A key performance metric in blockchains is the latency between when a transaction is broadcast and when it is confirmed (the socalled, confirmation latency). While improvements in consensus techniques can lead to lower confirmation latency, a fundamental lower bound on confirmation latency is the propagation latency of messages through the underlying peer-to-peer (p2p) network (in Bitcoin, the propagation latency is several tens of seconds). The de facto p2p protocol used by Bitcoin and other blockchains is based on random connectivity: each node connects to a random subset of nodes. The induced p2p network topology can be highly suboptimal since it neglects geographical distance, differences in bandwidth, hash-power and computational abilities across peers. We present Perigee, a decentralized algorithm that automatically learns an efficient p2p topology tuned to the aforementioned network heterogeneities, purely based on peers' interactions with their neighbors. Motivated by the literature on the multi-armed bandit problem, Perigee optimally balances the tradeoff between retaining connections to known well-connected neighbors, and exploring new connections to previously-unseen neighbors. Experimental evaluations show that Perigee reduces the latency to broadcast by 33%. Lastly Perigee is simple, computationally lightweight, adversary-resistant, and compatible with the selfish interests of peers, making it an attractive p2p protocol for blockchains.

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An important feature of Proof-of-Work (PoW) blockchains is full dynamic availability, allowing miners to go online and offline while requiring only 50% of the online miners to be honest. Existing Proofof-stake (PoS), Proof-of-Space and related protocols are able to achieve this property only partially, either putting the additional assumption that adversary nodes to be online from the beginning and no new adversary nodes come online afterwards, or use additional trust assumptions for newly joining nodes. We propose a new PoS protocol PoSAT which can provably achieve dynamic availability fully without any additional assumptions. The protocol is based on the longest chain and uses a Verifiable Delay Function for the block proposal lottery to provide an arrow of time. The security analysis of the protocol draws on the recently proposed technique of Nakamoto blocks as well as the theory of branching random walks. An additional feature of PoSAT is the complete unpredictability of who will get to propose a block next, even by the winner itself. This unpredictability is at the same level of PoW protocols, and is stronger than that of existing PoS protocols using Verifiable Random Functions.