#### 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 e_{1}, e_{2} where
gcd(e_{1}, e_{2}) = 1. You publish *n* along
with e_{1}, e_{2}. Show that if an adversary has
*C*_{1} = M^{ e1} mod n and
*C*_{2} = M^{ e2} mod n,
then she can efficientlyrecover *M*. (Note: *M* is the same for
*C*_{1} and *C*_{2}.)