applied-cryptography/appliedcrypto
1
0
Fork 0
mirror of https://github.com/billbuchanan/appliedcrypto.git synced 2026-02-21 19:27:58 +00:00
Code Issues Packages Projects Releases Wiki Activity

Update README.md

Browse Source
This commit is contained in:
Bill Buchanan
2023-02-27 05:15:16 +00:00
committed by GitHub
parent 6ad700c741
commit acb7948d08
1 changed files with 21 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

23
z_ctf/README.md
View File

@@ -1,4 +1,6 @@
# Cracking an encrypted key
# Encryption CTFs
These are a collection of CTFs related to encryption.
## Cracking an encrypted key
Bob has encrypted this RSA key pair with 128-bit AES. But he can't remember the password he applied. All he can remember is that it might have been his favouriate colour. Can you determine the two prime numbers (in hex) which make up the modulus?
```
-----BEGIN ENCRYPTED PRIVATE KEY-----
@@ -63,6 +65,23 @@ aXH3uxNfE8bxVAfFCxTJV0XOLTvEcwIhAJVPbRaEfyvMyskZDYHbQrfvgjyMTTyW
VTIsAZLHXvFp
-----END PRIVATE KEY-----
```
## Cracking RSA with Chinese Remainder Theory - Håstad’s Broadcast
Bob has used the RSA method with three different moduli to encrypt the same message for Alice. These modulus values are 181573934956808382047424502743618497959, 263663189152094019455553753982108272769, and 150466971419052326232703131045351509419. The corresponding ciphered values are 89486828865161621017578261527117772610, 176405275524632787228669332980053978025, and 120736618872251736750094696442087698014. Determine the English city in the message (assume he has used an exponent of 3).
### Answer
The method is defined [here](https://asecuritysite.com/cracking/rsa_ctf01). In this case, we have used 64-bit primes here and which generates 128-bit modulus values. The values of:
Cipher 1: 89486828865161621017578261527117772610, N1=181573934956808382047424502743618497959
Cipher 2: 176405275524632787228669332980053978025, N2=263663189152094019455553753982108272769
Cipher 3: 120736618872251736750094696442087698014, N3=150466971419052326232703131045351509419
We can solved M^e with CRT to get 8445460724692873078755117519791553896065429140561722150551706781
If we assume e=3, we take the third root to get: 2036453269898309954661
Next we convert this integer to bytes, and display as a string.
Decipher: b'newcastle'