无法使用公共模数攻击解码 RSA 消息？
cant decode RSA Message using common modulus attack?
我有相同的原始消息使用不同的 public e 和相同的 public n 加密，所以我想使用共模攻击但看不到原始消息信息。我的程序是
from base64 import *
c1 = "RBVdQw7Pllwb42GDYyRa6ByVOfzRrZHmxBkUPD393zxOcrNRZgfub1mqcrAgX4PAsvAOWptJSHbrHctFm6rJLzhBi/rAsKGboWqPAWYIu49Rt7Sc/5+LE2dvy5zriAKclchv9d+uUJ4/kU/vcpg2qlfTnyor6naBsZQvRze0VCMkPvqWPuE6iL6YEAjZmLWmb+bqO+unTLF4YtM1MkKTtiOEy+Bbd4LxlXIO1KSFVOoGjyLW2pVIgKzotB1/9BwJMKJV14/+MUEiP40ehH0U2zr8BeueeXp6NIZwS/9svmvmVi06Np74EbL+aeB4meaXH22fJU0eyL2FppeyvbVaYQ==" # 0x10001
c2 = "TSHSOfFBkK/sSE4vWxy00EAnZXrIsBI/Y6mGv466baOsST+qyYXHdPsI33Kr6ovucDjgDw/VvQtsAuGhthLbLVdldt9OWDhK5lbM6e0CuhKSoJntnvCz7GtZvjgPM7JDHQkAU7Pcyall9UEqL+W6ZCkiSQnK+j6QB7ynwCsW1wAmnCM68fY2HaBvd8RP2+rPgWv9grcEBkXf7ewA+sxSw7hahMaW0LYhsMYUggrcKqhofGgl+4UR5pdSiFg4YKUSgdSw1Ic/tug9vfHuLSiiuhrtP38yVzazqOZPXGxG4tQ6btc1helH0cLfw1SCdua1ejyan9l1GLXsAyGOKSFdKw==" #0x53cb7
n = "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"
c1 = int.from_bytes(b64decode(c1), 'big')
c2 = int.from_bytes(b64decode(c2), 'big')
n = int.from_bytes(b64decode(n), 'big')
# e==>c1 0x10001 = 65537
# e==>c2 0x53cb7 = 343223
s1 = -25421
s2 = 133132
c1_raised = int(pow(c2, s1, n))
c2_raised = int(pow(c1, s2, n))
res = ((c1_raised * c2_raised) % n)
print(res)
c1和c2都是密文。 s1 和 s2 我都是从在线扩展的 eculudian 算法计算器中得到的，并用 65537×133132 + 343223×−25421 = 1 验证。用于加密的密钥是 (c1, key1) 和 (c2, key2):
KEY1
-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAxqy430huZnHUpVZIA+HD
IUqOJ03grABD7CjIWJ83fH6NMIvD4wKFA4Q0S6eYiIViCkGOatlVV4KE/ATyifEm
s4oBgWJRzvmhT9TCSdlraQh/qRsuGtvcgMuW/wzLYSnY9nN9qFDEUfLtP2y2HDaJ
Hckk0Kso8mrfDtNXzoSNAv/gCRJxTM9jcsH0EIDoZ0egMD61zfbOkS8RRP1PVXQ8
eWh1oU/f+Pi2YhUMVr5YsJI5dx3ETZaQecStj9mTvGMLeFXS4C6L4Wgk3NWrOBMj
HBcxEQqL0CjXod+riS51KUVXuvxxrq9eSNsCZ6bbY9NQ+ZUGjuHK1tMt8RpJvSS6
lwIDAQAB
-----END PUBLIC KEY-----
KEY2
-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAxqy430huZnHUpVZIA+HD
IUqOJ03grABD7CjIWJ83fH6NMIvD4wKFA4Q0S6eYiIViCkGOatlVV4KE/ATyifEm
s4oBgWJRzvmhT9TCSdlraQh/qRsuGtvcgMuW/wzLYSnY9nN9qFDEUfLtP2y2HDaJ
Hckk0Kso8mrfDtNXzoSNAv/gCRJxTM9jcsH0EIDoZ0egMD61zfbOkS8RRP1PVXQ8
eWh1oU/f+Pi2YhUMVr5YsJI5dx3ETZaQecStj9mTvGMLeFXS4C6L4Wgk3NWrOBMj
HBcxEQqL0CjXod+riS51KUVXuvxxrq9eSNsCZ6bbY9NQ+ZUGjuHK1tMt8RpJvSS6
lwIDBTy3
-----END PUBLIC KEY-----
程序可以运行，但根据此 Converter site
输出没有意义
模数c6ac...ba97不是Base64编码的，而是十六进制编码的，所以：
n = int.from_bytes(bytes.fromhex(n), 'big')
此外，结果res要表示为字节数组或十六进制编码：
res = res.to_bytes(256, 'big').hex()
这给出了纯文本：
00...004854427b43306d6d6f6e5f4d3064556c7535535f31535f6234447d
