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44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03)
Lower Bounds for Non-Black-Box Zero Knowledge
Cambridge, Massachusettes
October 11-October 14
ISBN: 0-7695-2040-5
ASCII Text
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Boaz Barak, Yehuda Lindell, Salil Vadhan, "Lower Bounds for Non-Black-Box Zero Knowledge," Foundations of Computer Science, IEEE Annual Symposium on, pp. 384, 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), 2003.
 
 
BibTex
x
 
@article{ 10.1109/SFCS.2003.1238212,
author = {Boaz Barak and Yehuda Lindell and Salil Vadhan},
title = {Lower Bounds for Non-Black-Box Zero Knowledge},
journal ={Foundations of Computer Science, IEEE Annual Symposium on},
volume = {0},
year = {2003},
issn = {0272-5428},
pages = {384},
doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2003.1238212},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - CONF
JO - Foundations of Computer Science, IEEE Annual Symposium on
TI - Lower Bounds for Non-Black-Box Zero Knowledge
SN - 0272-5428
SP
EP
A1 - Boaz Barak,
A1 - Yehuda Lindell,
A1 - Salil Vadhan,
PY - 2003
KW - null
VL - 0
JA - Foundations of Computer Science, IEEE Annual Symposium on
ER -
 
Boaz Barak, Weizmann Institute of Science
Yehuda Lindell, IBM T.J. Watson Research
Salil Vadhan, Harvard University

We show new lower bounds and impossibility results for general (possibly non-black-box) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions:

  • 1. There does not exist a constant-round zero-knowledge strong proof (or argument) of knowledge (as defined by Goldreich (2001)) for a nontrivial language.
  • 2. There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP-complete language.
    The previous impossibility result for two-round zero knowledge, by Goldreich and Oren (J. Cryptology, 1994) was only for the case of auxiliary-input zero-knowledge proofs and arguments.
  • 3. There does not exist a constant-round public-coin proof system for a nontrivial language that is resettable zero knowledge. This result also extends to bounded resettable zero knowledge.
    In contrast, we show that under reasonable assumptions, there does exist such a (computationally sound) argument system that is bounded-resettable zero knowledge.

    • The complexity assumptions we use are not commonly used in cryptography. However, in all cases, we show that assumptions like ours are necessary for the above results.

    Most previously known lower bounds, such as those of Goldreich and Krawczyk (SIAM J. Computing, 1996), were only for black-box zero knowledge. However, a result of Barak (FOCS 2001) shows that many (or even most) of these black-box lower bounds do not extend to the case of general zero knowledge.

    Citation:
    Boaz Barak, Yehuda Lindell, Salil Vadhan, "Lower Bounds for Non-Black-Box Zero Knowledge," focs, pp.384, 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), 2003
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