Digital Signature and Hash Function $[14$ Points$]$

Recall that we use both a public key system and a hash function when computing digital

signatures.

a$.[2$ Points$]$ Precisely how is a digital signature computed and verified?

b$.[2$ Points$]$ Suppose that the public key system used to compute and verify signatures is

insecure meaning that one is able to recover the private key, but the hash function is

secure$.$ Show that you can forge signatures.

c$.[2$ Points$]$ Suppose that the hash function used to compute and verify signatures is

insecure, but the public key system is secure$.$ Show that you can forge signatures.

d$.[2$ Points$]$ Show that a digital signature provides integrity protection.

e$.[2$ Points$]$ Show that a digital signature provides non$-$repudiation.

f$.[2$ Points$]$ Suppose that Alice wants to sign the message M and send the result to Bob.

g$.[2$ Points$]$What does Alice send to Bob and how does Bob verify the signature?