Paper 2026/1986

Two-Anchor Holdout/Hermite: Solving the TII-254 McEliece Key Recovery Challenge

Abstract

We report on the solution to the TII-254 McEliece key recovery challenge -- currently the hardest solved challenge under the original brute-force metric ($2^{254}$). The parameters of TII-254 are $(m,t,n) = (8,12,223)$, defining a binary $[223,127]$ code specified by a full-rank $(96 \times 223)$ parity-check matrix. We state the method as a thirteen-step process, separating heuristic and non-heuristic choices. At a high level, we computed two complete $121$-dimensional relation kernels conditioned at distinct public coordinates, combined them to isolate a certified $80$-dimensional pair core, removed a $64$-dimensional common nuisance space, and identified the remaining $16$ dimensions as an $\mathbb{F}_{2^8}$ projective-line geometry. This yielded all $87$ visible locators, after which a deterministic completion search recovered the full support and polynomial. The two final Krylov sequences alone used $27.2$ GPU-hours on NVIDIA GH200s, excluding GPU reconstruction and CPU processing. We provide a self-contained artifact with compact recovery inputs and code, an independent key verifier, and Lean proofs of the reusable linear-algebraic steps.

Note: A solution and source code artifact is available: https://github.com/mjosaarinen/tii254-artifact