1: Bob believes that he has come up with a nifty hash function. He assigns a numeric value V_Char to each letter in the alphabet equal to the letter's position in the alphabet, i.e., V_A = 1, V_B = 2, ..., V_Z = 26. For a message, he calculates the hash value H = (V_{Char 1} x V_{Char 2} x V_{Char 3 ...}x V_{Char N}) mod(26).

Bob uses this function to send a one-word message, GLARE, to his banker Bill, along with his calculated hash value for the message. Alice is able to intercept the message, and generates an alternative message that has a hash value that collides with Bob's original hash value.

Give definition and properties of the hash function.

Show a message that Alice may have used to spoof Bob's message, and demonstrate that its hash value collides with Bob's original hash.

Q2: Consider the following plaintext message: THE SIXTEENTH PRESIDENT WAS ABRAHAM LINCOLN.

1. If this message is sent unencrypted and successfully received, what is its entropy? And why?
2. If this message is encrypted with DES using a random 56-bit key, what is the encrypted message's entropy? And why