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International Association for Cryptologic Research (IACR)
Abstract
We improve the fundamental security threshold of
eventual consensus Proof-of-Stake
(PoS) blockchain protocols under longest-chain rule,
reflecting for the first time the
positive effect of rounds with concurrent honest leaders. Current
analyses of these protocols
reduce consistency to the dynamics of an abstract, round-based block
creation process that is determined by three probabilities:
pAβ, the probability that a round has at least one adversarial leader;
phβ, the probability that a round has a single honest leader; and
pHβ, the probability that a round has multiple, but honest, leaders.
We present a
consistency analysis that achieves the optimal threshold phβ+pHβ>pAβ.
This is a first in the literature and can be applied
to both the simple synchronous setting and the setting with bounded
delays.
Moreover, we achieve the optimal consistency error eβΞ(k) where k is the confirmation time.
We also provide an efficient algorithm to explicitly calculate these error probabilities in the synchronous setting.
All existing consistency analyses either incur a penalty
for rounds with concurrent honest leaders,
or treat them neutrally.
Specifically, the consistency analyses in Ouroboros Praos (Eurocrypt 2018) and
Genesis (CCS 2018) assume that the probability of a uniquely honest
round exceeds that of the other two events combined
(i.e., phββpHβ>pAβ); the analyses in
Sleepy Consensus (Asiacrypt 2017) and Snow White (Fin. Crypto 2019)
assume that a uniquely honest round is more likely than an
adversarial round
(i.e., phβ>pAβ).
In addition,
previous analyses completely break down when uniquely honest rounds
become less frequent, i.e., phβ<pAβ.
These
thresholds determine the critical trade-off between the honest majority,
network delays, and consistency error.
Our new results can be directly applied to improve the
consistency guarantees of the existing protocols.
We complement these results with a consistency analysis in the setting
where uniquely honest slots are rare, even letting phβ=0, under
the added assumption that honest players adopt a consistent chain
selection rule
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