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# Post-Quantum Security of the Bitcoin Backbone and Quantum Multi-Solution Bernoulli Search

March/2021, ArXiv e-print

BITCOINBLOCKCHAINQUANTUM

Bitcoin and its underlying blockchain protocol have recently received significant attention in the context of building distributed systems and foundations of the consensus problem. At the same time, the rapid development in quantum computing makes the threats to cryptography more and more concerning. In this work, we revisit the formal security of the core of the Bitcoin consensus protocol, called the Bitcoin backbone (Eurocrypt 2015), in the presence of quantum adversaries -- i.e. adversaries equipped with quantum computers.

We show that the security of the Bitcoin backbone holds under a quantum analogue of the "honest majority" assumption that we develop. The critical ingredient of proving security of the blockchain is to analyze the quantum query complexity of a Chain-of-Proofs-of-Work search problem. This problem in turn reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. This can be viewed as an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the powerful recording technique due to Zhandry (Crypto 2019).

Our analysis indicates that the security of the Bitcoin backbone protocol is guaranteed provided that the number of adversarial quantum queries is bounded so that each quantum query is worth O(p^{−1/2}) classical ones, where p is the probability of success of a single classical query to the protocol's underlying hash function. Perhaps surprisingly, the wait time for safe settlement of transactions in the case of quantum adversaries matches (up to a constant) the safe settlement time in the classical case and thus does not result in any further overhead.