  In this work, we consider the long-standing open question of constructing
constant-round concurrent zero-knowledge protocols in the plain model.
Resolving this question is known to require non-black-box techniques.
  We consider non-black-box techniques for zero-knowledge based on knowledge
assumptions, a line of thinking initiated by the work of Hada and Tanaka
(CRYPTO 1998). Prior to our work, it was not known whether knowledge
assumptions could be used for achieving security in the concurrent setting, due
to a number of significant limitations that we discuss here. Nevertheless, we
obtain the following results:
  1. We obtain the first constant round concurrent zero-knowledge argument for
\textbf{NP} in the plain model based on a new variant of knowledge of exponent
assumption. Furthermore, our construction avoids the inefficiency inherent in
previous non-black-box techniques such that those of Barak (FOCS 2001); we
obtain our result through an efficient protocol compiler.
  2. Unlike Hada and Tanaka, we do not require a knowledge assumption to argue
the soundness of our protocol. Instead, we use a discrete log like assumption,
which we call Diffie-Hellman Logarithm Assumption, to prove the soundness of
our protocol.
  3. We give evidence that our new variant of knowledge of exponent assumption
is in fact plausible. In particular, we show that our assumption holds in the
generic group model.
  4. Knowledge assumptions are especially delicate assumptions whose
plausibility may be hard to gauge. We give a novel framework to express
knowledge assumptions in a more flexible way, which may allow for formulation
of plausible assumptions and exploration of their impact and application in
cryptography.
