Computer Network Security

If DES were a group [117], then given keys K1 and K2, there would exist a key K% such that

E(P, K3) = E(E{P, K1),K2) for all plaintext P,

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and we could also find such a key K3 if any of the encryptions were replaced by decryptions. If equation (6.39) holds, then triple DES is no more secure than single DES. It was established in [45] that DES is not a group and, consequently, triple DES is more secure than single DES. Show that TDES is not a group. Hint: Select TDES keys Κ and K2. You will be finished if you can verify that there does not exist any key K3 for which E(P,K3) = E(E(P,K1),K2) for all possible choices of P.

Consider the “simple” timing attack on RSA .

a. Extend the timing attack to recover the bit d?,. That is, assuming that bit d1 has been recovered, what conditions must Y and Z satisfy so that the attack presented in the text can be used to determine d2?

b. Extend the attack to recover d3, assuming that d1nd d2 have been recovered.

c. In practice, we need to recover about half of the private key bits. Why is this attack not a practical means for recovering such a large number of private key bits?

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