[optimiz3]

Collisions are when two different inputs hash to the same value, which breaks the security of the hash function.

If a hash function is cryptographically secure, it has the property where finding collisions is infeasable, which makes it suitable for evaluating equality.

This is why cryptographic hash functions are used as a proxy for passwords in order to avoid storing the plaintext.

[machinelearning]

"Collisions are when two different inputs hash to the same value, which breaks the security of the hash function" This is so wrong. Cryptographically secure hash functions merely claim that the probability of a collision is low. By your definition, it is impossible to find a secure hash function that works on an arbitrary input size.

"If a hash function is cryptographically secure, it has the property where finding collisions is infeasable, which makes it suitable for evaluating equality." This is so wrong.

It has a high probability of evaluating equality but in no way is it suitable. The primary benefit that cryptographic hash functions offer is that it is impractical to conduct a chosen plaintext attack.

"This is why cryptographic hash functions are used as a proxy for passwords in order to avoid storing the plaintext."

This is true, and is due to preimage resistance and the infeasibility of a chosen plaintext attack.