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How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates
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abstract
We use Shor's algorithm for the computation of elliptic curve private keys as a case study for resource estimates in the silicon-photonics-inspired active-volume architecture. Here, a fault-tolerant surface-code quantum computer consists of modules with a logarithmic number of non-local inter-module connections, modifying the algorithmic cost function compared to 2D-local architectures. We find that the non-local connections reduce the cost per key by a factor of 300-700 depending on the operating regime. At 10% threshold, assuming a 10-$\mu$s code cycle and non-local connections, one key can be generated every 10 minutes using 6000 modules with 1152 physical qubits each. By contrast, a device with strict 2D-local connectivity requires more qubits and produces one key every 38 hours. We also find simple architecture-independent algorithmic modifications that reduce the Toffoli count per key by up to a factor of 5. These modifications involve reusing the stored state for multiple keys and spreading the cost of the modular division operation over multiple parallel instances of the algorithm.
Forward citations
Cited by 4 Pith papers
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A distillation-teleportation protocol for fault-tolerant QRAM
An adaptive distillation-teleportation protocol implements a fault-tolerant QRAM query with poly(n) quantum resources and 1/poly(n) device fidelity, at the cost of an exponential classical dataset update each round.
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CaliScalpel: In-Situ and Fine-Grained Qubit Calibration Integrated with Surface Code Quantum Error Correction
CaliScalpel uses surface-code deformation to isolate drifted qubits for calibration while computation continues, with a new instruction set for heavy-hexagon hardware and drift-aware scheduling.
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Strategic Plan for Neutral Atom Quantum Computation
If qubit-count growth (~1.8x/yr) and gate-error reduction (~0.62x/yr) continue, neutral-atom quantum computers could reach practical quantum advantage within a decade, this roadmap projects.
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