We give the first construction of extractable one-way functions assuming only standard hardness assumptions (e.g.,subexponential security of Decision Diffie-Hellman or Quadratic Residousity). Our functions are extractable against adversaries with bounded polynomial advice and unbounded polynomial running time. We then use these functions to construct the first 2-message zero-knowledge arguments and 3-message zero-knowledge arguments of knowledge, against the same class of adversarial verifiers, from essentially the same assumptions.
The construction uses ideas from [Barak, FOCS01] and [Barak, Lindell, and Vadhan, FOCS03], and rely on the recent breakthrough construction of privately verifiable $\P$-delegation schemes [Kalai, Raz, and Rothblum]. The extraction procedure uses the program evaluating $f$ in a non-black-box way, which we show to be necessary.Category / Keywords: foundations / Knowledge Extraction, Extractable Functions, Zero-Knowledge, Non-Black-Box Techniques Date: received 29 Jul 2013, last revised 2 Aug 2013 Contact author: nirbitan at tau ac il Available format(s): PDF | BibTeX Citation Note: revision includes \thanks. Version: 20130802:131151 (All versions of this report) Discussion forum: Show discussion | Start new discussion