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

TL;DR

This paper demonstrates a quantum attack on a small elliptic curve cryptographic key using a 133-qubit quantum computer, showcasing the potential for quantum algorithms to break cryptography.

Contribution

It presents the first implementation of a Shor-style quantum attack on a 5-bit elliptic curve key using a large-scale quantum computer, with detailed circuit design and analysis.

Findings

Successfully extracted the secret key k=7 from the quantum interference pattern.

Demonstrated the feasibility of executing deep quantum circuits for cryptographic attacks.

Provided open access to code, circuits, and data for replication and further research.

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.