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.