Shor’s Algorithm Breaks 5-bit Elliptic Curve Key on 133-Qubit Quantum Computer

> Researchers successfully demonstrated a quantum attack on elliptic curve cryptography by breaking a 5-bit key using a modified Shor’s algorithm on IBM’s 133-qubit quantum processor. Despite the extreme complexity of the quantum circuit (over 67,000 layers deep), the system maintained sufficient quantum coherence to produce valid interference patterns. Classical post-processing of the quantum results correctly identified the secret key (k=7) within the top 100 candidate solutions.

> A key innovation lies in the method’s ability to **extract the secret key without directly encoding it into the quantum circuit, enhancing security against certain attacks.** The approach focuses on interfering over a specific subgroup of the elliptic curve, allowing researchers to reveal key information through quantum measurement, which manifests as a distinct pattern in the quantum data. The methodology begins by mapping the points of the elliptic curve to integers, simplifying calculations while preserving the necessary mathematical relationships.

> Quantum registers then represent parameters of the equation, including the exponent and a point index, initialised in a superposition of states using carefully timed pulses. A specifically constructed quantum oracle performs a reversible transformation, linking these registers through a function related to the secret key, designed to avoid directly referencing the key itself. A Quantum Fourier Transform is then applied, transforming the data into a frequency domain where the interference pattern becomes more apparent, revealing the modular phase relation and **ultimately the secret key.**

> Classical post-processing analyses the measurement results, identifying the most likely key candidates based on the observed interference pattern.

> The experiment validates that Shor’s algorithm remains effective even with very deep quantum circuits, suggesting potential scalability for attacking **larger cryptographic keys**. The approach used **modular arithmetic techniques to encode the problem without directly referencing the secret key**, and visualization of the results confirmed the expected quantum interference patterns.