(a) (10 points) Derive a general mathematical expression to find the probability of 2 people having colliding birthday in a room of n people under following assumptions: 1. Assuming a non leap year (hence 365 days). 2. Assuming that a person has an equally likely chance of being born on any day of the year. (b) (10 points) Suppose f(z) is a function with n-bit outputs and with inputs much larger than n bits (this implies that collisions must exist). We know that, with a birthday attack, we have probability 1/2 of finding a collision in approximately 2/2 steps. Suppose we repeat the birthday attack until we find a collision. Calculate the expected number of repetitions. (a) (10 points) Derive a general mathematical expression to find the probability of 2 people having colliding birthday in a room of n people under following assumptions: 1. Assuming a non leap year (hence 365 days). 2. Assuming that a person has an equally likely chance of being born on any day of the year. (b) (10 points) Suppose f(z) is a function with n-bit outputs and with inputs much larger than n bits (this implies that collisions must exist). We know that, with a birthday attack, we have probability 1/2 of finding a collision in approximately 2/2 steps. Suppose we repeat the birthday attack until we find a collision. Calculate the expected number of repetitions.