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It is well-known that one-way permutations (and even one-to-one one-way functions) imply the existence of non-interactive commitments. Furthermore the construction is black-box (i.e., the underlying one-way function is used as an oracle to implement the commitment scheme, and an adversary attacking the commitment scheme is used as an oracle in the proof of security). The authors rule out the possibility of black-box constructions of non-interactive commitments from general (possibly not one-to-one) one-way functions. As far as they know, this is the first result showing a natural cryptographic task that can be achieved in a black-box way from one-way permutations but not from one-way functions.
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