Hi,
1) What can an attacker do by being able to see H{K, m} because it is not encrypted? In my understanding (not at all an expert), they shouldn't be able to do much more if the hashing function is good since it won't reveal information. However, I don't see why to remove an obstacle. If in the future, an exploit is found for H, at least the hash will not have been sent as plaintext.
2) Elaborating on your proposal: Alice sends KB+{mi, KA−{H(nB, mi, counter)}} as you say. Bob decrypts using KB-, and then using KA+. Bob then does H(nB, mi, local_counter) where local_counter was set to 0 at the beginning of the communication. Therefore if msg 5 of sent by A is not received after msg 4 by B then the hashes won't match. So I'd say this should work.
I am not sure if your solution violates this part of the description "but do not modify the existing ones." but it doesn't really matter.
"Doesn't that imply that they will do the verification too late " - that depends on how the rest of the program is implemented. It could wait for the order validation step before using the data.
3) It abstractly means that x and y are fed to symmetric encryption or a hash function.
1) What can an attacker do by being able to see H{K, m} because it is not encrypted? In my understanding (not at all an expert), they shouldn't be able to do much more if the hashing function is good since it won't reveal information. However, I don't see why to remove an obstacle. If in the future, an exploit is found for H, at least the hash will not have been sent as plaintext.
2) Elaborating on your proposal: Alice sends KB+{mi, KA−{H(nB, mi, counter)}} as you say. Bob decrypts using KB-, and then using KA+. Bob then does H(nB, mi, local_counter) where local_counter was set to 0 at the beginning of the communication. Therefore if msg 5 of sent by A is not received after msg 4 by B then the hashes won't match. So I'd say this should work.
I am not sure if your solution violates this part of the description "but do not modify the existing ones." but it doesn't really matter.
"Doesn't that imply that they will do the verification too late " - that depends on how the rest of the program is implemented. It could wait for the order validation step before using the data.
3) It abstractly means that x and y are fed to symmetric encryption or a hash function.
