If we know the algorithm used for current day password hashing, how can we not just undo it to get the password?

Question

I have read that SHA-2 is currently unbroken due to the amount of resources and time it would take to crack the hashing, but if we have the step by step algorithm, why can we not just do the steps backwards?

In: Technology

Answer 1

Think of sudoku. What is easier? To solve a puzzle, or to check if a solution is correct?

Sudoku and this hashing alghorithm have something in common: They are NP problems.

What are NP problems? In computation we have sort problems by how complex they are to solve. For example: Ordering a list of names is less complex than evaluating the best move in a game of chess. There’s a set of problems that can “easily” be verified, but we have no idea if there’s a solution that isn’t “more complex” than checking if a solution is true, those are the NP problems (also one of the biggest questions of math. It is known as “NP = P?”)

>why can we not just do the steps backwards?

We don’t know if we can’t. But in the case we can, we don’t know how to do it.