3 (Hash Functions - 15 points) When it comes to coaching books, data integrity is always a concern for Ted and Coach Beard. In one of their resources, the following cyptographic hash function was proposed as a way to ensure spell integrity: (a) Given some plaintext spell (message), m=m1m2mn, first encrypt it using a substitution cipher with the following substitution table: Table 3. Substitution table used in Problem 2. (b) Next, convert the obtained ciphertext y=y1y2yn into a number using conversion table 1 . (c) Remove every element with an odd index from the obtained string of numbers, and add value 3 to each remaining elements in the string. (d) Then, add the remaining numbers, and subtract number 234 from the result. (e) Steps (c) and (d) can be described with the following formula: h(y)=(j=i+2n(yi+3))234,fori=0 (f) Finally, release a hash output h(y). Your tasks: (a) (10 points) Is the described hash function preimage resistant? Please explain your reasoning. (b) (5 points) Given some cryptographic hash function, if the set of possible hash outputs is limited to the set of cardinality 109, how many times would an attacker have to query that hash function before they can find two plaintext messages that are not the same, but hash into the same hash output? Please explain your