text: Most popular blockchain solutions, like Bitcoin, rely on proof-of-work, guaranteeing that the output of the consensus is agreed upon with high probability. However, this probability depends on the delivery of messages and that the computational power of the system is sufficiently scattered among pools of nodes in the network so that no pool can mine more blocks faster than the crowd. New approaches, like Ethereum, generalise the proof-of-work approach by letting individuals deploy their own private blockchain with high transaction throughput. As companies are starting to deploy private chains, it has become crucial to better understand the guarantees blockchains offer in such a small and controlled environment. In this paper, we present the , an execution that we experienced when building our private chain at NICTA Data61. Even though this anomaly has never been acknowledged before, it may translate into dramatic consequences for the user of blockchains. Named after the infamous Paxos anomaly, this anomaly makes dependent transactions, like "Bob sends money to Carole after he received money from Alice" impossible. This anomaly relies on the fact that existing blockchains do not ensure consensus safety deterministically: there is no way for Bob to make sure that Alice actually sent him coins without Bob using an external mechanism, like converting these coins into a fiat currency that allows him to withdraw. We also explore smart contracts as a potential alternative to transactions in order to freeze coins, and show implementations of smart contract that can suffer from the Blockchain anomaly and others that may cope with it.
  @cite_20: Bitcoin cryptocurrency demonstrated the utility of global consensus across thousands of nodes, changing the world of digital transactions forever. In the early days of Bitcoin, the performance of its probabilistic proof-of-work (PoW) based consensus fabric, also known as blockchain, was not a major issue. Bitcoin became a success story, despite its consensus latencies on the order of an hour and the theoretical peak throughput of only up to 7 transactions per second.
summary: Another part of this research @cite_20 discusses the probabilistic guarantees of proof-of-work systems and the deterministic guarantees of Byzantine fault tolerance. The proof-of-work consensus is compared to Byzantine agreement protocols along two axes, scalability and performance, where proof-of-work consensus protocols are considered as scalable but inefficient while Byzantine agreement protocols are considered as efficient but not scalable. For example, Bitcoin scales beyond 1000 nodes while achieving a performance lower than 100 transactions per second with a high latency, whereas standard Byzantine fault tolerant protocols achieve more than 10,000 transactions per second but scale only to tens of nodes.