Succinct LWE ⇒ Evasive LWE

Succinct LWE implies Evasive LWE.

Statement

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

is negligible. When $\ell =1$ there is no $\mathbf{W}$ block and $T$ reduces to $T_{\mathbf{B}}$ itself, making the condition equivalent to standard LWE. The assumption strengthens as $\ell$ grows — larger $\ell$ allows encoding more circuit-depth information in the trapdoor structure. Succinct LWE implies Evasive LWE. A circular small-secret variant (where the trapdoor preimage is related to a low-norm secret) is also used in applications.

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:

• One paragraph packs four claims (l=1 equivalence to LWE; monotonicity in l; Succinct LWE ⇒ Evasive LWE; circular small-secret variant). Recorded separately.
• A substantive reduction (“Succinct LWE implies Evasive LWE”) stated with NO citation at all — CLAUDE.md requires one.
• No parameter relation is given between the l of Succinct LWE and the sampler class of Evasive LWE, so the edge cannot be instantiated.