Communication security is extremely important in computer networks, and one way many network protocols achieve security is to encrypt messages. Typical cryptographic schemes for the secure transmission of messages over such networks are based on the fact that no efficient algorithms are known for factoring large integers. Hence, if we can represent a secret message by a large prime number p, we can transmit over the network the number r = p q, where q > p is another large prime number that acts as the encryption key. An eavesdropper who obtains the transmitted number r on the network would have to factor r in order to figure out the secret message p. Using factoring to figure out a message is very difficult without knowing the encryption key q. To understand why, consider the following naive factoring algorithm: For every integer p such that 1 < p < r, check whether p divides r. If so, print The secret message is p! and stop; if not, continue. a. Suppose that the eavesdropper uses the above algorithm and has a computer that can carry out in 1 microsecond (1 millionth of a second) a division between two integers of up to 100 bits each. Give an estimate of the time that it will take in the worst case to decipher the secret message if r has 100 bits. b. What is the worst-case time complexity of the above algorithm? Since the input to the algorithm is just one large number r, assume that the input size n is the number of bytes needed to store r, that is, n = (log2 r)/8, and that each division takes time O(n).