I had read definition of hash function on site .But I was confused that why it had two defines of H. It was "weakly collision-free" and "strongly collision-free". I think two defines have the same meaning.

Explain: A hash function H is said to be one-way if it is hard to invert, where ``hard to invert'' means that given a hash value h, it is computationally infeasible to find some input x such that H(x) = h. If, given a message x, it is computationally infeasible to find a message y not equal to x such that H(x) = H(y), then H is said to be a weakly collision-free hash function. A strongly collision-free hash function H is one for which it is computationally infeasible to find any two messages x and y such that H(x) = H(y).

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Hash-function: "weakly collision-free" and "strongly collision-free" ... it had two defines of H. It was "weakly collision-free" and "strongly collision... collision-free hash function. A strongly collision-free hash function H is one