No reduction from Evasive LWE to Evasive LWE

A reduction of class unstated from Evasive LWE to Evasive LWE would imply a contradiction.

Statement

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

The public-coin restriction — that $\mathrm{aux}$ contains $\mathrm{Samp}$‘s coin tosses — prevents obfuscation-based counterexamples where $\mathrm{aux}$ encodes a program with a hidden trapdoor for $\mathbf{P}$ — Wee22.

The assumption comes in public-coin and private-coin variants. Private-coin variants have known counterexamples — BUW24, AMYY25. A circular variant of evasive LWE was proposed for ABE for unbounded-depth circuits, but has also been shown vulnerable to zeroizing attacks — AMYY25.

Notes

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

• These are COUNTEREXAMPLES TO AN ASSUMPTION (the assumption is false as stated for private-coin and circular variants), which is a different object from a reduction barrier but shares Q=‘contradiction’. The data model needs to distinguish ‘assumption refuted’ from ‘reduction ruled out’.
• Three distinct results (private-coin counterexamples; the public-coin restriction that blocks obfuscation-based counterexamples; the circular-variant zeroizing attack) are packed into two sentences with four citations. Which citation supports which claim is only partly recoverable.
• This is the best-sourced barrier-adjacent passage on the wiki — every claim carries a wikilink — and is a good citation-density target for barrier pages.