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Authentication protocol using a keyed hash function: Alice and Bob share a secret key for a keyed hash function. The protocol is: Alice $\Rightarrow$ $m||h_{k}(m)$ $\Rightarrow$ Bob.

There are the following two methods: $h_{k}=E_{k}\circ h$ and $h_{k}=h\circ E_{k}$.

What are the advantages and disadvantages of the two protocols?

($E_{k}$ is a well designed one-key cipher and $h$ is a well-designed hash function. $\circ$ is function composition).

I was reading another question. And in our lecture notes, only the first one was mentioned, and the lecture notes says that if both components are well-designed, the first method should be secure. I have the following questions:

  1. Why would the first method be secure?
  2. What about the second method? The second was not mentioned in lecture notes, is it because it cannot be secure even if both components are secure?

Thanks!!

Bella
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