Recovering the key for double-DES takes three steps. Given the plaintext and the ciphertext you do the following:
- Encrypt the plaintext with all 2^56256 possible keys and write down the results
- Decrypt the ciphertext with all 2^56256 possible keys and write down the results
- Check where the results are the same. That is your key.
Note that all you had to do to recover the key was using DES 2 * 2^56× 256 times, which makes 2^57257.