6. There are several reasons why it is good practice to separate RSA digital signature key pairs and RSA encryption key pairs. (a) If Alice is using the same RSA key pair for both digital signatures and encryption, explain how Bob could forge Alices signature on a message of his choice if Alice is foolish enough to help him. (b) Why is this a more powerful attack than the existential forgery that we described in Section 7.3.4? c) What other reasons are there for keeping these key pairs separate? 8. What key lengths and lengths of hash function outputs would you currently recommend for use with digital signatures based on: (a) RSA? (b) DSA? (c) ECDSA? 14. There have been many digital signatures proposed with additional properties. One of these is blind signatures. (a) What is a blind signature? (b) Provide a physical world analogy for a blind signature. (c) What potential applications are there for blind signatures? (d) Describe one method of producing blind signatures that is based on RSA.