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The traditional setting for concurrent zero knowledge considers a server that proves a statement in zero-knowledge to multiple clients in multiple concurrent sessions, where the server’s actions in a session are independent of all other sessions. Persiano and Visconti [ICALP 05] show how keeping a limited amount of global state across sessions allows the server to significantly reduce the overall complexity while retaining the ability to interact concurrently with an unbounded number of clients. Specifically, they show a protocol that has only slightly super-constant number of rounds; however the communication complexity in each session of their protocol depends on the number of other sessions and has no a-priori bound. This has the drawback that the client has no way to know in advance the amount of resources required for completing a session of the protocol up to the moment where the session is completed.

Client-Server Concurrent Zero Knowledge with Constant Rounds and Guaranteed Complexity