u662f\u7531\u67d0\u500b\u4eba\u767c\u7d66\u4f60\u7684\uff0c\u800c\u4e0d\u662f\u5047\u50b3\u8056\u65e8\u5462? \u7576\u67d0\u4eba\u8981\u50b3”I love you”\u7d66\u4f60\u6642\uff0c\u4ed6\u8981\u5148\u5c07”I love you”\u5148\u7528\u81ea\u5df1\u7684\u79c1\u5bc6\u91d1\u9470\u52a0\u5bc6\uff0c\u5916\u9762\u90a3\u5c64\u518d\u7528\u4f60\u7684\u516c\u958b\u91d1\u9470\u52a0\u5bc6\uff0c\u4e5f\u5c31\u662f\u52a0\u5bc6\u4e86\u5169\u6b21\uff0c\u5c31\u50cf\u5305\u88f9\u4e00\u6a23\u5305\u4e86\u5169\u5c64\uff0c\u7576\u4f60\u6536\u5230\u5305\u88f9\u5f8c\u6700\u5916\u9762\u90a3\u5c64\u662f\u4ed6\u7528\u4f60\u7684\u516c\u958b\u91d1\u9470\u52a0\u5bc6\u7684\u561b\uff0c\u6240\u4ee5\u4f60\u5c31\u7528\u81ea\u5df1\u7684\u79c1\u5bc6\u91d1\u9470\u89e3\u5bc6\u6253\u958b\u4f86\uff0c\u63a5\u4e0b\u4f86\u4f60\u5c31\u8981\u62ff\u5c0d\u65b9\u7684\u516c\u958b\u91d1\u9470\u6253\u958b\u88e1\u9762\u9019\u5c64\uff0c\u56e0\u70ba\u4ed6\u7b2c\u4e00\u5c64\u662f\u4f7f\u7528\u4ed6\u7684\u79c1\u5bc6\u91d1\u9470\u52a0\u5bc6\u7684\u561b\uff0c\u5982\u679c\u6253\u5f97\u958b\u7684\u8a71\u5c31\u8868\u793a\uff0c\u4fdd\u8b49\u78ba\u8a8d\u662f\u5c0d\u65b9\u52a0\u5bc6\u7684\uff0c\u9019\u6a23\u5c31\u80fd\u78ba\u8a8d\u8ddf\u4f60\u8aaa”I love you”\u7684\u9019\u500b\u4eba\u7684\u8eab\u4efd\u662f\u78ba\u5b9a\u7684\u3002<\/p>\n

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