Module-SIS ⇒ DS

Module-SIS implies DS.

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

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

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:

• No citation; FIPS 204 and Dilithium are bare text with no reference page.
• CONFLICTS with content/Assumptions/learning-with-errors.md line 127, which attributes Dilithium to “Module LWE/SIS”. Dilithium rests on both MLWE and MSIS, so the Module-SIS-only attribution here is incomplete and the two pages disagree.
• content/Primitives/digital-signature.md exists but is not wikilinked here.