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Constant-Round Concurrent Zero Knowledge in the Bounded Player Model
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Vipul Goyal, Abhishek Jain, Rafail Ostrovsky, Silas Richelson, Ivan Visconti
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In[18] Goyal et al. introduced bounded player model for secure computation. In the bounded player model, there are an 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 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 results relies on a new technique where the simulator obtains a trapdoor corresponding to a player identity by putting together on formation 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 in the plain model, without relaxations.

**comment:**
ASIACRYPT (1) 2013: 21-40

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