Q$3.$ Cryptographic Hash Functions $(10$ Marks$)$

a$)$ Explain the three cryptographic properties required for a secure hash function Give a suitable

example for each property requirement.

b$)$ Derive the time complexity of the trivial attack algorithms with respect to each cryptographic

property for an ideal hash function. A hash function is said to be ideal if it possesses all the

three cryptographic properties. By trivial algorithm, we mean that the attack algorithm does not

make any assumption about the input hash function.

c$)$ Give the relationship between these cryptographic properties in terms of one implying other.

No need to give the reason.