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Suppose Dr. Smart has designed a 4DES cipher which encrypts data m in the following way: c= Dk4(Dk3(Ek2(Ek1(m)))), where E and D denote the encryption and decryption operation of DES.

To break this cipher and learn the key pair from pair, a brute-force method is to try all possible combinations of , but this requires about 2²²⁴ trials which is too much.

Design a more practical attack for finding the paor of keys used with significantly less effort. You can assume that the attacker is able to obtain a few pairs.

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