Hardware-Verified Shor-Based ECDLP Key Recovery from 4-Bit to 18-Bit on IBM Quantum Systems

We report hardware-verified ECDLP private key recovery up to 18 bits (n = 130,579) — the largest on record — extending prior public demonstrations at 6-bit (Tippeconnic, September 2025) on IBM ibm_torino. Using Shor-based period finding on IBM Quantum superconducting processors, we present 14 successful hardware runs spanning subgroup orders from n = 7 to n = 130,579. Every recovered private key was classically verified by confirming d·G = Q on the curve y² = x³ + 7. The central technical contribution is a carry-ripple (CDKM) modular arithmetic oracle that achieves near-unity routing overhead on IBM's heavy-hex qubit topology, enabling hardware execution at circuit depths exceeding 300,000 layers on 77-qubit circuits. A fifteenth hardware run (8-bit, QFT-based oracle) produced no recoveries and is reported for completeness. All IBM job IDs are provided for independent audit.