Digital signatures and DES algorithm

Question

Consider the following two statements:
i. A hash function (these are often used for computing digital signatures) is an injective function.
ii. encryption technique such as DES performs a permutation on the elements of its input alphabet.
Which one of the following options is valid for the above two statements?

	(A) Both are false
	(B) Statement (i) is true and the other is false
	(C) Statement (ii) is true and the other is false
	(D) Both are true

Comments

message1-(HASH FUNCTION)-message digest1

for a single message a hash function gives a single digest

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There is nothing like Perfect hash function exist that is injective in network world.Why?
Because We always map messages to a small set of domain Choose any encryption method you are bounded to a Finite Codomain where not at that time but at some point of time in future other message will map to same key

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yes you are right @saxena0612 but  here for digital signature you cannot use

Answer 1

strong collision resistance ensure that we can not find two message that hash to same digest so it is one to one (injective)

and  second is also correct