3. Now we are going to use the rule \(f(M) = M^e\) (mod \(p\)), where both \(e\) and \(p\) are public. We use \(e = 7\) and \(p = 143\).

  1. If you were given an enciphered (exponentiated) message, what would you need to find to undo the exponentiation?

  2. Is this different than what you did in problem 2? If so, how? If not, why not?

  3. What are the benefits of using the product of two large primes for \(p\)?