LWE ⇒ PRC

LWE implies PRC.

Statement

Migrated verbatim from pseudorandom-error-correcting-code § Other results:

• PRCs can be constructed from LWE: the LWE ciphertext structure naturally yields a pseudorandom, decodable code robust to bounded noise — CG24

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:

• SUSPECTED MIS-ATTRIBUTED ASSUMPTION (recorded, not fixed): CG24’s PRC constructions are usually stated from (sparse/planted) LPN — see also content/References/‘GG24 - New constructions of pseudorandom codes.md’ — not from LWE. Verify which assumption the cited construction actually uses before migrating the hypothesis as [[learning-with-errors]].
• The ‘LWE ciphertext structure naturally yields …’ clause is a hand-wave, not a construction.