Module-SVP ⇒ Module-SIS

Module-SVP implies Module-SIS.

Statement

Migrated verbatim from shortest-integer-solution § Module-SIS:

Hardness of Module-SIS reduces to worst-case problems on module lattices — LS15. Module-SIS is the hardness assumption underlying the NIST post-quantum signature standard Dilithium (ML-DSA, FIPS 204).

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 backwards from the standard convention: “Hardness of Module-SIS reduces to worst-case problems on module lattices” should read “worst-case module-lattice problems reduce to Module-SIS”.
• The worst-case problem is unnamed, so the hypothesis node is a placeholder.
• Identical wording to content/Assumptions/learning-with-errors.md line 129, which has the same directional problem.