One-way functions with respect to various resource bounds Informally, one-way functions are defined with respect to PTIME algorithms. They are computable in polynomial time but not invertible in average-case polynomial time. The existence of such functions is an important open problem in theoretical computer science.

I'm interested in one-way functions (not necessarily for cryptographic applications) defined with respect to different resource bounds. Such resource bounds could be LOGSPACE or bounded nondeterminism. 


  Is there a candidate (natural) problem which is one-way with respect to LOGSPACE algorithms? Is there a candidate (natural) problem which is one-way with respect to nondeterministic linear time algorithms ($\text{NTIME(n)}$)?


I'm fine with worst-case hardness of invertiblity with respect to the above resource bounds.
Regarding log-space:  Several candidate one-way functions are computable in log-space or below (and are supposedly secure even against poly-time adversaries).  You can find several pointers for example in the Cryptography in NC$^0$ paper.

Two specific examples include:

Integer multiplication (there are some subtleties for standard OWF, but if you only care about worst-case this is enough)

The Impagliazzo-Naor candidate based on subset-sum:
$f(a_1,...,a_n,S) := (a_1,..., a_n, \sum_{i \in S} a_i \mod 2^n)$.