a) For the following protocol, discuss what the effects of the homomorphism mutation, assuming there are two instances of this protocol running and using the same shared symmetric key between A and B as shown below:
1. A -?> B: A, encrypt(N1A, KAB)
2. B -?> A: encrypt(inc(N1A), N1B), KAB)
3. A -?> B: encrypt(inc(N1B), KAB)
4. B -?> A: encrypt((K1’AB, N1’B, N1A), KAB)
1. A -?> B: A, encrypt(N2A, KAB)
2. B -?> A: encrypt(inc(N2A), N2B), KAB)
3. A -?> B: encrypt(inc(N2B), KAB)
4. B -?> A: encrypt((K2’AB, N2’B, N2A), KAB)
Where inc(x) = x + 1 and KAB is a long-?term permanent shared symmetric key between A and B, and K1’AB , K2’AB are session symmetric keys, which are short-?lived. Discuss the implication of this kind of mutation on the forward secrecy property, i.e. whether leaking K1’AB will have any impact on the secrecy of future communications based on completing the second instance above.
b) For the following protocol, discuss the secrecy of the long-?term shared key KAB, in light of the xor mutation:
1. A -?> B: A, encrypt(NA, KAB)
2. B -?> A: (encrypt(inc(NA), KAB), encrypt((NB), KAB))
3. A -?> B: encrypt(encrypt(inc(NB), NA), KAB) Where inc(x) = x + 1.
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