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The Bitcoin Backbone Protocol: Analysis and Applications, by Juan Garay and Aggelos Kiayias and Nikos Leonardos

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Bitcoin is the first and most popular decentralized cryptocurrency to date. In this work, we extract and analyze the core of the Bitcoin protocol, which we term the Bitcoin {\em backbone}, and prove two of its fundamental properties which we call {\em common prefix} and {\em chain quality}. Our proofs hinge on appropriate and novel assumptions on the ``hashing power'' of the adversary relative to network synchronicity; our results are shown to be tight under high synchronization. Next, we propose and analyze applications that can be built ``on top'' of the backbone protocol, specifically focusing on Byzantine agreement (BA) and on the notion of a public transaction ledger. Regarding BA, we observe that Nakamoto's suggestion falls short of solving it, and present a simple alternative which works assuming that the adversary's hashing power is bounded by $1/3$. The public transaction ledger captures the essence of Bitcoin's operation as a cryptocurrency, in the sense that it guarantees the ``liveness'' and ``persistence'' of committed transactions. Based on this notion we describe and analyze the Bitcoin system as well as a more elaborate BA protocol, proving them secure assuming high network synchronicity and that the adversary's hashing power is strictly less than $1/2$, while the adversarial bound needed for security decreases as the network desynchronizes.

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