Why can’t sha256 be reversed easily?

Question

Can’t the steps be reversed one by one to get back the original?

In: Mathematics

Answer 1

There are other operations that are very hard to reverse. Like a sum of many numbers into one. If I add N numbers (with N > 1) and the result is 18429491, how can you say which numbers were used to derive that result? They can be whatever…

Also, there’s the [Pigeonhole Principle](https://en.wikipedia.org/wiki/Pigeonhole_principle)…

In sha256, there are only 256 bits of information, but you can hash any number of bits into those 256 bits. So there must be multiple sources that produce the same hash (even though it’s pretty much impossible to find a collision).