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Our technical document presents revised calculations regarding quantum computational elements (specifically qubits and operational gates) required to solve the 256-bit elliptic curve discrete logarithm challenge underlying current cryptographic systems. We quantify these requirements through logical qubit counts (error-corrected quantum units comprising numerous physical qubits) and Toffoli gate operations (computationally intensive quantum procedures that predominantly determine algorithm execution duration). We have engineered two quantum processing sequences implementing Shor's cryptographic-breaking methodology: one configuration utilizing under 1,200 logical qubits with 90 million gate operations, and an alternative employing fewer than 1,450 logical qubits with 70 million gate operations. Our analysis indicates these circuits could operate on superconducting quantum systems with under 500,000 physical qubits within minutes, based on hardware performance parameters consistent with Google's advanced quantum processing units. This represents an 80% reduction in physical qubit requirements for elliptic curve decryption, continuing the persistent refinement of quantum algorithm translation into fault-tolerant circuits.
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max_memory: u64,
Jacques-Henri Jourdan, Université Paris-Saclay