Security of cryptographic hash functions: Difference between revisions

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The meaning of "hard": the "difficulty" of a problem depends on its size - give a practical example
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The second approach is theoretical and is based on the [[computational complexity theory]]. If problem A is hard, there exists a formal [[Reduction (complexity)|security reduction]] from a problem which is widely considered unsolvable in [[polynomial time]], such as [[integer factorization]] problem or [[discrete logarithm]] problem.
 
However, non-existence of a polynomial time algorithm does not automatically ensure that the system is secure. ItThe isdifficulty equallyof importanta toproblem choosealso thedepends parameterson sensiblyits (e.gsize. aFor lengthexample, of[[RSA thepublic numberskey thatcryptography]] relies on the systemdifficulty worksof with)[[integer factorization]]. For instanceHowever, factoring 21it is easyconsidered althoughsecure inonly generalwith [[integerkeys factorization]]that isare consideredat aleast hard1024 problembits large.
 
==Classical hash functions - practical approach to security==