Breaking a 5-Bit Elliptic Curve Key using a 133-Qubit Quantum Computer

Abstract

This experiment breaks a 5-bit elliptic curve cryptographic key using a Shor-style quantum attack. Executed on IBM's 133-qubit ibm_torino with Qiskit Runtime 2.0, a 15-qubit circuit, comprised of 10 logical qubits and 5 ancilla, interferes over an order-32 elliptic curve subgroup to extract the secret scalar k from the public key relation Q = kP, without ever encoding k directly into the oracle. From 16,384 shots, the quantum interference reveals a diagonal ridge in the 32 x 32 QFT outcome space. The quantum circuit, over 67,000 layers deep, produced valid interference patterns despite extreme circuit depth, and classical post-processing revealed k = 7 in the top 100 invertible (a, b) results. All code, circuits, and raw data are publicly available for replication.