In Goyal et al. introduced the bounded player model for secure computation. In the bounded player model, there are an a priori bounded number of players in the system, however, each player may execute any unbounded (polynomial) number of sessions. They showed that even though the model consists of a relatively mild relaxation of the standard model, it allows for round-efficient concurrent zero knowledge. Their protocol requires a super-constant number of rounds. In this work we show, constructively, that there exists a constant-round concurrent zero-knowledge argument in the bounded player model. Our result relies on a new technique where the simulator obtains a trapdoor corresponding to a player identity by putting together information obtained in multiple sessions. Our protocol is only based on the existence of a collision-resistance hash-function family and comes with a "straight-line" simulator. We note that this constitutes the strongest result known on constant-round concurrent zero knowledge in the plain model (under well accepted relaxations) and subsumes Barak's constant-round bounded concurrent zero-knowledge result. We view this as a positive step towards getting constant round fully concurrent zero-knowledge in the plain model, without relaxations.
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