Can’t the steps be reversed one by one to get back the original?
In: Mathematics
No. Its surprisingly easily to come up with mathematical steps that can’t be reversed, even if you know the step rules exactly! All you need is for *at least one step to lose information*. An example makes it easier to see.
Let’s use these rules to hash a sentence:
1. Take the first letter of each word in the sentence you’re hashing.
2. Assign A=1, B=2 etc.
3. Add the numbers.
**Sentence:** The quick brown fox jumps over the lazy dog.
**Hash:**
1. TQBFJOTLD
2. 20 17 2 6 10 15 20 12 4
3. 106
So the hash of that sentence is 106. Note that you’ll get 106 every time you apply those rules to that sentence, it’s not random. In fact, any sentence you pick will only generate one and only one hash, every time. But you still can’t reverse it back from 106 to the sentence, even if I tell you the complete set of rules!
You don’t even know how many words there are whose first letters add up to 106, so the search space is huge. And you could use those same hash rules to hash a whole book or program or whatever and then it would be impossible to even brute force with a supercomputer.
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