或 UTF-8 解码：
HTB{C0mmon_M0dUlu5S_1S_b4D}
我有相同的原始消息使用不同的 public e 和相同的 public n 加密，所以我想使用共模攻击但看不到原始消息信息。我的程序是
from base64 import *
c1 = "RBVdQw7Pllwb42GDYyRa6ByVOfzRrZHmxBkUPD393zxOcrNRZgfub1mqcrAgX4PAsvAOWptJSHbrHctFm6rJLzhBi/rAsKGboWqPAWYIu49Rt7Sc/5+LE2dvy5zriAKclchv9d+uUJ4/kU/vcpg2qlfTnyor6naBsZQvRze0VCMkPvqWPuE6iL6YEAjZmLWmb+bqO+unTLF4YtM1MkKTtiOEy+Bbd4LxlXIO1KSFVOoGjyLW2pVIgKzotB1/9BwJMKJV14/+MUEiP40ehH0U2zr8BeueeXp6NIZwS/9svmvmVi06Np74EbL+aeB4meaXH22fJU0eyL2FppeyvbVaYQ==" # 0x10001
c2 = "TSHSOfFBkK/sSE4vWxy00EAnZXrIsBI/Y6mGv466baOsST+qyYXHdPsI33Kr6ovucDjgDw/VvQtsAuGhthLbLVdldt9OWDhK5lbM6e0CuhKSoJntnvCz7GtZvjgPM7JDHQkAU7Pcyall9UEqL+W6ZCkiSQnK+j6QB7ynwCsW1wAmnCM68fY2HaBvd8RP2+rPgWv9grcEBkXf7ewA+sxSw7hahMaW0LYhsMYUggrcKqhofGgl+4UR5pdSiFg4YKUSgdSw1Ic/tug9vfHuLSiiuhrtP38yVzazqOZPXGxG4tQ6btc1helH0cLfw1SCdua1ejyan9l1GLXsAyGOKSFdKw==" #0x53cb7
n = "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"
c1 = int.from_bytes(b64decode(c1), 'big')
c2 = int.from_bytes(b64decode(c2), 'big')
n = int.from_bytes(b64decode(n), 'big')
# e==>c1 0x10001 = 65537
# e==>c2 0x53cb7 = 343223
s1 = -25421
s2 = 133132
c1_raised = int(pow(c2, s1, n))
c2_raised = int(pow(c1, s2, n))
res = ((c1_raised * c2_raised) % n)
print(res)
c1和c2都是密文。 s1 和 s2 我都是从在线扩展的 eculudian 算法计算器中得到的，并用 65537×133132 + 343223×−25421 = 1 验证。用于加密的密钥是 (c1, key1) 和 (c2, key2):
KEY1
-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAxqy430huZnHUpVZIA+HD
IUqOJ03grABD7CjIWJ83fH6NMIvD4wKFA4Q0S6eYiIViCkGOatlVV4KE/ATyifEm
s4oBgWJRzvmhT9TCSdlraQh/qRsuGtvcgMuW/wzLYSnY9nN9qFDEUfLtP2y2HDaJ
Hckk0Kso8mrfDtNXzoSNAv/gCRJxTM9jcsH0EIDoZ0egMD61zfbOkS8RRP1PVXQ8
eWh1oU/f+Pi2YhUMVr5YsJI5dx3ETZaQecStj9mTvGMLeFXS4C6L4Wgk3NWrOBMj
HBcxEQqL0CjXod+riS51KUVXuvxxrq9eSNsCZ6bbY9NQ+ZUGjuHK1tMt8RpJvSS6
lwIDAQAB
-----END PUBLIC KEY-----
KEY2
-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAxqy430huZnHUpVZIA+HD
IUqOJ03grABD7CjIWJ83fH6NMIvD4wKFA4Q0S6eYiIViCkGOatlVV4KE/ATyifEm
s4oBgWJRzvmhT9TCSdlraQh/qRsuGtvcgMuW/wzLYSnY9nN9qFDEUfLtP2y2HDaJ
Hckk0Kso8mrfDtNXzoSNAv/gCRJxTM9jcsH0EIDoZ0egMD61zfbOkS8RRP1PVXQ8
eWh1oU/f+Pi2YhUMVr5YsJI5dx3ETZaQecStj9mTvGMLeFXS4C6L4Wgk3NWrOBMj
HBcxEQqL0CjXod+riS51KUVXuvxxrq9eSNsCZ6bbY9NQ+ZUGjuHK1tMt8RpJvSS6
lwIDBTy3
-----END PUBLIC KEY-----
程序可以运行，但根据此 Converter site
输出没有意义模数c6ac...ba97不是Base64编码的，而是十六进制编码的，所以：
n = int.from_bytes(bytes.fromhex(n), 'big')
此外，结果res要表示为字节数组或十六进制编码：
res = res.to_bytes(256, 'big').hex()
这给出了纯文本：
00...004854427b43306d6d6f6e5f4d3064556c7535535f31535f6234447d
或 UTF-8 解码：
HTB{C0mmon_M0dUlu5S_1S_b4D}