Pigeonhole principle: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pigeonhole_principle" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Pigeonhole_principle</a><p>I think you&#x27;ve correctly picked up on the difference between &quot;uniquely&quot; and &quot;infeasable&quot;.<p>It&#x27;s not possible to use a hash function to give every possible input a unique reference.  But a cryptographic hash function aims to make the inputs to &quot;hash collisions&quot; be very different.  So, for real world files the hash is unique, because the file that would produce a hash collision would be malformed and useless.<p>In general when you hash a message you don&#x27;t want an attacker to make subtle changes and get the same hash.<p>&quot;Here is my electronic payment for £100&quot; should never have the same hash as &quot;Here is my electronic payment for £10,000. Nice to meet you on the weekend&quot;.