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[–] captbrogers ago  (edited ago)

Yes, cryptography is just math. Very advanced math, but it is math. If you forget to carry a number when adding two numbers of giant fractions, how much can it affect the outcome of the equation?

That's just a math equation with two variables and one operation, now imagine a very complex formula with dozens of variables doing multiple operations. If one number is off at all, how much can it affect the outcome? That is the reason it has to check the entire string (or file, whatever the case may be). If it didn't check the entire string, something could be changed somewhere and then it would defeat the purpose of using it to check integrity. When checking that two things match, it doesn't help much to only partially check thing.