Alon Rosen 
Concurrent Zero-Knowledge 
With Additional Background by Oded Goldreich

Zero-knowledge proofs are fascinating and extremely useful constructs. Their fascinating nature is due to their seemingly contradictory de?nition; ze- knowledge proofs are convincing and yet yield nothing beyond the validity of the assertion being proved. Their applicability in the domain of cryptography is vast; they are typically used to force malicious parties to behave according to a predetermined protocol. In addition to their direct applicability in cr- tography, zero-knowledge proofs serve as a good benchmark for the study of variousproblemsregardingcryptographicprotocols(e.g., “securecomposition of protocols”). A fundamental question regarding zero-knowledge protocols refers to the preservation of security (i.e., of the zero-knowledge feature) when many – stances are executed concurrently, and in particular under a purely as- chronous model. The practical importance of this question, in the days of extensive Internet communication, seems clear. It turned out that this qu- tion is also very interesting from a theoretical point of view. In particular, this question served as a benchmark for the study of the security of concurrent executions of protocols and led to the development of techniques for coping with the problems that arise in that setting.

Table of Content

A Brief Introduction to Zero-Knowledge (by Oded Goldreich).- to Concurrent Zero-Knowledge.- Preliminaries.- c Proof Systems for .- c in Logarithmically Many Rounds.- A Simple Lower Bound.- Black-Box c Requires Logarithmically Many Rounds.- Conclusions and Open Problems.- A Brief Account of Other Developments (by Oded Goldreich).