**Pseudorandom Generators from Regular One-way Functions: New Constructions with Improved Parameters**

*Yu Yu*

**Abstract: **We revisit the problem of basing pseudorandom generators on regular one-way functions, and present the following constructions:

(1) For any known-regular one-way function (on $n$-bit inputs) that is known to be $\eps$-hard to invert, we give a neat (and tighter) proof for the folklore construction of pseudorandom generator of seed length $\Theta(n)$ by making a single call to the underlying one-way function.

(2) For any unknown-regular one-way function with known $\eps$-hardness, we give a new construction with seed length $\Theta(n)$ and $O(n/\log{(1/\eps)})$ calls. Here the number of calls is also optimal by matching the lower bounds of Holenstein and Sinha [FOCS 2012].

Both constructions require the knowledge about $\eps$, but the dependency can be removed while keeping nearly the same parameters. In the latter case, we get a construction of pseudo-random generator from any unknown-regular one-way function using seed length $\tilde{O}(n)$ and $\tilde{O}(n/\log{n})$ calls, where $\tilde{O}$ omits a factor that can be made arbitrarily close to constant (e.g. $\log\log\log{n}$ or even less). This improves the \emph{randomized iterate} approach by Haitner, Harnik and Reingold [CRYPTO 2006] which requires seed length $O(n{\log}{n})$ and $O(n/\log{n})$ calls.

**Category / Keywords: **foundations / one-way functions, pseudorandom generators, randomized iterate

**Date: **received 13 May 2013, last revised 19 May 2013

**Contact author: **yuyuathk at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20130519:154316 (All versions of this report)

**Short URL: **ia.cr/2013/270

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