On the Complexity of Non-adaptively Increasing the Stretch of Pseudorandom Generators
- Cite this paper as:
- Miles E., Viola E. (2011) On the Complexity of Non-adaptively Increasing the Stretch of Pseudorandom Generators. In: Ishai Y. (eds) Theory of Cryptography. TCC 2011. Lecture Notes in Computer Science, vol 6597. Springer, Berlin, Heidelberg
We study the complexity of black-box constructions of linear-stretch pseudorandom generators starting from a 1-bit stretch oracle generator G. We show that there is no construction which makes non-adaptive queries to G and then just outputs bits of the answers. The result extends to constructions that both work in the non-uniform setting and are only black-box in the primitive G (not the proof of correctness), in the sense that any such construction implies NP/poly \(\ne\) P/poly. We then argue that not much more can be obtained using our techniques: via a modification of an argument of Reingold, Trevisan, and Vadhan (TCC ’04), we prove in the non-uniform setting that there is a construction which only treats the primitive G as black-box, has polynomial stretch, makes non-adaptive queries to the oracle G, and outputs an affine function (i.e., parity or its complement) of the oracle query answers.