New SelectCopy architecture and qubit-constrained optimizations reduce QROM Toffoli cost from ~2N/λ to ~(1 + 1/b)N/λ while preserving the ability to trade dirty qubits for lower gate count.
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2026 2representative citing papers
Resource estimates show Shor's algorithm can break 256-bit ECDLP with fewer than 1450 logical qubits and 90 million Toffoli gates on fast-clock quantum hardware, enabling on-spend attacks on cryptocurrency mempools.
citing papers explorer
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Halving the cost of QROM
New SelectCopy architecture and qubit-constrained optimizations reduce QROM Toffoli cost from ~2N/λ to ~(1 + 1/b)N/λ while preserving the ability to trade dirty qubits for lower gate count.
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Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
Resource estimates show Shor's algorithm can break 256-bit ECDLP with fewer than 1450 logical qubits and 90 million Toffoli gates on fast-clock quantum hardware, enabling on-spend attacks on cryptocurrency mempools.