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I'm answering the questions I posed. While cygnusv answer was correct for the idea I presented, it was not helpful to me as I had already identified and solved that issue, but failed to present the correct algorithm in my question. I'm not saying cygnusv is wrong; the answers presented are very much correct and I gave a +1. However, there were more questions ...


(Q1) Assuming that you talk about the size of the secret key elements which equals the input size of the OWF when you talk about the "input", this should be at least as much as the output size. Consider a function $f: \{0,1\}^m \rightarrow \{0,1\}^n$.The thing to worry about when you choose $m < n$ is a brute force search for a preimage, which in this ...


Security is clearly broken if there is a polynomial-length period with non-negligible probability (where by this I mean if a random point falls in a cycle with a poly-length period with non-negligible probability). In order to find a preimage, just go forward until you get back to the starting point, keeping the previous value each time.

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