Comp 3704
Introduction to Cryptography
Homework 7
Due Tuesday, March 11, 2003

1. If p is prime, prove directly there are exactly two square roots of unity in Z_p (The word "unity" means the number 1).
2. Do problem 5.16, page 222-223
3. Do problem 5.33, page 225
4. Do problem 6.9, page 269. You may just decrypt the first 12 letters.
5. Read Example 7.1 on page 282. Construct a similar toy example, including what requirements you used or how you computed each number, and include verification of the signature.
6. First read p 284-285 about the protocol failure of re-using the random key k. Do problem 7.1 on page 311
7. Optional problem: 5.18, page 223