Under general complexity asumptions, which hold for example if the Discrete Logarithm Problem is hard, we construct (1) rZK proof-systems for NP: (2) constant-round resettable witness-indistinguishable proof-systems for NP; and (3) constant-round rZK arguments for NP in the public key model where verifiers have fixed, public keys associated with them.
In addition to shedding new light on what makes zero knowledge possible (by constructing ZK protocols that use randomness in a dramatically weaker way than before), rZK has great relevance to applications. Firstly, we show that rZK protocols are closed under parallel and concurrent execution and thus are guaranteed to be secure when implemented in fully asynchronous networks, even if an adversary schedules the arrival of every message sent. Secondly, rZK protocols enlarge the range of physical ways in which provers of a ZK protocols can be securely implemented, including devices which cannot reliably toss coins on line, nor keep state betweeen invocations. (For instance, because ordinary smart cards with secure hardware are resattable, they could not be used to implement securely the provers of classical ZK protocols, but can now be used to implement securely the provers of rZK protocols.)
Category / Keywords: Zero-Knowledge, Concurrent Zero-Knowledge, Public-Key Cryptography, Witness-Indistinguishable Proofs, Smart Cards, Identification Schemes, Commitment Schemes, Discrete Logarithm Problem. Publication Info: Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive. Date: received October 25th, 1999. Supercedes Theory of Cryptography Library Record 99-15. Revised, June 22nd, 2000. Contact author: oded at wisdom weizmann ac il Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation Short URL: ia.cr/1999/022 Discussion forum: Show discussion | Start new discussion