Module-SVP ⇒ Module LWE

Module-SVP implies Module LWE.

Statement

Migrated verbatim from learning-with-errors § Module LWE:

Hardness of Module LWE reduces to worst-case problems on module lattices — LS15.

Notes

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Direction language is backwards from the standard convention: “Hardness of Module LWE reduces to worst-case problems on module lattices” should read “worst-case module-lattice problems reduce to Module LWE”.
• The worst-case problem is unnamed (“worst-case problems on module lattices”), so the hypothesis node is a placeholder.