Please correct me if I got it wrong.
I am trying to learn MinHash algorithm by implementing one. The hash function needs better to be min-wise independent instead of pairwise independent. I'm testing both to understand the different effects on the algorithm.
I read that pairwise independence or strong universality means that no pairs of different numbers in input set to be hashed into the same output value.
If I do output = (i + 1) % n then no pair of different numbers will be hashed into same value, yet I see a strong correlation of input and output. The output is not random.
Can I say this algorithm has strong universality? If yes, what is the property called, when a hash algorithm that can greatly randomize the input?
(Reviewer: please check comments!)