Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation

Mihir Bellare; Igors Stepanovs; Stefano Tessaro

Paper 2013/873

Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation

Mihir Bellare, Igors Stepanovs, and Stefano Tessaro

Abstract

We show how to extract an arbitrary polynomial number of simultaneously hardcore bits from any one-way function. In the case the one-way function is injective or has polynomially-bounded pre-image size, we assume the existence of indistinguishability obfuscation (iO). In the general case, we assume the existence of differing-input obfuscation (diO), but of a form weaker than full auxiliary-input diO. Our construction for injective one-way functions extends to extract hardcore bits on multiple, correlated inputs, yielding new D-PKE schemes. Of independent interest is a definitional framework for differing-inputs obfuscation in which security is parameterized by circuit-sampler classes.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: A minor revision of an IACR publication in ASIACRYPT 2014
Keywords: Hardcore predicates indistinguishability obfuscation one-way functions.
Contact author(s): mihir @ eng ucsd edu
History: 2014-09-15: last of 4 revisions; 2013-12-29: received; See all versions
Short URL: https://ia.cr/2013/873
License: CC BY

BibTeX

@misc{cryptoeprint:2013/873,
      author = {Mihir Bellare and Igors Stepanovs and Stefano Tessaro},
      title = {Poly-Many Hardcore Bits for Any One-Way Function and a Framework for Differing-Inputs Obfuscation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/873},
      year = {2013},
      url = {https://eprint.iacr.org/2013/873}
}