Construction:UOWHF from OWP

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A universal one-way hash function can be constructed by composing any one-way permutation with any universal hash function.

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Construction

Let \mathcal{U}_n = \{ U_k \}_{k \in \{0,1\}^n} be a universal hash function family, and let f be a one-way permutation. Then the following family is a universal one-way hash function family:

\mathcal{H}_n = \{ H_k = U_k \circ f \}_{k \in \{0,1\}^n}, where "\circ" denotes function composition.
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