An Amazon Web Services cryptographer has published a preliminary paper claiming a polynomial-time quantum algorithm for the Dihedral Coset Problem (DCP). If validated, this could theoretically enable efficient quantum solutions to certain lattice problems — specifically approximations of the Shortest Vector Problem and Learning With Errors — which underpin NIST-standardized post-quantum cryptography schemes. The algorithm removes a key dependency on a subset-sum oracle that blocked prior approaches and claims tolerance for faulty quantum samples up to roughly 1/log(n). However, the paper does not demonstrate a practical attack on any deployed cryptographic standard, does not estimate required quantum hardware resources, and has not yet undergone peer review. Researchers including Daniele Micciancio, Vinod Vaikuntanathan, and Thomas Vidick are expected to scrutinize the proof closely before any conclusions about real-world security can be drawn.
Table of contents
A Missing PieceDifficultyDesigned to Tolerate Faulty SamplesWhat’s in it for Post-Quantum Cryptography?Questions this post answers
What is the Dihedral Coset Problem and why does it matter for post-quantum cryptography?
The Dihedral Coset Problem (DCP) is a hidden subgroup problem where a quantum computer must recover a hidden quantity from quantum samples. It matters for post-quantum cryptography because earlier work by Oded Regev showed reductions from lattice problems — specifically the Shortest Vector Problem and Learning With Errors — to DCP, meaning an efficient DCP algorithm could yield efficient algorithms for those lattice problems that underpin most NIST-standardized post-quantum schemes. Security engineers tracking PQC migration risks follow developments like this on daily.dev before they reach standardization bodies.
Does the new Amazon quantum algorithm for DCP break NIST post-quantum cryptography standards like CRYSTALS-Kyber or CRYSTALS-Dilithium?
No, the paper does not break any deployed NIST post-quantum standard. It is a complexity-theoretic result claiming polynomial-time algorithms for certain approximations of lattice problems, not a key-recovery attack on specific schemes. The paper does not analyze any cryptographic standard, does not map approximation factors to practical parameters, and does not estimate the logical qubits or quantum gates needed to run the algorithm at cryptographically relevant sizes. Teams planning PQC migrations need to track whether theoretical advances like this eventually translate to practical threats — daily.dev surfaces that research as it develops.