Abstract
The fast probabilistic consensus (FPC) is a leaderless voting consensus protocol that allows a set of nodes to agree on a value of a single bit. FPC is robust and efficient in Byzantine infrastructures and presents a low communicational complexity. In this paper, we introduce a modification of the Fast Probabilistic Consensus protocol (FPC) capable of achieving consensus on a maximal independent set of a graph —hence named Fast Probabilistic Consensus on a Set (FPCS)— that still preserves the robustness, effectiveness, and low communicational complexity of FPC.
This paper shows that FPCS effectively resolves the problem (with high probability) of achieving consensus on a maximal independent set of a graph of conflicts (i.e. a maximal set of nonconflicting transactions) in the particular case of n-spend conflicts, even when a significant (up to 1/3) proportion of nodes is malicious. These nodes intend to delay the consensus or even completely break it (meaning that nodes would arrive at different conclusions about the maximal independent set). Furthermore, the paper provides explicit estimates on the probability that the protocol finalizes in the consensus state in a given time.
Our study refers to a specific implementation of cryptocurrencies, but the results hold for more general majority models.
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Notes
- 1.
and, preferably, maximal — we explain the meaning of that later.
- 2.
For the sake of better presentation we will always assume that qN and \((1-q)N\) are integers.
- 3.
Remember we want our protocol to be resistant to the largest q possible.
- 4.
We assume that this maximum is unique, otherwise we could choose the one with largest hash.
- 5.
Rigorously, that \(v_1=\textrm{argmin}_{u \in \mathbb {T}}\mathop {\textrm{hash}}(\text {Id}_u, X_t)\).
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Nitchai, R.C., Popov, S., Müller, S. (2023). FPCS: Solving n-Spends on a UTXO-Based DLT. In: Machado, J.M., et al. Blockchain and Applications, 5th International Congress. BLOCKCHAIN 2023. Lecture Notes in Networks and Systems, vol 778. Springer, Cham. https://doi.org/10.1007/978-3-031-45155-3_44
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