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Each half of the key is 28 bits long, so there will be $2^{28}$ possible choices for each of them. In the first part of your attack, you start with the known block of plaintext and encrypt it for the first 8 rounds using each possible left half of the key. This gives you $2^{28}$ "half-encrypted" 64-bit blocks. This is less than the birthday bound, so ...

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CD CD is collectively referring to the C and D Registers. Their use and operation while simultaneous is independent. C and D are concatenated together to specify PC2. Permuted Choice 2 PC2 is a selection permutation. You might notice that the first 24 bits of the selected Key are from the C Register (CD(1 to 28)) and the second 24 bits are from the D ...

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Luby rackoff results are based on assuming the Round Function to be Secure Pseudo Random Functions. Where as the round functions of DES are not that secure enough which needs more rounds (Triple DES needs 48 rounds )

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