Question

7. Someone shows you the hash function that appears below and claims that it meets all of the criteria for a good hash function; however, you disagree. Briefly explain why you disagree.
Given that X = (X0, X1, X2, ..., X[n - 1]) where each Xi is a byte.

h(X) = (X0 + X1 + X2 + ... + X[n - 1]) mod 256

Answer 1

1. Collision resistance: A good hash function has to produce different output for similar strings (i.e, the characters are same but arrangement is different). The above hash function doesn't meet this condition. Suppose we have 123 and 321 both these will have the same hash function output if we use the above function

So the above function doesn't provide collision resistance

2. Second preimage resistance: Two different inputs should not produce the same hash output

Suppose we have a string whose sum of bits equals 256 and another string whose sum of bits is 512, both the strings will give a hash function output of 0

Hence the above hash function fails second preimage resistance also

So it's not a good hash function