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From a cryptographic sense, what value is added from setting the domain to be the image in the mapping?

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  • $\begingroup$ Welcome to Cryptography.SE! $\endgroup$
    – e-sushi
    Dec 19 '17 at 9:07
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A one-way permutation (OWP) is more structured than a one-way function, and hence a stronger object. This makes the task of constructing higher cryptographic objects from OWPs easier and also, at times, leads to more efficient constructions. For example, consider pseudo-random generators (PRGs): it is quite straightforward to construct a PRG from a OWP; but constructing a PRG from a OWF took a lot more effort -- you can read more here.

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    $\begingroup$ Yes. But for small domain ( e.g $\{0,1\}^{256}$ ), a public OWP is much harder to construct than a public OWF. If one has such OWP, I want to know ! Thus I asked. $\endgroup$
    – fgrieu
    Dec 19 '17 at 13:56
  • $\begingroup$ That's an interesting question! $\endgroup$
    – ckamath
    Dec 19 '17 at 15:04

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