Pseudorandom generators from regular one-way functions: New constructions with improved parameters

We revisit the problem of basing pseudorandom generators on regular one-way functions, and present the following constructions: For any known-regular one-way function (on n-bit inputs) that is known to be epsilon-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. For any unknown-regular one-way function with known epsilon-hardness, we give a new construction with seed length Theta(n) and 0(n/ log(l/epsilon)) calls. Here the number of calls is also optimal by matching the lower bounds of Holenstein and Sinha (2012) [6]. Both constructions require the knowledge about epsilon, 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 (O) over tilde (n) and (O) over tilde (n/ logn) calls, where (O) over tilde omits a factor that can be made arbitrarily close to constant (e.g. log log logn or even less). This improves the randomized iterate approach by Haitner et al. (2006) [4] which requires seed length O (n . log n) and O (n/logn) calls. (C) 2014 Elsevier B.V. All rights reserved.