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3. For DES, what is the probability that two different keys will encrypt at least 1...

3. For DES, what is the probability that two different keys will encrypt at least 1 plaintext message to the same ciphertext output?

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Answer #1

Getting same ciphertext output from the same plaintext with two different keys is called as key clustering.

Semi weak keys which are the keys that are inverse to each other is a key cluster. Ek2 (Ek1 (P)) = P, wher k1 is key 1, k2 is key 2.

Key domain of DES = 256

The total number of weak keys =4

The total number of semi weak keys =12

The total number of possible weak keys =48

The total number of keys resulting same ciphertext = 64 (4 + 12 + 48)

The probability of choosing the clustered keys = Key domain of DES / total number of keys resulting same ciphertext

= ( 64 (4 + 12 + 48) ) / 256

= (64(64)) / 256

= 4096 / 256

= 5.6843189 * 10-16

The probability of choosing the clustered keys is 5.6843189 * 10-16 which is nearly zero and highly impossible.

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