Survey maps lattice assumptions if the Dihedral Coset Problem falls
Original title: Beyond LWE: Post-Quantum Assumptions under a Counterfactual Break of the Dihedral Coset Problem
A refuted 2026 quantum-algorithm claim frames which assumptions would move and which deployed parameters would not.
The survey considers what a genuine quantum break of the Dihedral Coset Problem would imply for lattice and non-lattice assumptions. It separates noiseless, prescribed-failure and extrapolated solvers, compares more than thirty assumptions, and says a printed Wen and Zheng bound gives no certificate at the ML-KEM ring and modulus. Chen's withdrawn 2024 LWE algorithm, even with a proposed repair, would cover only a many-sample small-noise regime and no deployed parameter set. Classical structural attacks on Classic McEliece are summarized and left to a companion paper.
Unconfirmed: The motivating 2026 DCP algorithm is described as refuted, and Chen's 2024 LWE algorithm is withdrawn.
- Regev's rare-corruption observation covers some polynomial approximation factors.
- Tables split rigorous consequences, heuristics and unverified applications.
- The survey distinguishes breaking a proof assumption from attacking a scheme.
- Its checklist requires a complete efficient reduction before scenario planning.
From the original article
1 min read at arxiv.orgA refuted 2026 claim of an efficient quantum algorithm for the Dihedral Coset Problem (DCP) motivates this survey of the consequences of a genuine breakthrough. We distinguish a noiseless cyclic coset-state solver, a solver with a prescribed failure exponent, and an extrapolated-state solver.
By Ramses Fernandez · arxiv.org
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