1. Why do MD4 (older), MD5, SHA-1 and SHA-2 require a padding of messages that are already a multiple of 512 bits?

2. Suppose Alice, Bob, and Carol want to use secret key technology to authenticate to each other. If they all used the same secret key K, then Bob could impersonate Carol to Alice(actually any three can impersonate the other to the third). Suppose instead that each had their own secret key, so Alice uses K_A, Bob uses K_B, and Carol uses K_C. This means that each one, to prove his or her identity , responds to a challenge with a function of his or her secret key and the challenge. Is this more secure than having them all use the same secret key K? (Hint: what does Alice need to know in order to verify Carol's answer to Alice's challenge?)