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In this work, we consider the long-standing open question of constructingconstant-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 knowledgeassumptions, a line of thinking initiated by the work of Hada and Tanaka(CRYPTO 1998). Prior to our work, it was not known whether knowledgeassumptions could be used for achieving security in the concurrent setting, dueto a number of significant limitations that we discuss here. Nevertheless, weobtain 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 exponentassumption. Furthermore, our construction avoids the inefficiency inherent inprevious non-black-box techniques such that those of Barak (FOCS 2001); weobtain our result through an efficient protocol compiler.  2. Unlike Hada and Tanaka, we do not require a knowledge assumption to arguethe soundness of our protocol. Instead, we use a discrete log like assumption,which we call Diffie-Hellman Logarithm Assumption, to prove the soundness ofour protocol.  3. We give evidence that our new variant of knowledge of exponent assumptionis in fact plausible. In particular, we show that our assumption holds in thegeneric group model.  4. Knowledge assumptions are especially delicate assumptions whoseplausibility may be hard to gauge. We give a novel framework to expressknowledge assumptions in a more flexible way, which may allow for formulationof plausible assumptions and exploration of their impact and application incryptography.

On Constant-Round Concurrent Zero-Knowledge from a Knowledge Assumption