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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.

Zero-knowledge proofs. --- Data encryption (Computer science) --- Cryptography. --- Computer science. --- Computer programming. --- Data structures (Computer science). --- Computers. --- Computer Science. --- Programming Techniques. --- Data Structures, Cryptology and Information Theory. --- Theory of Computation. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Informatics --- Science --- Programming --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Proofs, Zero-knowledge --- Protocols, Zero-knowledge --- Zero-knowledge protocols --- Data structures (Computer scienc. --- Information theory. --- Data Structures and Information Theory. --- Data structures (Computer science) --- Communication theory --- Communication