Paper 2013/468
How To Construct Extractable One-Way Functions Against Uniform Adversaries
Nir Bitansky and Ran Canetti and Omer Paneth
Abstract
A function $f$ is extractable if it is possible to algorithmically ``extract,'' from any program that outputs a value $y$ in the image of $f,$ a preimage of $y$. When combined with hardness properties such as one-wayness or collision-resistance, extractability has proven to be a powerful tool. However, so far, extractability has not been explicitly shown. Instead, it has only been considered as a non-standard {\em knowledge assumption} on certain functions. 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.
Note: revision includes \thanks.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Knowledge ExtractionExtractable FunctionsZero-KnowledgeNon-Black-Box Techniques
- Contact author(s)
- nirbitan @ tau ac il
- History
- 2014-06-02: last of 3 revisions
- 2013-08-02: received
- See all versions
- Short URL
- https://ia.cr/2013/468
- License
-
CC BY