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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?

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  • $\begingroup$ Why is brute-force not good enough? $\endgroup$
    – mikeazo
    Commented Nov 9, 2017 at 19:33
  • $\begingroup$ 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 $\endgroup$
    – user53029
    Commented Nov 9, 2017 at 19:38
  • $\begingroup$ Okay, so what you really want is a "computationally feasible way to universally break" the cipher. $\endgroup$
    – mikeazo
    Commented Nov 9, 2017 at 19:46

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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...

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