Homework Assignment #3 (Due by 10/24/2017)

*Notes:
This homework assignment covers topic 5.
You must use text editor (e.g. MS Word) to complete your homework.*

1. (10 points) Problem 3 on page 196.

2. (10 points) Problem 7 on page 196.

3. (10 points) Problem 8 on page 196.

4. (10 points) Problme 9 on page 196.

5. (10 points) Problem 2 on page 182.

6. (10 points) Problem 3 on page 182.

7. (10 points) Problem 4 on page 182.

8. (10 points) Problem 6 on page 183.

9. (10 points) Problem 8 on page 183.

10. (10 points) This problem illustrates the point that the Diffie-Hellman protocol is not secure without the step where you take the modulus; i.e. the "Indiscrete Log Problem" is not a hard problem! You are Eve, and have captured Alice and Bob and imprisoned them.

You overhear the following dialog.

Bob: Oh, let's not bother with the prime in the Diffie-Hellman protocol, it will make things easier.

Alice: Okay, but we still need a base g to raise things to. How about g=3?

Bob: All right, then my result is 27.

Alice: And mine is 243.

What is Bob's secret xB and Alice's secret xA? What is their secret combined key? (Don't forget to show your steps.)