DLOG ⊆ NP

DLOG is contained in NP.

Statement

Migrated verbatim from co-nondeterministic-polynomial-time § Known relationships:

• Integer factorization and discrete logarithm are both in $\mathbf{NP}\cap \mathbf{coNP}$: there are short certificates for both “yes” and “no” answers. This is one reason these problems are considered unlikely to be NP-complete — an NP-complete problem in coNP would imply $\mathbf{NP}=\mathbf{coNP}$.

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:

• IMPRECISE (recorded, not fixed): the decision version of discrete logarithm is in NP cap coNP only when the group order or its factorization is known and certifiable; the page states it unconditionally.
• Not wikilinked, though content/Assumptions/discrete-logarithm.md exists.
• Uncited.