The paper "The Bitcoin Backbone Protocol: Analysis and Applications" by Juan Garay, Aggelos Kiayias, and Nikos Leonardos focuses on the core of the Bitcoin protocol, termed the Bitcoin *backbone*. The authors analyze two fundamental properties of the backbone: the *common prefix* and the *chain quality* in a static setting with a fixed number of players. They prove that these properties hold under certain assumptions about the adversary's hashing power relative to network synchronicity. The paper then proposes and analyzes applications built on top of the backbone protocol, specifically focusing on Byzantine agreement (BA) and the concept of a public transaction ledger. For BA, the authors show that Nakamoto's proposal falls short of solving the problem, presenting an alternative solution that works assuming the adversary's hashing power is bounded by 1/3. For the public transaction ledger, they demonstrate how the backbone protocol can be used to ensure the liveness and persistence of committed transactions, provided there is an honest majority and high network synchronicity. The authors also discuss related work, including previous proposals for decentralized currencies and Byzantine agreement protocols, and provide a detailed model and definitions for the analysis. They conclude by presenting two simple Byzantine agreement protocols based on the backbone protocol and a robust public ledger application.The paper "The Bitcoin Backbone Protocol: Analysis and Applications" by Juan Garay, Aggelos Kiayias, and Nikos Leonardos focuses on the core of the Bitcoin protocol, termed the Bitcoin *backbone*. The authors analyze two fundamental properties of the backbone: the *common prefix* and the *chain quality* in a static setting with a fixed number of players. They prove that these properties hold under certain assumptions about the adversary's hashing power relative to network synchronicity. The paper then proposes and analyzes applications built on top of the backbone protocol, specifically focusing on Byzantine agreement (BA) and the concept of a public transaction ledger. For BA, the authors show that Nakamoto's proposal falls short of solving the problem, presenting an alternative solution that works assuming the adversary's hashing power is bounded by 1/3. For the public transaction ledger, they demonstrate how the backbone protocol can be used to ensure the liveness and persistence of committed transactions, provided there is an honest majority and high network synchronicity. The authors also discuss related work, including previous proposals for decentralized currencies and Byzantine agreement protocols, and provide a detailed model and definitions for the analysis. They conclude by presenting two simple Byzantine agreement protocols based on the backbone protocol and a robust public ledger application.