Let&#x27;s remember the context of this discussion. We are talking about hash functions in cryptographic protocols. No one is proposing that you use a hash function to test the equality of two values when you&#x27;re not constrained to the parameters of some cryptographic problem. E.g. when the two values you want to check are known.<p>&gt; <i>&quot;Granted collisions may not occur frequently, but a collision could occur at any time.&quot;</i><p>Your reasoning sounds something like this: &quot;The risk of a collision is greater than zero, therefore you should worry about collisions.&quot;<p>Which is like saying: &quot;The risk of being hit by a meteorite is greater than zero, therefore you should worry about meteorites.&quot;<p>The problem with such reasoning is that it ignores probability.<p>&gt; <i>&quot;Just because the chance of it happening is small, does not mean you will have to try 1 quadrillion per second for 10 quadrillion years before a collision occurs.&quot;</i><p>You&#x27;re right! It means that you would have to try 1 quadrillion per second for 10 quadrillion years before having <i>a 50% chance of hitting a collision.</i><p>If you don&#x27;t like that 50% number, then let&#x27;s use 10^(-15); a probability of 1 in 1 quadrillion. According to the birthday problem [0], and using the same collision resistance (2^128) and hash rate (1 quadrillion per second) from my previous example, you would have to work for 475 million years before having a 10^(-15) probability of hitting a collision.<p>Accidental collisions simply are not a realistic problem to worry about. I don&#x27;t believe that any such collisions are known to have ever occurred in the wild with modern crypto hash functions.<p>Denying collision resistance renders hash functions almost useless, even for protocols where pre-image resistance is the key property. Think about that. Even if you were confident that a hash input wasn&#x27;t crafted to conduct a pre-image attack, but you were concerned about collisions, then you should mistrust the hash result simply because it may have been an accidental collision.<p>I&#x27;m sorry you disagree with my reason for downvoting your initial comment. But I did so (or tried to) because (1) I feel it was not a correct answer to the question, and (2) it contained misinformation by implying that the likelihood of collisions is much greater than it actually is.<p>[0] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Birthday_attack#Mathematics" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Birthday_attack#Mathematics</a> - Look at the table. My numbers were taken directly from the 256-bit row.