[EC:LiuMonZha23](https://arxiv.org/abs/2211.11994) Authors: Jiahui Liu, Hart Montgomery, Mark Zhandry Publisert på [[Eurocrypt'23]] Breaks all (?) known lattice-based constructions. New framework: "The Walkable Invariant Framework" Main Theorem: - Random walk "by sigma_i-mixes" - plus Hard path-finding - plus knowledge of path - erlik sikre [[Kvantepenger]] Can be applied to "justify" security of Quantum Money from Knots, FGHLS'12. (But unclear whether the "random walk by ..."-assumption holds.) Gives a construction from isogenies(!) over supersingular elliptic curves, "only one missing piece" for the security proof to work: - Path finding = computing isogenies, believed to be hard - knowledge of path = analog of knowledge of exponent - Missing piece: unknown how to create uniform superposition over X for minting. Er dette noe jeg kunne jobbet med Jonathan og gjengen på? (Sjekk i så fall om han har besvart noen av spørsmålene selv siden, for eksempel i [ITCS:Zhandry24 - Quantum Money from Abelian Group Actions](https://arxiv.org/pdf/2307.12120.pdf).) Er to til konstruksjonforslag i paperet, verdt å sjekke ut.