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Alice wants to encrypt her messages securely, but she can afford only an encryption machine that uses a 25bit key. To increase security, she chooses
Alice wants to encrypt her messages securely, but she can afford only an encryption machine that uses a 25bit key. To increase security, she chooses 4 keys K1,K2,K3,K4 and encrypts four times: c=EK1(EK2(EK3(EK4(m)))). Eve finds several plaintext-ciphertext pairs (m, c) encrypted with this set of keys. Describe how she can find (with high probability) the keys K1, K2, K3, K4. (For this problem, assume that Eve can do at most 260 computations, so she cannot try all 2100 combinations of keys.) (Note: If you use only one of the plaintext-ciphertext pairs in your solution, you probably have not done enough to determine the keys.)
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