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Is there any example of a Hash function that is collision-resistant but may not be puzzle-friendly, similarly example of a hash function that is puzzle-friendly but not collision-resistant?

Puzzle friendliness: A hash function $H$ is said to be puzzle‐friendly if for every possible $n$‐bit output value $y$, if $k$ is chosen from a distribution with high min‐entropy, then it is infeasible to find $x$ such that $H(k|| x) = y$ in time significantly less than $2^n$ ($k$ and $y$ is given).

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  • $\begingroup$ I am thinking of an example in which a Hash function is collision-resistant but not puzzle-friendly, and another example in which function is puzzle-friendly but not collision-resistant. $\endgroup$ – mohit nihalani Mar 3 at 20:37
  • $\begingroup$ Puzzle friendliness. A hash function H is said to be puzzle‐friendly if for every possible n‐bit output value y, if k is chosen from a distribution with high min‐entropy, then it is infeasible to find x such that H(k ‖ x) = y in time significantly less than 2^n. $\endgroup$ – mohit nihalani Mar 3 at 20:43
  • $\begingroup$ I don't see the relation with collision. This is rather finding a suffix to attack. $\endgroup$ – kelalaka Mar 3 at 20:49
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    $\begingroup$ stackoverflow.com/questions/42042840/… It seems to be something from the cryptocurrency community, rather than a common cryptographic definition. $\endgroup$ – SAI Peregrinus Mar 3 at 20:50
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    $\begingroup$ Consider $SHAx(k||x) = SHA256(k||x) || k||x$ collision resistant but no puzzle-friendly and no pre-image resistance. $\endgroup$ – kelalaka Mar 3 at 21:14

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