Lower Bounds for Non-Black-Box Zero Knowledge
Boaz Barak, Yehuda Lindell and Salil Vadhan
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
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.
There does not exist a constant-round zero-knowledge
strong proof (or argument) of knowledge (as defined by
Goldreich (2001)) for a nontrivial language.
There does not exist a two-round zero-knowledge
proof system with perfect completeness for an
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.
- 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.
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.
Postscript, gzipped Postscript.