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Hash functions are a many-to-one reduction of the input down to some 'word' within a limited space (e.g. 256 bits). Of course this is naturally not reversible in the sense of being able to recover the original input, since infinitely many possible inputs could have resulted in that hash, known as 'collisions'. This is not a case of information being recovered in a number of bits too small to have contained it (even compressed), because the purpose of the hash is verification, i.e. hash the second input and compare the hashes.
Of course a match could be a collision with a malicious input, but with a chance of only 1 in 2256 chance for a 256-bit hash. We say a hash algorithm is 'cryptographically secure' if there is no fast algorithm for producing such a collision, i.e. it could be done only by random guessing. If we take e.g. 1 million guesses per second, that would take up to 3669.3 trillion trillion trillion trillion trillion years.
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[–] SithEmpire 0 points 4 points 4 points (+4|-0) ago
Hash functions are a many-to-one reduction of the input down to some 'word' within a limited space (e.g. 256 bits). Of course this is naturally not reversible in the sense of being able to recover the original input, since infinitely many possible inputs could have resulted in that hash, known as 'collisions'. This is not a case of information being recovered in a number of bits too small to have contained it (even compressed), because the purpose of the hash is verification, i.e. hash the second input and compare the hashes.
Of course a match could be a collision with a malicious input, but with a chance of only 1 in 2256 chance for a 256-bit hash. We say a hash algorithm is 'cryptographically secure' if there is no fast algorithm for producing such a collision, i.e. it could be done only by random guessing. If we take e.g. 1 million guesses per second, that would take up to 3669.3 trillion trillion trillion trillion trillion years.