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We apply our methods to the logical resources required to break the 256 elliptic curve encryption, which is used to secure public keys in the Bitcoin network. We use the logical resource requirements of the latest algorithmic developments, which improve on the previous state of the art by ~2 orders of magnitude. There is a small window of time, approximately 10–60 min, in which the public keys are available and vulnerable after the initiation of a transaction. We quantify the number of physical qubits required to break the encryption in one hour as a function of code cycle time and the base physical error rate. It would require approximately 317 × 106 physical qubits to break the encryption within one hour using the surface code and a code cycle time of 1 μs, a reaction time of 10 μs, and physical gate error of 10-3. To instead break the encryption within one day, it would require only 13 × 106 physical qubits. If the base physical error rate was instead the more optimistic value of 10-4, 33 × 106 physical qubits would be required to break the encryption in 1 h. This large physical qubit requirement implies that the Bitcoin network will be secure from quantum computing attacks for many years (potentially over a decade).
https://avs.scitation.org/doi/10.1116/5.0073075 
