1. A professor posts the grades for a class using the last four digits of the student id number of each student. In a class of 250 students, what is the probability that at least two students have the same four digits

2. Let P be prime and let b be an integer which is not divisible by p. Let h(x) = b2*x (mod p). Explain why h(x) is not a good cryptographic hash function? (Hint: This can be accomplished by using Fermat's Little Theorem.)

1. Suppose a message M is divided into blocks of length 160 bits: {M1, M2, ..., Mk} Let h(x) = M1 M2...Mk. Check if the hash function f is:
   1. preimage resistant
   2. collision resistant