AI & ML
Structural cryptanalysis of classic McEliece: Assessment of claims, costs and evidence
arXiv cs.CR0 views
arXiv:2610.31196v1 Announce Type: new Abstract: For the last two years, classical structural attacks on McEliece with binary Goppa codes progressed further, at the parameters of Classic McEliece, than in the previous four decades: a subexponential and then a quasi-polynomial distinguisher, key recoveries for public challenges with brute-force labels up to $254$, and conditional key-recovery estimates of about $2^{89}$ to $2^{128}$ per run of a large sparse linear-algebra computation, depending on the parameter set and on whether and how memory access is charged. On September 2026 the German BSI advised against new deployments of the scheme. This paper gives a version-aware critical assessment of these results. It separates proved distinguishers, conditional cost estimates and actual recoveries; analyses in detail Saarinen's HOVER algorithm, his conditional cost analysis and his recovery of the TII-254 challenge, together with Weis's cost study of Holdout/Hermite key recovery; and compares the other key-recovery routes and the objections raised against them. Our own analysis finds that the cost model is now the main quantitative uncertainty, with about thirty bits between the cheapest and the most expensive model for the same computation; that for the four larger parameter sets every model considered leaves the conditional estimates far below the targeted levels, whereas for mceliece348864 the shortfall is of the order of the spread between models; that the structural estimates are lower than Grover-accelerated information-set decoding for the four larger sets in essentially every model and comparable for mceliece348864; and that none of this is a demonstrated attack, since the underlying heuristics have been tested only on instances tens of thousands to hundreds of thousands of times smaller than the target. We close with open questions.
Source:https://arxiv.org/abs/2610.31196PreviousBelT Block CipherNextWeaponizing the Exit: Input Privacy Leakage via Exit Routing Manipulation in Multi-Exit Networks
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