As public-key cryptography is computationally intensive and drains the battery of Barack's device, he comes up with an alternative approach. First, he shares a secret key k with Hillary but not with Bill. Next, together with a joke x, he sends over the value d = h(k||x), where h is a cryptographic hash function. Does value d provide assurance to Hillary that Barack is the author of x and that x

was not modified by Bill? Justify your answer.

What will be an ideal response?

Value d is a message authentication code (MAC), which gives Hillary assurance
of the authorship and integrity of Barack's jokes. The reason is that a cryptographic hash
function is one-way, Bill cannot recover the key k from value d, Thus, Hillary knows that
only Barack could have computed value d from joke x. Also, if Bill replaces joke x with a
joke of his, x0, it would infeasible for Bill to compute the MAC value corresponding to x0.