CSCI 3104 - Algorithms - Fall 2010

Problem Set #3

Due: 3pm, Sep 20th, 2010

1. Text problem 1.20. Do not use a computer; show your work.

2. What is the smallest 59-pseudoprime? Use a computer to search; include your source code.

3. Text problem 1.27.

4. Text problem 1.42.

5. Here is one way in which RSA can be misused: suppose you have n = pq for distinct large primes p and q, and distinct encryption exponents e1, e2 where gcd(e1, e2) = 1. You publish n along with e1, e2. Show that if an adversary has C1 = M e1 mod n and C2 = M e2 mod n, then she can efficientlyrecover M. (Note: M is the same for C1 and C2.)