Cryptographic hash functions find their application in the c

Cryptographic hash functions find their application in the construction of effi- cient digital signatures. Recall, a digital signature procedure prescribes that a hash value of a message is to be signed, instead of signing the message directly. Which property a hash function has to satisfy in order to be useful for the digital signature? Please explain.

Solution

h should destroy all homomorphic structures in the underlying public key cryptosystem h should be computed on the entire message h should be a one-way function so that messages are not disclosed by their signatures it should be computationally infeasible given a message and its hash value to compute another message with the same hash value should resist birthday attacks (finding any 2 messages with the same hash value, perhaps by iterating through minor permutations of 2 messages)