根据前面大佬帖子的指引,晚上试了下,成功的解决了疑问
原始N:
93AF7A8E3A6EB93D1B4D1FB7EC29299D2BC8F3CE5F84BFE88E47DDBDD5550C3CE3D2B16A2E2FBD0FBD919E8038BB05752EC92DD1498CB283AA087A93184F1DD9DD5D5DF7857322DFCD70890F814B58448071BBABB0FC8A7868B62EB29CC2664C8FE61DFBC5DB0EE8BF6ECF0B65250514576C4384582211896E5478F95C42FDED
它是个合数,要想得到私钥D,必须先找到因子P/Q,然后根据φ(N)=(P-1)*(Q-1)得到φ(N),再由D = 1/E mod (φ(N))得到私钥D,但大数分解为P/Q是很难的,所以已知公钥N/E是没办法拿到D的.
但大佬们找到一个好办法(前提是没有签名,不验证N合法性),更改N(改变一个字节,5C-->CB)变成一个素数,而素数的φ(N)=N-1 就直接拿到了,再由D = 1/E mod (φ(N))就可以拿到D,直接GAME OVER.
使用RDLP工具测试通过
N1:93AF7A8E3A6EB93D1B4D1FB7EC29299D2BC8F3CE5F84BFE88E47DDBDD5550C3CE3D2B16A2E2FBD0FBD919E8038BB05752EC92DD1498CB283AA087A93184F1DD9DD5D5DF7857322DFCD70890F814B58448071BBABB0FC8A7868B62EB29CC2664C8FE61DFBC5DB0EE8BF6ECF0B65250514576C4384582211896E5478F9CB42FDED
φ(N):93AF7A8E3A6EB93D1B4D1FB7EC29299D2BC8F3CE5F84BFE88E47DDBDD5550C3CE3D2B16A2E2FBD0FBD919E8038BB05752EC92DD1498CB283AA087A93184F1DD9DD5D5DF7857322DFCD70890F814B58448071BBABB0FC8A7868B62EB29CC2664C8FE61DFBC5DB0EE8BF6ECF0B65250514576C4384582211896E5478F9CB42FDEC
E:13
D:7498027049140B81158DBAB99F7ED002D1B9980EB732E85947E7E4F42F2832151FA6562B67D4D8A0A3221ED1045DC0F0B9258FF611A4F8B8C99AE78199ED9E4DAEC2F9579F3FF31C79C4A219B6EAA4002F8235D8634E1C7A01D332571D710D64DD64D44D814126B7BF8D60167845A5B1BE47FF687B79364413BBF3B7BB6AC877
附件是提到的工具,其他更多算法工具可以到我的网盘里翻
https://od.cloudsploit.top/zh-CN/tools/Tuts%204%20You%20-%20Collection%202011/Crypto%20Tools/
最后于 2023-12-5 08:29
被wusha编辑
,原因: