Post-Quantum Cryptography from Quantum Stabilizer Decoding

2026-03-19

AI Summary

This work addresses the overreliance of post-quantum cryptography on a limited set of hardness assumptions, which introduces single-point failure risks. We propose the random quantum stabilizer code decoding problem as a novel post-quantum hardness assumption that is inherently quantum yet classically expressible. Building upon this assumption, we construct a public-key encryption scheme and a round-optimal oblivious transfer protocol. A key technical contribution is a new obfuscation technique tailored for linear subspaces with symplectic structure, enabling a tight security reduction. The resulting schemes achieve efficiency comparable to the best-known LPN-based constructions, and we provide evidence that our assumption is independent of the Learning Parity with Noise (LPN) assumption. This work thus establishes a new theoretical foundation and offers practical cryptographic primitives for post-quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes -- a quantum analog of the well-studied LPN problem -- is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practical: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE, and our OT is round-optimal. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suit of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions.

Problem

• Post-Quantum Cryptography
• Quantum Stabilizer Decoding
• Hardness Assumptions
• LPN
• Cryptographic Primitives

Innovation

• quantum stabilizer decoding
• post-quantum cryptography
• LPN hardness
• symplectic algebraic structure
• scrambling techniques