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A '''one-way permutation''' is a one-way function that is also a permutation—that is, a one-way function that is [[Bijection|bijective]]. One-way permutations are an important [[cryptographic primitive]], and it is not known if their existence is implied by the existence of one-way functions.
A [[Trapdoor function|trapdoor one-way function]] or trapdoor permutation is a special kind of one-way function. Such a function is hard to invert unless some secret information, called the ''trapdoor'', is known.
A '''collision-free hash function''' ''f'' is a one-way function that is also ''collision-resistant''; that is, no [[randomized polynomial time]] algorithm can find a [[hash collision|collision]]—distinct values ''x'', ''y'' such that ''f''(''x'') = ''f''(''y'')—with non-negligible probability.<ref>{{cite journal |last=Russell |first=A. |title=Necessary and Sufficient Conditions for Collision-Free Hashing |journal=[[Journal of Cryptology]] |volume=8 |issue=2 |pages=87–99 |year=1995 |doi=10.1007/BF00190757 |s2cid=26046704 }}</ref>
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