Towards quantum machine learning for assessing the resilience of post-quantum cryptography

As post-quantum cryptography (PQC) becomes increasingly standardized and deployed, it is critical to evaluate whether emerging quantum technologies could be used to identify vulnerabilities in these new protocols. This paper investigates whether Quantum Generative Adversarial Networks (QGANs)—a hybrid quantum-classical machine learning architecture—can effectively learn the probability distributions of data generated by post-quantum cryptographic schemes.

The author employs a hybrid QGAN framework where a quantum circuit acts as the generator and a classical neural network acts as the discriminator. The generator is tasked with learning the probability distribution of four-bit word samples derived from SPHINCS+ hash-based digital signatures. The study tests three different quantum circuit topologies (ansatze): N-local, real-amplitudes, and hardware-efficient circuits. The performance of these models is evaluated by measuring the Kullback-Leibler (KL) divergence between the learned distribution and the original signature data.

The results confirm that QGANs are capable of learning the underlying probability distributions of post-quantum signature data. Among the tested architectures, the hardware-efficient ansatz provided the most accurate approximation, likely due to its higher number of trainable parameters. Interestingly, the real-amplitudes ansatz performed better than the N-local ansatz despite having fewer parameters, suggesting that the ability to probe the space of quantum states is not the sole determinant of learning performance. The study concludes that these hybrid methods provide a viable initial step for future quantum-assisted cryptanalysis.

This research bridges the gap between quantum machine learning and cybersecurity. By demonstrating that quantum computers can model the statistical properties of post-quantum primitives, the paper highlights a potential pathway for future adversaries to optimize attacks, such as reducing the search space for key recovery or identifying non-random patterns in cryptographic outputs. It serves as a foundational step for assessing the long-term resilience of PQC standards against near-term quantum devices.

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