<p>It is known that (worst-case) one-way permutations exist if and only if $P\ne UP \cap coUP$. Almost all candidates that I know are based on hard number theortic problems. I came across a combinatorial construction of <a href="https://eprint.iacr.org/2005/352.pdf" rel="nofollow">one-way permutations based on quasigroup string transformations</a>.</p>

<blockquote>
  <p>What other combinatorial candidates for one-way permutations are known?</p>
</blockquote>

CC BY-SA 3.0
2016-09-22T19:20:58.170Z
@RickyDemer No, just basic worst-case one-way permutation would be fine.
Mohammad Al-Turkistany
CC BY-SA 3.0
2016-09-23T05:34:20.657Z
Relevant: eprint 2015/752: http://eprint.iacr.org/2015/752
D.W.
CC BY-SA 3.0
2016-09-25T07:14:03.277Z
@RickyDemer Yes. To understand how to convert worst-case hardness into average-case hardness.
Mohammad Al-Turkistany
<cc.complexity-theory><permutations>
Candidates for combinatorial one-way permutation
Mohammad Al-Turkistany
# Candidates for combinatorial one-way permutation

(Asked by: username_0 on 2016-09-22)

It is known that (worst-case) one-way permutations exist if and only if $P\ne UP \cap coUP$. Almost all candidates that I know are based on hard number theortic problems. I came across a combinatorial construction of [one-way permutations based on quasigroup string transformations](https://eprint.iacr.org/2005/352.pdf).

> What other combinatorial candidates for one-way permutations are known?

**Tags:** cc.complexity-theory, permutations

> **Comments:**
> **username_0**: @RickyDemer No, just basic worst-case one-way permutation would be fine.  
> **username_1**: Relevant: eprint 2015/752: http://eprint.iacr.org/2015/752  
> **username_0**: @RickyDemer Yes. To understand how to convert worst-case hardness into average-case hardness.  

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## 0 answers

