Round-Optimal, Fully Secure Distributed Key Generation

Protocols for distributed (threshold) key generation (DKG) in the discrete-logarithm setting have received a tremendous amount of attention in the past few years. Several synchronous DKG protocols have been proposed, but most such protocols are not fully secure: they either allow corrupted parties to bias the key, or are not robust and allow malicious parties to prevent successful generation of a key. We explore the round complexity of fully secure DKG in the honest-majority setting where it is feasible. We show the impossibility of one-round, statistically unbiased DKG protocols (even if not robust), regardless of any prior setup. On the positive side, we show various round-optimal protocols for fully secure DKG offering tradeoffs in terms of their efficiency, necessary setup, and required assumptions.