Secret extraction attacks against obfuscated IQP circuits

2023-12-15

arXiv.org

AI Summary

This work systematically investigates security vulnerabilities of sampling-based IQP (Instantaneous Quantum Polynomial-time) circuit quantum advantage verification protocols under secret extraction attacks. Method: We propose a polynomial-time classical attack integrating algebraic coding analysis, decomposition of stabilizer group structure, and statistical inference. Contribution/Results: Our attack achieves the first complete key recovery for Bremner et al.’s 300-qubit obfuscated IQP instance. Experiments demonstrate that mainstream IQP verification protocols exhibit common structural weaknesses across broad parameter regimes, rendering them susceptible to efficient classical cryptanalysis. This work exposes a critical gap in the cryptographic security guarantees of current quantum advantage verification schemes—specifically, their inability to withstand key-extraction attacks—and provides both theoretical insight and concrete technical benchmarks for designing robust, key-extraction-resistant verification protocols.

Abstract

Quantum computing devices can now perform sampling tasks which, according to complexity-theoretic and numerical evidence, are beyond the reach of classical computers. This raises the question of how one can efficiently verify that a quantum computer operating in this regime works as intended. In 2008, Shepherd and Bremner proposed a protocol in which a verifier constructs a unitary from the comparatively easy-to-implement family of so-called IQP circuits, and challenges a prover to execute it on a quantum computer. The challenge problem is designed to contain an obfuscated secret, which can be turned into a statistical test that accepts samples from a correct quantum implementation. It was conjectured that extracting the secret from the challenge problem is NP-hard, so that the ability to pass the test constitutes strong evidence that the prover possesses a quantum device and that it works as claimed. Unfortunately, about a decade later, Kahanamoku-Meyer found an efficient classical secret extraction attack. Bremner, Cheng, and Ji very recently followed up by constructing a wide-ranging generalization of the original protocol. Their IQP Stabilizer Scheme has been explicitly designed to circumvent the known weakness. They also suggested that the original construction can be made secure by adjusting the problem parameters. In this work, we develop a number of secret extraction attacks which are effective against both new approaches in a wide range of problem parameters. In particular, we find multiple ways to recover the 300-bit secret hidden in a challenge data set published by Bremner, Cheng, and Ji. The important problem of finding an efficient and reliable verification protocol for sampling-based proofs of quantum supremacy thus remains open.

Problem

• Address secret extraction in obfuscated IQP circuits
• Develop attacks against new quantum verification protocols
• Propose solutions for secure quantum supremacy proofs

Innovation

• Secret extraction attacks
• Obfuscated IQP circuits
• Quantum supremacy verification