# An entangling-probe attack on Shor's algorithm for factorization

## TL;DR

This paper explores a novel entangling-probe attack on Shor's quantum factorization algorithm, revealing vulnerabilities that could allow an attacker to steal solutions without detection and discussing potential countermeasures.

## Contribution

It introduces an entangling-probe attack method on Shor's algorithm and analyzes its effectiveness and detection strategies.

## Key findings

- Attacker can steal exact solutions using entangling probes.
- Legitimate users receive random answers under attack.
- The probability of error can be exploited by attackers.

## Abstract

We investigate how to attack Shor's quantum algorithm for factorization with an entangling probe. We show that an attacker can steal an exact solution of Shor's algorithm outside an institute where the quantum computer is installed if he replaces its initialized quantum register with entangled qubits, namely the entangling probe. He can apply arbitrary local operations to his own probe. Moreover, we assume that there is an unauthorized person who helps the attacker to commit a crime inside the institute. He tells garbage data obtained from measurements of the quantum register to the attacker secretly behind a legitimate user's back. If the attacker succeeds in cracking Shor's algorithm, the legitimate user obtains a random answer and does not notice the attacker's illegal acts. We discuss how to detect the attacker. Finally we estimate a probability that the quantum algorithm inevitably makes an error, of which the attacker can take advantage.