Hash Function Tutorial Introduction

Hash Function TutorialA hash function (in the unrestricted sense) is a function h which has, as a minmum, the following two properties:
compression -h maps an input x of arbitrary finite bitlength, to an output h(x) of fixed bitlength n.
ease of computation – given h and an input x, h(x) is easy to compute.

Relationships between properties h Collision resistance implies 2nd-preimage resistance of hash functions Justification: Suppose h has collision resistance. Fix an input xj . If h does not have 2nd-preimage resistance, then it is feasible to find a distinct input xi such that h(xi) = h(xj), in which case (xi, xj) is a pair of distinct inputs hashing to the same output, contradiction collision resistance.

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