Abstract:
Ben-Or and Linial (1985) introduced the full information model for coin-tossing protocols involving n processors with unbounded computational power using a common bro...View moreMetadata
Abstract:
Ben-Or and Linial (1985) introduced the full information model for coin-tossing protocols involving
n
processors with unbounded computational power using a common broadcast channel for all their communications. For most adversarial settings, the characterization of the exact or asymptotically optimal protocols remains open. Furthermore, even for the settings where near-optimal asymptotic constructions are known, the exact constants or poly-logarithmic multiplicative factors involved are not entirely well-understood. This work studies
n
-processor coin-tossing protocols where every processor broadcasts an arbitrary-length message once. An adaptive Byzantine adversary, based on the messages broadcast so far, can corrupt
k=1
processor. A bias-
X
coin-tossing protocol outputs 1 with probability
X
; otherwise, it outputs 0 with probability (
1-X
). A coin-tossing protocol's insecurity is the maximum change in the output distribution (in the statistical distance) that a Byzantine adversary can cause. Our objective is to identify bias-
X
coin-tossing protocols achieving near-optimal minimum insecurity for every
X\in[0,1]
. Lichtenstein, Linial, and Saks (1989) studied bias-
X
coin-tossing protocols in this adversarial model where each party broadcasts an independent and uniformly random bit. They proved that the elegant “threshold coin-tossing protocols” are optimal for all
n
and
k
. Furthermore, Goldwasser, Kalai, and Park (2015), Kalai, Komargodski, and Raz (2018), and Haitner and Karidi-Heller (2020) prove that
k=\mathcal{O}(\sqrt{n} \cdot \mathsf{polylog}(n)
) corruptions suffice to fix the output of any bias-
X
coin-tossing protocol. These results encompass parties who send arbitrary-length messages, and each processor has multiple turns to reveal its entire message. We use an inductive approach to constructing coin-tossing protocols using a potential function as a proxy for measuring any bias-
X
coin-tossing protocol's susc...
Date of Conference: 12-20 July 2021
Date Added to IEEE Xplore: 01 September 2021
ISBN Information: