Can’t the steps be reversed one by one to get back the original?
In: Mathematics
Modulo arithmetic. You now how the hours on a clock can’t go past “23”, because they loop back to “0”? Same thing.
Let me multiply two numbers together, and I’ll show you the “remainder” or “modulus” (let’s say after dividing by 100, to make it really easy and so I’ll give you the last two digits). You have to guess the two original numbers that I thought of and multiplied together.
What were the original numbers:
81
Sure, it *COULD* be 9 x 9. But it could also be anything else that ends in 81, like 37 x 13 (481).
Now that’s just one very simple calculation but in fact it has basically an infinite number of possible solutions.
Modulo arithmetic (and Galois fields and other mathematical constructs that use the same kind of maths) means that one way is really easy, the other way is really hard. Combine it with prime numbers, factorisation and other tricks and – again – one way is really easy and the other way is impossibly difficult to get right.
And hence you have a lovely one-way function, like a hash (e.g. SHA256), or certain techniques used in encryption.
You’re baking a cake, and you can’t get the eggs back from it when you’re done.
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