Hash functions and digital signatures

Question 1

Hash functions must possess collision resistance property in order to be used in cryptography. Collision resistance can be weak and strong.

a) Explain the difference between the weak and the strong collision resistance. How are the weak and the strong collision resistances related?
b) Explain how we use hash functions in the procedure for signing the messages digitally

Question 2

Hash functions must possess three basic properties in order to be used in cryptography. They are often constructed in an iterative way.

a) Enumerate and explain the three basic properties of cryptographic hash functions.
b) Explain the Merkle-Damgård iterative construction of cryptographic hash functions.

Question 3

a) Explain the collision resistance property of hash functions.
b) What is the relation between the second pre-image property and the collision resistance property of hash functions?

Question 4

Explain the Merkle-Damgård construction method for hash functions.

Question 5

Explain the sponge construction method for hash functions.