FAC ⊆ TFNP
Statement
Migrated verbatim from total-function-np § Relevance to cryptography:
Integer factorization and discrete logarithm — the two most historically important hard problems in cryptography — are both in TFNP, formalizing the intuition that they are “hard search problems with guaranteed solutions.” Recent work has used TFNP subclass hardness (especially PPAD) as a basis for constructing cryptographic primitives from weaker or more structured assumptions.
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.
class: free because a containment between complexity classes is proved
by any argument at all; the reduction-class axis does not discriminate
here, and unstated would wrongly suggest the information is missing.
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- Uncited.
[[factoring]]is not wikilinked although content/Assumptions/factoring.md exists.- ‘the two most historically important hard problems in cryptography’ is marketing prose (house-style anti-pattern).