Georgia Tech's Jo and Lee Cut the Quantum Elliptic Curve Attack to 5n/2 Logical Qubits and Near-Quadratic Toffoli Gates, IACR ePrint 2026/2014, 14 September 2026
Sunghyeon Jo and Gye Jin Lee of Georgia Tech and QED Audit posted an IACR ePrint on September 14, 2026 that solves the elliptic curve discrete logarithm problem with 5n/2 + o(n) logical qubits and near-quadratic Toffoli gates, lowering both the width and the gate bound of the July construction by Luo and colleagues. We read how an invariant of the extended Euclidean algorithm lets the circuit keep three of four values and rebuild the fourth, why the widely quoted 640 logical qubits for P-256 is a leading term and not a circuit size, and what this offensive quantum cryptanalysis result changes for ECDH and ECDSA still fielded across defense systems.
Circle's August 31 Disclosure Reads 813 Logical Qubits Off Eigen Labs' ECDSA.fail Leaderboard: What a Google and Stanford Estimate Says a secp256k1 Attack Actually Costs
Circle's August 31 disclosure tells developers that breaking elliptic curve signatures now takes 813 logical qubits, a figure lifted from one axis of Eigen Labs' ECDSA.fail circuit competition. We put it back beside the March 2026 Google, Stanford, and Ethereum Foundation estimate, under 1,200 logical qubits and 90 million Toffoli gates on fewer than half a million physical qubits, and beside Willow's actual 105 physical qubits, to show how a defense buyer should read quantum cryptanalysis headlines while setting a post-quantum migration schedule.