Module LWE + Module-SIS ⇒ DS

Module LWE together with Module-SIS implies DS.

Statement

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

• Dilithium / ML-DSA (FIPS 204): EUF-CMA digital signatures from Module LWE/SIS

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:

• “Module LWE/SIS” is ambiguous: the slash cannot be read as conjunction or disjunction. Dilithium needs BOTH, so it is recorded as conjunctive, but the page does not say so.
• No citation; FIPS 204 is bare text.
• Conflicts with content/Assumptions/shortest-integer-solution.md line 72, which attributes Dilithium to Module-SIS alone.
• EUF-CMA proof for Dilithium is in the ROM (Fiat-Shamir with aborts); no model stated.