Lattices

Status	Problem	Tags
	1+1 adaptively secure lattice threshold signature Resolved. Oriole (Jiang, Wee, Zhu, ePrint 2026/793, posted April 2026, a month after Tweed) gives a lattice-based threshold signature with exactly this shape – two rounds, only the second message-dependent, adaptive security against \(T-1\) corruptions with no erasures, from MSIS and MLWE in the ROM – verified here directly against the paper’s PDF (Definition of adp-TS-sUF-4 in its Figure 4, and the Theorem 2 + Theorem 3 reduction chain to MSIS), not just its abstract. The proof is human-written and published, but not yet independently re-verified line-by-line by this site, nor formalized in Lean.	Learning With Errors Threshold Signatures Tight Reductionsromseparationresearch-solved
	Ring-LWE error parity Open: whether recovering the Ring-LWE error modulo two is as hard as recovering the error itself. The easy direction is trivial; the source states it has no formal reduction for this one and relies on two heuristics instead, one of which changes the error distribution. 6 open	Learning With Errorsequivalence
	CHV Online Threshold Conjecture 1 of the source, its online threshold conjecture. The source gives an online algorithm achieving \(\kappa=O(\sqrt{\alpha}/B)\) and an overlap-gap argument against stable algorithms; the conjecture pins the constant \(\sqrt{\pi/8}\) as the exact place where online algorithms stop. Separately it proves, under worst-case lattice hardness, that no polynomial-time algorithm solves CHV for \(\kappa=O(1/(B n^{1/2+\varepsilon}))\). 4 open	Average Case Hardness Collision Resistant Hashing Locality Preserving Hashing Overlap Gap Propertytight-bound
	Single-session lattice Chevallier-Mames tightness Open: whether the one-session lattice translation of the Chevallier-Mames signature has a tight SUF-CMA reduction to search Module-LWE, or whether the paper’s two-fold parallel repetition (which doubles signature size and signing time) is inherent to a tight proof of this shape. 4 open	Learning With Errors Signature Schemes Tight Reductionsromtight-bound