Break simplified DES Given that theres no initial permutation only 16 32 bit long randomly generated keys and the round function is simply f(x) = x ⊕ Ki. Also there are 10 64bit plaintext/cyphertext pairs given. 



Now I have to show a way to universally break this cypher, but I can only think of brute-force. Any suggestions?
Here's a hint on one avenue of approach (actually, there are several possible):

Suppose we had two plaintexts $X$ and $X'$, which are identical except in one bit.  Now, consider $\text{SimpleDES}_K(X)$ and $\text{SimpleDES}_K(X')$; how are they related?

If that's too difficult, consider how both $\text{SimpleDES}_K(X)$ and $\text{SimpleDES}_K(X')$ are related after 1 round, after 2 rounds, etc...