a. Barack often sends funny jokes to Hillary. He does not care about confidentiality of these messages but wants to get credit for the jokes and prevent Bill from claiming authorship of or modifying them. How can this be achieved using public-key cryptography? b. 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 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