Nakamoto consensus (NC) powers major proof-of-work (PoW) and proof-of-stake (PoS) blockchains such as Bitcoin or Cardano. Given a network of nodes with certain communication and computation capacities, against what fraction of adversarial power (the resilience) is Nakamoto consensus secure for a given block production rate? Prior security analyses of NC used a bounded delay model which does not capture network congestion resulting from high block production rates, bursty release of adversarial blocks, and in PoS, spamming due to equivocations. For PoW, we find a new attack, called teasing attack, that exploits congestion to increase the time taken to download and verify blocks, thereby succeeding at lower adversarial power than the private attack which was deemed to be the worst-case attack in prior analysis. By adopting a bounded bandwidth model to capture congestion, and through an improved analysis method, we identify the resilience of PoW NC for a given block production rate. In PoS, we augment our attack with equivocations to further increase congestion, making the vanilla PoS NC protocol insecure against any adversarial power except at very low block production rates. To counter equivocation spamming in PoS, we present a new NC-style protocol Sanitizing PoS (SaPoS) which achieves the same resilience as PoW NC.

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