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?

• Why is brute-force not good enough? – mikeazo Nov 9 '17 at 19:33
• I got told that brute-forcing a 512bit key would take too long and that there is another way, but I just can't think of any – user53029 Nov 9 '17 at 19:38
• Okay, so what you really want is a "computationally feasible way to universally break" the cipher. – mikeazo Nov 9 '17 at 19:46

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...