$[50$ pts$]$ Problem $1($book $5\mathrm{.}1)$:

a$)$ In some resources, a cryptographic hash function must

satisfy three primary security properties as below to be

considered secure:

b$)$ Preimage Resistance

c$)$ Second Preimage Resistance

d$)$ Collision Resistance

Provide a definition for each of these requirements and

explain why each of these properties are important.