CSAW CTF 2012 write-up: CryptoMat (web400)

Here is the description of the challenge:
CryptoMat is a site where you can send encrypted messages to other users. Dog is a user on the site and has the key. Figure out how to get into his account and obtain it.

The first thing we had to do was finding out how the encryption algorithm works. After a few attempts, we discovered that the title wasn’t used for the encryption and that, given a plaintext P and a key k, we have
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