DDH + LPN + LWE + NC1-PRG ⇒ iO

DDH together with LPN together with LWE together with NC1-PRG implies iO.

Statement

Migrated verbatim from indistinguishability-obfuscation § Other results:

First iO from well-founded assumptions: sub-exponential LWE, LPN, pseudorandom generators in $NC^{1}$ , and DDH — JLS21

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:

Genuinely conjunctive - four hypotheses together.
SUSPECT: JLS21’s assumption set is sub-exponential LWE, LPN over large fields, PRGs of constant locality (NC0, not NC1), and sub-exponential SXDH on pairing-friendly groups (not plain DDH). Both ‘NC^1’ and ‘DDH’ look wrong. Report only; do not fix.
‘sub-exponential’ qualifies LWE in the text but it applies to the whole assumption set; ambiguous as written.
‘pseudorandom generators in NC^1’ has no wiki object identifier.