Recall the linear cryptanalysis of TDES. Assume that equation (6.33) holds with probability (3/4)^{3} « 0.42. Also assume that the key satisfies fco®fci = 0. Then if we conduct the attack using 100 known plaintexts, what are the expected counts for c\ θρι = 0 and c\ Θ pio = 1? Compare your answer with the empirical results presented in the text. Why do you think the theoretical and empirical results differ?

Suppose that Bob’s knapsack public key is

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T = [2195,4390,1318, 2197,7467,5716,3974,3996,7551,668]

Suppose that Alice encrypts a message with Bob’s public key and the resulting ciphertext is C_{1} = 8155. Implement the LLL attack and use your program to solve for the plaintext P_{1}. For the same public key, find the plaintext P_{2} for the ciphertext C_{2} = 14748. Can you determine the private key?

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