File size: 5,745 Bytes
8897300 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | # Writeup for MissingBits
## Solution
We are given a key, but there are some lines missing.
From the End of the key we know that it is a RSA private key (`-----END RSA PRIVATE KEY-----`)
Using the apearence of the key and this informations means that we are working
with a RSA private key in PEM-Format.
This means, that every line is base64 encoded and the whole key is a list of DER Sequenzes
representing integers
Decoding the key yields:
```text
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????
c70881814053b5a4b252f76ba9f80011db91767cd16ca73012178cc70203010001028201000a9a25ba23342c18ab2933
9f4167dacc4cb21a383e14e13d0717efd006a92c55371be258ad865c44cfed2b27bd61a64571c846747a2463a1c8755e
7530d86713803a197ce4592c55061551aca07fd1297a48dafef4a3e4e13c34870074406bdda67a81d2f18beab56b92a1
d67126b05e858981a9b0f90deb7a2f6e8c3f08ab7837b51026a644430dfcd2b340d2c3907a79b35d114ea5703c3d115b
1ba8ad19188fd6007db697509d68204399fec7cff693e9370915baff120ff5d3005598768d5a266de9cbc609e1402241
6d8691e08f01d33cd8a97a857de1c230d97ea499a698572fb36644ef57eaca346277a643a92e065ed4ae45033450becb
510541698102818100e4188b37b163c203ae4f814ac457738b376afede66bd192c6e604ffc95a4defc5061e0a63223d0
c6b414a9d1c61b11bc88c2301fb76784d68f6bcd65acff5f08aca28ff71a11b7b8966126f9574cff165017e3e209cd5f
ce2617a61cfdc2e01cf3efa4bcac4cd846a20def05db99ec5d6f856b13685ca6c9834cd340bcb32a2102818100f122e2
85b030a36974cda97c18c21e9b3afe00fc4bc3e7e67786abc9500ca2ff003641bc283330766bef927deb2fb59a2b29b9
7da92abd7478e7f4063def27895cf1ea869619249f8a37956a7dbba46fdbcd5ab2ca614764ff5c4611075b81cde7b84e
a57cb491416a55ac49582b3eb611f42d36684e801ea60facafcd8569e7028181009c99e943346c1c3130c4ef2ca8fead
9a8052da67513c3503574892c204efac14a90f7a1040ce6c317043db8fe5a68217e20108cf4db929efb18a3efbb6b9a1
c2afdbf061a3a9546ccbfa29aaf8f0291665a8f151288fb35e32b2fbde5daf24f55bd9454e3031962f7065869c8bf7f2
daf78d2f45a4da2fbc9c83eb6a3fe3f66102818100d28bba2c2ece1930f02aceecab157bf1e04d7e80cc8acec63de119
c7da1c5e89b71ea8c0e87ce1b8d4bfc73229136c46a39f77f5cfaaa0e7bcd6130d0c30f05d91092dd4bbe45244f74357
34377a8ab69cbe2e8e640512788e3b7c764bed4b66850839ab673aa685ee99c5a7f8d3319b7a0bb11a8b72d78d6b43ce
6d664f324b0281806275b9649c00af1229c351007c76f125cd13aa974654317f6140eb12ae0d23bb7b26ba7f2aba3713
3c942b59cb68370d195e74230e4573689c6883517742429483a075467d90d1162e08078d0e7f8aa819134f5f03bbbcb0
f8653fe14e84330fae2fb74d8dab03d638f1f74ae8e919830c19860d0ba5b9d3b41bb87d5d0ce5f9
```
From Wikipedia we know, that an Integer starts with `02` in DER.
This Value is then followed by the size and then the value.
Searching the above Key for `02` yields the following values:
The first value we find is the following:
- 0203010001: Size: 3, Value: 0x010001
From there we can just parse the following values by reading the sizes that are encoded
d
02820100: Size 0x100 Bytes, Value: 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
p
028181: Size 0x81, Value:
0x00e4188b37b163c203ae4f814ac457738b376afede66bd192c6e604ffc95a4defc5061e0a63223d0c6b414a9d1c61b11bc88c2301fb76784d68f6bcd65acff5f08aca28ff71a11b7b8966126f9574cff165017e3e209cd5fce2617a61cfdc2e01cf3efa4bcac4cd846a20def05db99ec5d6f856b13685ca6c9834cd340bcb32a21
q
028181: Size 0x81, Value:
0x00f122e285b030a36974cda97c18c21e9b3afe00fc4bc3e7e67786abc9500ca2ff003641bc283330766bef927deb2fb59a2b29b97da92abd7478e7f4063def27895cf1ea869619249f8a37956a7dbba46fdbcd5ab2ca614764ff5c4611075b81cde7b84ea57cb491416a55ac49582b3eb611f42d36684e801ea60facafcd8569e7
Using these values we can reconstruct N and decrypt the message
```python
#!/bin/python3
# pip install pycryptodome
from Crypto.Util.number import bytes_to_long
from Crypto.Util.number import long_to_bytes
d = 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
p = 0x00e4188b37b163c203ae4f814ac457738b376afede66bd192c6e604ffc95a4defc5061e0a63223d0c6b414a9d1c61b11bc88c2301fb76784d68f6bcd65acff5f08aca28ff71a11b7b8966126f9574cff165017e3e209cd5fce2617a61cfdc2e01cf3efa4bcac4cd846a20def05db99ec5d6f856b13685ca6c9834cd340bcb32a21
q= 0x00f122e285b030a36974cda97c18c21e9b3afe00fc4bc3e7e67786abc9500ca2ff003641bc283330766bef927deb2fb59a2b29b97da92abd7478e7f4063def27895cf1ea869619249f8a37956a7dbba46fdbcd5ab2ca614764ff5c4611075b81cde7b84ea57cb491416a55ac49582b3eb611f42d36684e801ea60facafcd8569e7
ct = open("../dist/ciphertext_message", "rb").read()
pt = pow(
bytes_to_long(ct), d, p*q
)
print(long_to_bytes(pt))
```
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