Theory of Cryptography Conference

TCC 2011: Theory of Cryptography pp 522-539

On the Complexity of Non-adaptively Increasing the Stretch of Pseudorandom Generators

  • Eric Miles
  • Emanuele Viola
Conference paper

DOI: 10.1007/978-3-642-19571-6_31

Volume 6597 of the book series Lecture Notes in Computer Science (LNCS)
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

Abstract

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.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Eric Miles
    • 1
  • Emanuele Viola
    • 1
  1. 1.Northeastern UniversityUSA