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When we say a function is one-way we typically mean a function is encodable in $P$ but its decryption is not in $P$ but in $UP$.

Likewise we say a function is logspace one-way if the function is encodable $L$ but its decryption is not in $L$ but still in $UL$ ($L$ vs $UL$ has not been settled yet). Since decryption is possible in $UL$ we rule out usual candidates such as factoring, lattice based schemes etc.

Are there any such candidate functions?

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